CN105373692A

Movatterモバイル変換

Info

Publication number: CN105373692A
Application number: CN201510385967.0A
Authority: CN
Inventors: 张安; 毕文豪; 汤志荔
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2015-07-03
Filing date: 2015-07-03
Publication date: 2016-03-02
Anticipated expiration: 2035-07-03
Also published as: CN105373692B

Abstract

本发明提供了一种基于区间二元语义的驾驶舱人机功能分配方法，首先进行人机优势能力比较，组成人、机能力优势集合；然后采用模糊层次分析法确定人、机能力优势集合中各元素的权重系数；划分民机驾驶舱系统的自动化等级后通过比较人机能力优势来确定自动化等级的范围；最终采用基于区间二元语义的IT-WAA算子和IT-WHA算子的多属性群决策方法确定功能分配自动化等级。本发明可以充分利用决策者的语义信息，精确地处理多阶段、多专家的语言信息，能够很好地避免信息丢失，使决策结果更为准确。The invention provides a cockpit human-machine function allocation method based on interval binary semantics. Firstly, the man-machine superiority capability is compared to form a human-machine capability superiority set; then the fuzzy analytic hierarchy process is used to determine the The weight coefficient of each element; after dividing the automation level of the civil aircraft cockpit system, the scope of the automation level is determined by comparing the advantages of human-machine capabilities; finally, the multi-level combination of the IT-WAA operator and the IT-WHA operator based on the interval binary semantics is adopted. The attribute group decision-making method determines the automatic level of function allocation. The invention can make full use of the semantic information of decision makers, accurately process multi-stage and multi-expert language information, can well avoid information loss, and make decision-making results more accurate.

Description

Translated fromChinese

基于区间二元语义的驾驶舱人机功能分配方法Cockpit Human-Machine Function Allocation Method Based on Interval Binary Semantics

技术领域technical field

本发明涉及一种民机驾驶舱的自动化设计技术。The invention relates to an automatic design technology of a cockpit of a civil aircraft.

背景技术Background technique

我国大型运输机项目早已正式立项，研制具有自主知识产权的大型运输机需要大量相关技术的支持，驾驶舱人机功能分配正是其中的关键技术之一。飞机驾驶舱是驾驶员执行飞行任务的主要活动场所。随着驾驶舱逐渐向智能化、自动化的方向发展，人机之间的关系也在相应地发生变化，驾驶员的决策与管理职能逐渐加强，而操纵职能逐渐弱化。虽然自动化技术在驾驶舱中的应用一定程度上降低了驾驶员的工作负荷，但同时也引起了驾驶员情景感知意识水平下降等诸多问题。因此，为了使人机顺利协调互补地工作，发挥人机系统的最大效率，就必须按照科学的准则和方法，综合考虑功能需求、驾驶员的操作负荷、自动化可靠性、系统费用等多方面因素，将系统的功能合理地分配给驾驶员和机器，使系统设计在整体上高效、安全、可靠和经济，为设计人员提供充分的依据以开展后继的软硬件设计和开发工作。驾驶舱人机功能分配可以看成是一个典型的多属性群决策问题。多属性群决策问题是现代决策科学的一个重要研究领域，其理论和方法已广泛应用于工程设计、城市规划、经济管理、军事和社会等领域。my country's large-scale transport aircraft project has already been formally established. The development of large-scale transport aircraft with independent intellectual property rights requires the support of a large number of related technologies, and the allocation of man-machine functions in the cockpit is one of the key technologies. The aircraft cockpit is the main activity place for the pilot to perform flight tasks. As the cockpit gradually develops in the direction of intelligence and automation, the relationship between man and machine is also changing accordingly. The driver's decision-making and management functions are gradually strengthened, while the control function is gradually weakened. Although the application of automation technology in the cockpit reduces the driver's workload to a certain extent, it also causes many problems such as the decline of the driver's situational awareness level. Therefore, in order to make the man-machine work smoothly and coordinately and complement each other, and maximize the efficiency of the man-machine system, it is necessary to comprehensively consider functional requirements, driver's operating load, automation reliability, system cost and other factors in accordance with scientific principles and methods. , reasonably allocate the functions of the system to the driver and the machine, so that the overall system design is efficient, safe, reliable and economical, and provide sufficient basis for designers to carry out subsequent software and hardware design and development work. The allocation of man-machine functions in the cockpit can be regarded as a typical multi-attribute group decision-making problem. Multi-attribute group decision making is an important research field of modern decision science, and its theories and methods have been widely used in engineering design, urban planning, economic management, military and social fields.

在实际决策中，由于驾驶舱人机功能分配问题自身的的复杂性以及人类思维的模糊性、不确定性，当人机工程学专家受一些主、客观因素的限制时，往往难以用定量化的方法来描述决策信息，无法对决策属性进行准确测度，只能给出与功能分配相关评价因素的模糊语言值。而这种模糊语言值本身又是人机工程学专家依据其个人偏好提出不同语言评价集，给出各自的语言评价信息，而且常常是一个模糊语言范围。为解决这一问题，许多学者采用定性的语言，将语言评价信息转化为模糊数，并依据扩展原理进行模糊数运算与分析。然而对于语言评价信息的处理，采用过于主观的定性决策方法和非常客观的定量化决策方法去描述决策信息，即对个体语言评价信息通过集结得到的群评价信息往往不能用事先定义的语义评价集中的单个语义短语来准确表达，而必须有一个近似过程，从而容易造成决策信息丢失和扭曲，使得决策结果与实际不符。In actual decision-making, due to the complexity of the allocation of human-machine functions in the cockpit and the ambiguity and uncertainty of human thinking, when ergonomics experts are limited by some subjective and objective factors, it is often difficult to quantify The method to describe the decision-making information cannot accurately measure the decision-making attributes, and can only give the fuzzy language value of the evaluation factors related to the function allocation. And this kind of fuzzy language value itself is that ergonomics experts put forward different language evaluation sets according to their personal preferences, and give their own language evaluation information, and it is often a fuzzy language range. In order to solve this problem, many scholars adopt qualitative language, transform language evaluation information into fuzzy numbers, and carry out fuzzy number calculation and analysis according to the expansion principle. However, for the processing of language evaluation information, an overly subjective qualitative decision-making method and a very objective quantitative decision-making method are used to describe the decision-making information. However, there must be an approximation process, which will easily cause loss and distortion of decision-making information, making the decision-making results inconsistent with reality.

发明内容Contents of the invention

为了克服现有技术的不足，本发明提供一种基于区间二元语义的驾驶舱功能分配的方法。In order to overcome the deficiencies of the prior art, the present invention provides a method for cockpit function allocation based on interval binary semantics.

本发明解决其技术问题所采用的技术方案包含以下步骤：The technical solution adopted by the present invention to solve its technical problems comprises the following steps:

(1)进行人机优势能力比较，分别组成人、机能力优势集合H＝{h₁,h₂,h₃,h₄,h₅}和M＝{m₁,m₂,m₃,m₄,m₅}，其中，h₁表示预测推理能力，h₂表示视觉感知能力，h₃表示模式识别能力，h₄表示经验学习能力，h₅表示环境感知能力，m₁表示数据存储管理能力，m₂表示快速准确计算能力，m₃表示规则推理能力，m₄表示并行处理能力，m₅表示连续工作重复决策能力；(1) Comparing man-machine superiority and ability, forming man-machine and machine ability superiority sets H={h₁ ,h₂ ,h₃ ,h₄ ,h₅ } and M={m₁ ,m₂ ,m₃ ,m₄ , m₅ }, among them, h₁ represents the ability of predictive reasoning, h₂ represents the ability of visual perception, h₃ represents the ability of pattern recognition, h₄ represents the ability of experience learning, h₅ represents the ability of environmental perception, m₁ represents the ability of data storage management , m₂ means fast and accurate calculation ability, m₃ means rule reasoning ability, m₄ means parallel processing ability, m₅ means continuous work repetitive decision-making ability;

(2)采用模糊层次分析法来确定人、机能力优势集合中各元素的权重系数；(2) Use the fuzzy analytic hierarchy process to determine the weight coefficient of each element in the human and machine ability advantage set;

(3)划分民机驾驶舱系统的自动化等级1～10级，1级为系统不提供任何帮助，人必须完成所有的决策和操纵，2级为系统提供整套的决策或行动方案，3级为系统缩小方案选择范围，4级为系统提供一个建议方案，5级为如果人同意则执行这个方案，6级为在执行方案前允许人在限定时间内否决，7级为自动执行，仅在必要时通知人，8级为如果人需要则告知他，是否通知人全由计算机决定，9级为系统决定所有的工作，10级为拒绝人的干预；(3) Divide the automation level of the civil aircraft cockpit system from 1 to 10. Level 1 means that the system does not provide any assistance and humans must complete all decision-making and manipulation. Level 2 provides the system with a complete set of decision-making or action plans. Level 3 is The system narrows the range of options, level 4 provides the system with a suggested plan, level 5 implements the plan if people agree, level 6 allows people to veto the plan within a limited time before implementing it, and level 7 automatically executes it only when necessary Notify the person from time to time, level 8 is to inform the person if he needs it, whether to notify the person is completely determined by the computer, level 9 is the system to decide all the work, and level 10 is to refuse human intervention;

(4)通过比较人机能力优势来确定自动化等级的范围，采用如下定义：(4) Determine the scope of the automation level by comparing the advantages of man-machine capabilities, using the following definition:

定义1：设(s_k,a_k)和为两个二元语义信息，其中s_k是预先定义好的语言评价集中的第k个元素，a_k∈[-0.5,0.5)表示经过集结计算后得到了语言信息与最贴近元素s_k之间的差别；且则称 ${(s_{k}, a_{k})}^{~} = [({\underset{&OverBar;}{s}}_{k}, {\underset{&OverBar;}{a}}_{k}), ({\overset{&OverBar;}{s}}_{k}, {\overset{&OverBar;}{a}}_{k})]$ 为一个区间二元语义；Definition 1: Let (s_k ,a_k ) and are two binary semantic information, where s_k is a pre-defined language evaluation set The kth element in , a_k ∈ [-0.5,0.5) represents the difference between the language information and the closest element s_k obtained after the aggregation calculation; and then called ${({the s}_{k}, a_{k})}^{~} = [({\underset{&OverBar;}{the s}}_{k}, {\underset{&OverBar;}{a}}_{k}), ({\overset{&OverBar;}{the s}}_{k}, {\overset{&OverBar;}{a}}_{k})]$ is an interval binary semantics;

定义2：为预先定义的语言评价集，(s_i,a_i),(s_j,a_j)两个二元语义信息组成区间二元语义信息[(s_i,a_i),(s_j,a_j)]，i≤j,a_i≤a_j，设[β₁,β₂]为语言评价集S^T经集结得到的区间实数，β₁,β₂∈[0,T-1],β₁≤β₂，令Definition 2: is a pre-defined language evaluation set, (s_i ,a_i ),(s_j ,a_j ) two binary semantic information constitute interval binary semantic information [(s_i ,a_i ),(s_j ,a_j )], i≤j,a_i ≤a_j , let [β₁ ,β₂ ] be the interval real numbers obtained by the language evaluation set S^T through assembly, β₁ ,β₂ ∈[0,T-1],β₁ ≤β₂ , let

$Δ Δ [[{β β}_{11},, {β β}_{22}]] = = [[(({s the s}_{i i},, {a a}_{i i})),, (({s the s}_{j j},, {a a}_{j j}))]] = = \{\begin{matrix} {s the s}_{i i},, & k k = = r r o o u u n no d d (({β β}_{11})) \\ {s the s}_{j j},, & k k = = r r o o u u n no d d (({β β}_{22})) \\ {a a}_{i i} = = {β β}_{11} - - i i,, & {a a}_{i i} &Element; &Element; [[- - 0.5 0.5,, 0.5 0.5)) \\ {a a}_{j j} = = {β β}_{22} - - j j,, & {a a}_{j j} &Element; &Element; [[- - 0.5 0.5,, 0.5 0.5)) \end{matrix}$

则称函数Δ为区间实数[β₁,β₂]对应的区间二元语义信息的转换函数，其中round为四舍五入取整算子；Then the function Δ is called the conversion function of the interval binary semantic information corresponding to the interval real number [β₁ ,β₂ ], where round is the rounding operator;

定义3：令Δ^-1[（s_i,a_i),(s_j,a_j)]＝[i+a_i,j+a_j]＝[β₁,β₂]，则称Δ^-1为函数的Δ的逆函数；Definition 3: If Δ^-1 [(s_i ,a_i ),(s_j ,a_j )]=[i+a_i ,j+a_j ]=[β₁ ,β₂ ], it is called Δ^-1 is the inverse function of Δ of the function;

定义4：设(s_k,a_k)^～，(s_t,a_t)^～为任意两个区间二元语义，Definition 4: Let (s_k , a_k )^～ , (s_t , a_t )^～ be any two interval binary semantics,

则称 $p [{(s_{k}, a_{k})}^{~} &GreaterEqual; {(s_{t}, a_{t})}^{~}] = m a x {1 - m a x [\frac{Δ^{- 1} ({\overset{&OverBar;}{s}}_{i}, {\overset{&OverBar;}{a}}_{i}) Δ^{- 1} ({\underset{&OverBar;}{s}}_{k}, {\underset{&OverBar;}{a}}_{k})}{l_{{(s_{k}, a_{k})}^{~}} + l_{{(s_{t}, a_{t})}^{~}}}, 0], 0}$ 为(s_k,a_k)^～≥(s_t,a_t)^～的可能度；then called $p [{({the s}_{k}, a_{k})}^{~} &Greater Equal; {({the s}_{t}, a_{t})}^{~}] = m a x {1 - m a x [\frac{Δ^{- 1} ({\overset{&OverBar;}{the s}}_{i}, {\overset{&OverBar;}{a}}_{i}) Δ^{- 1} ({\underset{&OverBar;}{the s}}_{k}, {\underset{&OverBar;}{a}}_{k})}{l_{{({the s}_{k}, a_{k})}^{~}} + l_{{({the s}_{t}, a_{t})}^{~}}}, 0], 0}$ is the possibility of (s_k , a_k )^～ ≥ (s_t , a_t )^～ ;

定义5：设IT-WAA；若为一组区间二元语义信息，j＝1,2,…,n，ω＝(ω₁,ω₂,…,ω_n)^T为相应的权重，且ω_j∈[0,1],j＝(1,2,…,n)， $Φ_{ω} [{(s_{1}, a_{1})}^{~}, {(s_{2}, a_{2})}^{~}, ..., {(s_{n}, a_{n})}^{~}] = {Δ [Σ_{j = 1}^{n} ω_{j} Δ^{- 1} ({\underset{&OverBar;}{s}}_{j}, {\underset{&OverBar;}{a}}_{j})], Δ [Σ_{j = 1}^{n} ω_{j} Δ^{- 1} ({\overset{&OverBar;}{s}}_{j}, {\overset{&OverBar;}{a}}_{j})]}$ 则称Φ_w为区间二元语义加权算术平均算子；Definition 5: Set IT-WAA; if is a set of interval binary semantic information, j=1,2,…,n, ω=(ω₁ ,ω₂ ,…,ω_n )^T is the corresponding weight, and ω_j ∈[0,1],j =(1,2,...,n), $Φ_{ω} [{({the s}_{1}, a_{1})}^{~}, {({the s}_{2}, a_{2})}^{~}, ..., {({the s}_{no}, a_{no})}^{~}] = {Δ [Σ_{j = 1}^{no} ω_{j} Δ^{- 1} ({\underset{&OverBar;}{the s}}_{j}, {\underset{&OverBar;}{a}}_{j})], Δ [Σ_{j = 1}^{no} ω_{j} Δ^{- 1} ({\overset{&OverBar;}{the s}}_{j}, {\overset{&OverBar;}{a}}_{j})]}$ Then Φ_w is called the interval binary semantic weighted arithmetic mean operator;

定义6：设IT-WHA：若为一组区间二元语义信息，ω＝(ω₁,ω₂,…,ω_n)^T为相应的权重，且ω_j∈[0,1]， $Φ_{ω, w} [{(s_{1}, a_{1})}^{~}, {(s_{2}, a_{2})}^{~}, ..., {(s_{n}, a_{n})}^{~}] = {Δ [Σ_{j = 1}^{n} w_{j} Δ^{- 1} ({\underset{&OverBar;}{s}}_{j}, {\underset{&OverBar;}{a}}_{j})], Δ [Σ_{j = 1}^{n} w_{j} Δ^{- 1} ({\overset{&OverBar;}{s}}_{j}, {\overset{&OverBar;}{a}}_{j})]},$ 其中w＝(w₁,w₂,…,w_n)^T是相关联的加权向量，且w_j∈[0,1]， $v_{j} = [({\underset{&OverBar;}{s}}_{π (j)}, {\underset{&OverBar;}{a}}_{π (j)}), ({\overset{&OverBar;}{s}}_{π (j)}, {\overset{&OverBar;}{a}}_{π (j)})]$ 是加权的二元语义变量组 $({\tilde{μ}}_{1}, {\tilde{μ}}_{2}, ..., {\tilde{μ}}_{n}) ({\tilde{μ}}_{j} = {nω}_{j} {(s_{j}, a_{j})}^{~})$ 第j大元素，且n为平衡因子，则称Φ_ω,w为区间二元语义混合加权算子；Definition 6: Let IT-WHA: If is a set of interval binary semantic information, ω=(ω₁ ,ω₂ ,…,ω_n )^T is the corresponding weight, and ω_j ∈[0,1], $Φ_{ω, w} [{({the s}_{1}, a_{1})}^{~}, {({the s}_{2}, a_{2})}^{~}, ..., {({the s}_{no}, a_{no})}^{~}] = {Δ [Σ_{j = 1}^{no} w_{j} Δ^{- 1} ({\underset{&OverBar;}{the s}}_{j}, {\underset{&OverBar;}{a}}_{j})], Δ [Σ_{j = 1}^{no} w_{j} Δ^{- 1} ({\overset{&OverBar;}{the s}}_{j}, {\overset{&OverBar;}{a}}_{j})]},$ where w=(w₁ ,w₂ ,…,w_n )^T is the associated weight vector, and w_j ∈[0,1], $v_{j} = [({\underset{&OverBar;}{the s}}_{π (j)}, {\underset{&OverBar;}{a}}_{π (j)}), ({\overset{&OverBar;}{the s}}_{π (j)}, {\overset{&OverBar;}{a}}_{π (j)})]$ is the weighted set of binary semantic variables $({\tilde{μ}}_{1}, {\tilde{μ}}_{2}, ..., {\tilde{μ}}_{no}) ({\tilde{μ}}_{j} = {nω}_{j} {({the s}_{j}, a_{j})}^{~})$ The jth largest element, and n is a balance factor, then Φ_{ω, w} is called an interval binary semantic mixed weighting operator;

定义7：设在语言评价集下得到的区间语言评价矩阵为 $\tilde{R} = {([{\underset{&OverBar;}{r}}_{i j}, {\overset{&OverBar;}{r}}_{i j}])}_{m \times n},$ 其中为属性值；设定基本语言评价集为 $S^{T} = {s_{i}^{T} | i &Element; {0, 1, ..., T - 1}},$ 采用转换函数ζ将转换为以基本语言评价集S^T表示下的区间二元语义评价矩阵Definition 7: Set in the language evaluation set The interval language evaluation matrix obtained from the following is $\tilde{R} = {([{\underset{&OverBar;}{r}}_{i j}, {\overset{&OverBar;}{r}}_{i j}])}_{m \times no},$ in is the attribute value; set the basic language evaluation set to $S^{T} = {{the s}_{i}^{T} | i &Element; {0, 1, ..., T - 1}},$ Using the transfer function ζ will Converted to an interval binary semantic evaluation matrix represented by the basic language evaluation set S^T

式中 ${\overset{&OverBar;}{a}}_{i j} &Element; [- 0.5, 0.5);$ In the formula ${\overset{&OverBar;}{a}}_{i j} &Element; [- 0.5, 0.5);$

在上述定义基础上，给出基于IT-WAA算子的自动化等级范围确定方法，具体过程如下：On the basis of the above definitions, a method for determining the range of automation levels based on IT-WAA operators is given. The specific process is as follows:

a)：决策者集合为D＝{d₁,d₂,…,d_k,…,d_t}，共t位决策者；每位决策者d_k分别给出人、机能力优势对待分配功能的区间语言评估值和k＝1,2,…,t，并得到评估矩阵 ${\tilde{H}}_{k} = {([{\underset{&OverBar;}{h}}_{i j}^{k}, {\overset{&OverBar;}{h}}_{i j}^{k}])}_{n \times m}, {\tilde{Q}}_{k} = {([{\underset{&OverBar;}{q}}_{i j}^{k}, {\overset{&OverBar;}{q}}_{i j}^{k}])}_{n \times l};$ a): The set of decision makers is D＝{d₁ ,d₂ ,…,d_k ,…,d_t }, there are t decision makers in total; each decision maker d_k respectively gives the human and machine ability superiority treatment allocation function The interval language evaluation value of and k=1,2,…,t, and get the evaluation matrix ${\tilde{h}}_{k} = {([{\underset{&OverBar;}{h}}_{i j}^{k}, {\overset{&OverBar;}{h}}_{i j}^{k}])}_{no \times m}, {\tilde{Q}}_{k} = {([{\underset{&OverBar;}{q}}_{i j}^{k}, {\overset{&OverBar;}{q}}_{i j}^{k}])}_{no \times l};$

b)：设定基本语言评价集S^T，将和转化成基于S^T表示的一致化区间二元语义评价矩阵和利用IT-WAA算子将和集结为群区间二元语义评价矩阵和b): Set the basic language evaluation set S^T , set and Transformed into a consistent interval binary semantic evaluation matrix based on S^T representation and Use the IT-WAA operator to and Assembled into a binary semantic evaluation matrix between clusters and

c)：根据IT-WAA算子以及人、机能力优势权重和τ将和按行集结，计算出人、机方案区间二元语义综合评价值和计算出人、机能力对待分配功能的综合评估结果和之间的可能度c): According to the IT-WAA operator and the weight of advantages of human and machine capabilities and τ will be and Gather by row to calculate the binary semantic comprehensive evaluation value of the man-machine scheme interval and Calculate the comprehensive evaluation results of human and machine capabilities for assigned functions and possibility between

d)：根据可能度结果p确定待分配功能的自动化等级范围：d): Determine the automation level range of the function to be assigned according to the possibility result p:

$\{\begin{matrix} c c e e i i l l ((p p \times \times 55)) A A - - 11 \leq \leq L L O o A A \leq \leq c c e e i i l l ((p p \times \times 55)) + + 11 \\ L L O o A A &Element; &Element; {{11,, 22,, ... ...,, 1010}} \end{matrix}$

其中，ceil(x)为上取整函数；Among them, ceil(x) is the upper integer function;

(5)采用基于区间二元语义的IT-WAA算子和IT-WHA算子的多属性群决策方法确定功能分配自动化等级，具体过程如下：(5) Using the multi-attribute group decision-making method based on interval binary semantics of IT-WAA operator and IT-WHA operator to determine the automation level of function allocation, the specific process is as follows:

针对某个功能多属性决策问题，设A＝{a₁,a₂,…,a_n′}是方案集，其元素表示自动化等级的n'种情况；给定功能分配评估准则集合G＝{g₁,g₂,…,g_m′}，其元素分别对应驾驶舱人机功能分配的五个主要评估准则，g₁为态势感知；g₂为脑力负荷；g₃为决策风险；g₄为可靠性；g₁为系统成本；属性权重的权重向量为η＝(η₁,η₂,…,η_m′)，且其向量为η_l≥0(l＝1,2,…,m′)，Aiming at a multi-attribute decision-making problem for a certain function, let A={a₁ ,a₂ ,…,a_n′ } be a program set, whose elements represent n’ cases of automation level; given function assignment evaluation criteria set G={ g₁ ,g₂ ,…,g_m′ }, its elements correspond to the five main evaluation criteria for the distribution of cockpit man-machine functions, g₁ is situational awareness; g₂ is mental load; g₃ is decision risk; g₄ is reliability; g₁ is system cost; the weight vector of attribute weight is η=(η₁ ,η₂ ,…,η_m′ ), and its vector is η_l ≥ 0(l=1,2,…,m '),

a)t位决策者的权重向量为决策者d_k∈D给出方案a_i∈A在属性g_j∈G下的区间语言评估值并得到评估矩阵a) The weight vector of t decision makers is The decision maker d_k ∈ D gives the interval language evaluation value of the scheme a_i ∈ A under the attribute g_j ∈ G and get the evaluation matrix

b)将转化成基于基本语言评价集S^T′表示的一致化区间二元语义评价矩阵利用IT-WAA算子对中第i行的语言评估信息进行集结，得到决策者d_k对方案a_i的综合属性评估值i＝1,2,…,n′；b) will Transformed into a consistent interval binary semantic evaluation matrix based on the basic language evaluation set S^T′ Using the IT-WAA operator pair The language evaluation information of the i-th row in is assembled to obtain the comprehensive attribute evaluation value of the decision maker d_k for the scheme a_i i=1,2,...,n';

c)利用IT-WHA算子对t位决策者的综合属性评估值进行集结，得到关于方案a_i的群体综合评估值其中，w＝(w₁,w₂,…,w_t)是IT-WHA算子的加权向量，w_k∈[0,1](k＝1,2,…,t)且是加权的二元语义变量组第k大元素，λ＝(λ₁,λ₂,…,λ_t)^T为相应的权重，且λ_k∈[0,1]，且t为平衡因子；c) Using the IT-WHA operator to evaluate the comprehensive attributes of t decision makers Gather together to get the group comprehensive evaluation value of scheme a_i Among them, w=(w₁ ,w₂ ,…,w_t ) is the weight vector of IT-WHA operator, w_k ∈[0,1](k=1,2,…,t) and is the weighted set of binary semantic variables the kth largest element, λ=(λ₁ ,λ₂ ,…,λ_t )^T is the corresponding weight, and λ_k ∈[0,1], And t is the balance factor;

d)计算出方案a_i综合评估值γⁱ(λ,w)与a_j综合评估值γ^j(λ,w)之间的可能度p′_ij＝p[γⁱ(λ,w)≥γ^j(λ,w)]，从而得到可能度矩阵d) Calculate the_{possibility p′ ij}^＝^p [γ_i⁽ λ,w)_≥γ^j (λ,w)], so as to obtain the possibility matrix

e)求出可能度矩阵p′的排序向量v＝(v₁,v₂,…,v_n′)，并按其分量大小对方案进行排序，即得到最优方案；其中最后按其分量大小对方案进行排序，即得到最优的功能分配方案。e) Calculate the sorting vector v=(v₁ ,v₂ ,…,v_n′ ) of the possibility degree matrix p′, and sort the schemes according to their component sizes to get the optimal scheme; where Finally, the schemes are sorted according to the size of their components, and the optimal function allocation scheme is obtained.

本发明的有益效果是：采用上述方法对民机驾驶舱人机自动化系统进行功能分配可以克服以往方法在进行多粒度区间语言评价信息集结和运算时容易造成信息损失和扭曲的缺点。上述方法可以充分利用决策者的语义信息，精确地处理多阶段、多专家的语言信息，能够很好地避免信息丢失，使决策结果更为准确。The beneficial effect of the present invention is that: adopting the method to allocate functions to the man-machine automation system of the cockpit of a civil aircraft can overcome the shortcomings of previous methods that easily cause information loss and distortion when multi-granularity interval language evaluation information is assembled and calculated. The above method can make full use of the semantic information of decision makers, accurately process multi-stage and multi-expert language information, and can well avoid information loss and make decision-making results more accurate.

具体实施方式detailed description

下面结合实施例对本发明进一步说明，本发明包括但不仅限于下述实施例。The present invention will be further described below in conjunction with the examples, and the present invention includes but not limited to the following examples.

本发明包含以下步骤：The present invention comprises the following steps:

(1)进行人机优势能力比较，即选取与驾驶舱功能关系较为密切的人机优势，组成人、机能力优势集合，分别表示为：H＝{h₁,h₂,h₃,h₄,h₅}和M＝{m₁,m₂,m₃,m₄,m₅}，各元素含义如表1所示。(1) Comparing man-machine superiority and capability, that is, selecting the man-machine superiority closely related to the cockpit function to form a human-machine capability superiority set, respectively expressed as: H={h₁ ,h₂ ,h₃ ,h₄ ,h₅ } and M={m₁ ,m₂ ,m₃ ,m₄ ,m₅ }, the meaning of each element is shown in Table 1.

表1人、机能力优势集合Table 1. A collection of human and machine capability advantages

(2)采用模糊层次分析法(FuzzyAnalyticHierarchyProcess，FAHP)来确定人、机能力优势集合中各元素的权重系数。(2) Use Fuzzy Analytic Hierarchy Process (FAHP) to determine the weight coefficient of each element in the human and machine capability advantage set.

(3)划分民机驾驶舱系统的自动化等级，采用Sheridan、Verplank和Parasuraman等人提出的人机交互系统的自动化级别划分方法，如表2所示。(3) To divide the automation level of the civil aircraft cockpit system, the automation level division method of the human-computer interaction system proposed by Sheridan, Verplank and Parasuraman et al. is used, as shown in Table 2.

表2自动化级别Table 2 Automation level

(4)通过比较人机能力优势来确定自动化等级的范围。在该步骤中需要用到如下定义。(4) Determine the scope of the automation level by comparing the advantages of man-machine capabilities. The following definitions are required in this step.

定义1：设(s_k,a_k)和为两个二元语义信息，其中s_k是预先定义好的语言评价集中的第k个元素，a_k∈[-0.5,0.5)表示经过集结计算后得到了语言信息与最贴近元素s_k之间的差别。s_k，a_k，且则称 ${(s_{k}, a_{k})}^{~} = [({\underset{&OverBar;}{s}}_{k}, {\underset{&OverBar;}{a}}_{k}), ({\overset{&OverBar;}{s}}_{k}, {\overset{&OverBar;}{a}}_{k})]$ 为一个区间二元语义。Definition 1: Let (s_k ,a_k ) and are two binary semantic information, where s_k is a pre-defined language evaluation set The kth element in , a_k ∈ [-0.5,0.5) represents the difference between the language information and the closest element s_k obtained after aggregation calculation.s_k ,a_k , and then called ${({the s}_{k}, a_{k})}^{~} = [({\underset{&OverBar;}{the s}}_{k}, {\underset{&OverBar;}{a}}_{k}), ({\overset{&OverBar;}{the s}}_{k}, {\overset{&OverBar;}{a}}_{k})]$ is an interval binary semantics.

定义2：为预先定义的语言评价集，(s_i,a_i),(s_j,a_j(i≤j,a_i≤a_j)两个二元语义信息组成区间二元语义信息[(s_i,a_i),(s_j,a_j])。设[β₁,β₂](β₁,β₂∈[0,T-1],β₁≤β₂)为语言评价集S^T经集结得到的区间实数，令Definition 2: is a pre-defined language evaluation set, (s_i ,a_i ),(s_j ,a_j (i≤j,a_i ≤a_j ) two binary semantic information constitute interval binary semantic information [(s_i , a_i ),(s_j ,a_j ]). Let [β₁ ,β₂ ](β₁ ,β₂ ∈[0,T-1],β₁ ≤β₂ ) be the language evaluation set S^T The obtained interval real number, let

$Δ Δ [[{β β}_{11},, {β β}_{22}]] = = [[(({s the s}_{i i},, {a a}_{i i})),, (({s the s}_{j j},, {a a}_{j j}))]] = = \{\begin{matrix} {s the s}_{i i},, & k k = = r r o o u u n no d d (({β β}_{11})) \\ {s the s}_{j j},, & k k = = r r o o u u n no d d (({β β}_{22})) \\ {a a}_{i i} = = {β β}_{11} - - i i,, & {a a}_{i i} &Element; &Element; [[- - 0.5 0.5,, 0.5 0.5)) \\ {a a}_{j j} = = {β β}_{22} - - j j,, & {a a}_{j j} &Element; &Element; [[- - 0.5 0.5,, 0.5 0.5)) \end{matrix} - - - - - - ((11))$

则称函数Δ为区间实数[β₁,β₂]对应的区间二元语义信息的转换函数，其中round为四舍五入取整算子。Then the function Δ is called the conversion function of the interval binary semantic information corresponding to the interval real number [β₁ , β₂ ], where round is a rounding operator.

定义3：令Definition 3: order

Δ^-1[(s_i,a_i),(s_j,a_j)]＝[i+a_i,j+a_j]＝[β₁,β₂](2)Δ^-1 [(s_i ,a_i ),(s_j ,a_j )]=[i+a_i ,j+a_j ]=[β₁ ,β₂ ](2)

则称Δ^-1为函数的Δ的逆函数。Then Δ^-1 is called the inverse function of Δ of the function.

定义4：设(s_k,a_k)^～，(s_t,a_t)^～为任意两个区间二元语义，则称Definition 4: Let (s_k , a_k )^～ , (s_t , a_t )^～ be any two interval binary semantics, then it is called

$p p [[{(({s the s}_{k k},, {a a}_{k k}))}^{~ ~} &GreaterEqual; &Greater Equal; {(({s the s}_{t t},, {a a}_{t t}))}^{~ ~}]] = = m m a a x x {{11 - - m m a a x x [[\frac{{Δ Δ}^{- - 11} (({\overset{&OverBar; &OverBar;}{s the s}}_{t t},, {\overset{&OverBar; &OverBar;}{a a}}_{t t})) - - {Δ Δ}^{- - 11} (({\underset{&OverBar; &OverBar;}{s the s}}_{k k},, {\underset{&OverBar; &OverBar;}{a a}}_{k k}))}{{l l}_{{(({s the s}_{k k},, {a a}_{k k}))}^{~ ~}} + + {l l}_{{(({s the s}_{t t},, {a a}_{t t}))}^{~ ~}}},, 00]],, 00}} - - - - - - ((33))$

为(s_k,a_k)^～≥(s_t,a_t)^～的可能度。is the possibility degree of (s_k , a_k )^~ ≥ (s_t , a_t )^~ .

定义5：设IT-WAA：若 $μ_{j} = {(s_{j}, a_{j})}^{~} = [({\underset{&OverBar;}{s}}_{j}, {\underset{&OverBar;}{a}}_{j}), ({\overset{&OverBar;}{s}}_{j}, {\overset{&OverBar;}{a}}_{j})] (j = 1, 2, ..., n)$ 为一组区间二元语义信息，ω＝(ω₁,ω₂,…,ω_n)^T为相应的权重，且ω_j∈[0,1],j＝(1,2,…,n)，Definition 5: Let IT-WAA: If $μ_{j} = {({the s}_{j}, a_{j})}^{~} = [({\underset{&OverBar;}{the s}}_{j}, {\underset{&OverBar;}{a}}_{j}), ({\overset{&OverBar;}{the s}}_{j}, {\overset{&OverBar;}{a}}_{j})] (j = 1, 2, ..., no)$ is a set of interval binary semantic information, ω=(ω₁ ,ω₂ ,…,ω_n )^T is the corresponding weight, and ω_j ∈[0,1],j=(1,2,…,n) ,

${Φ Φ}_{ω ω} [[{(({s the s}_{11},, {a a}_{11}))}^{~ ~},, {(({s the s}_{22},, {a a}_{22}))}^{~ ~},, ... ...,, {(({s the s}_{n no},, {a a}_{n no}))}^{~ ~}]] = = {{Δ Δ [[{Σ Σ}_{j j = = 11}^{n no} {ω ω}_{j j} {Δ Δ}^{- - 11} (({\underset{&OverBar; &OverBar;}{s the s}}_{j j},, {\underset{&OverBar; &OverBar;}{a a}}_{j j}))]],, Δ Δ [[{Σ Σ}_{j j = = 11}^{n no} {ω ω}_{j j} {Δ Δ}^{- - 11} (({\overset{&OverBar; &OverBar;}{s the s}}_{j j},, {\overset{&OverBar; &OverBar;}{a a}}_{j j}))]]}} - - - - - - ((44))$

则称Φ_w为区间二元语义加权算术平均(IT-WAA)算子。Then Φ_w is called Interval Binary Semantic Weighted Arithmetic Average (IT-WAA) operator.

定义6：设IT-WHA：若 $μ_{j} = {(s_{j}, a_{j})}^{~} = [({\underset{&OverBar;}{s}}_{j}, {\underset{&OverBar;}{a}}_{j}), ({\overset{&OverBar;}{s}}_{j}, {\overset{&OverBar;}{a}}_{j})] (j = 1, 2, ..., n)$ 为一组区间二元语义信息，ω＝(ω₁,ω₂,…,ω_n)^T为相应的权重，且ω_j∈[0,1]，Definition 6: Let IT-WHA: If $μ_{j} = {({the s}_{j}, a_{j})}^{~} = [({\underset{&OverBar;}{the s}}_{j}, {\underset{&OverBar;}{a}}_{j}), ({\overset{&OverBar;}{the s}}_{j}, {\overset{&OverBar;}{a}}_{j})] (j = 1, 2, ..., no)$ is a set of interval binary semantic information, ω=(ω₁ ,ω₂ ,…,ω_n )^T is the corresponding weight, and ω_j ∈[0,1],

${Φ Φ}_{ω ω,, w w} [[{(({s the s}_{11},, {a a}_{11}))}^{~ ~},, {(({s the s}_{22},, {a a}_{22}))}^{~ ~},, ... ...,, {(({s the s}_{n no},, {a a}_{n no}))}^{~ ~}]] = = {{Δ Δ [[{Σ Σ}_{j j = = 11}^{n no} {w w}_{j j} {Δ Δ}^{- - 11} (({\underset{&OverBar; &OverBar;}{s the s}}_{j j},, {\underset{&OverBar; &OverBar;}{a a}}_{j j}))]],, Δ Δ [[{Σ Σ}_{j j = = 11}^{n no} {w w}_{j j} {Δ Δ}^{- - 11} (({\overset{&OverBar; &OverBar;}{s the s}}_{j j},, {\overset{&OverBar; &OverBar;}{a a}}_{j j}))]]}} - - - - - - ((55))$

其中w＝(w₁,w₂,…,w_n)^T是相关联的加权向量(位置向量)，且w_j∈[0,1]， $v_{j} = [({\underset{&OverBar;}{s}}_{π (j)}, {\underset{&OverBar;}{a}}_{π (j)}), ({\overset{&OverBar;}{s}}_{π (j)}, {\overset{&OverBar;}{a}}_{π (j)})]$ 是加权的二元语义变量组 $({\tilde{μ}}_{1}, {\tilde{μ}}_{2}, ..., {\tilde{μ}}_{n}) ({\tilde{μ}}_{j} = {nω}_{j} {(s_{j}, a_{j})}^{~})$ 第j大元素，且n为平衡因子，则称Φ_ω,w为区间二元语义混合加权(IT-WHA)算子。where w=(w₁ ,w₂ ,…,w_n )^T is the associated weight vector (position vector), and w_j ∈[0,1], $v_{j} = [({\underset{&OverBar;}{the s}}_{π (j)}, {\underset{&OverBar;}{a}}_{π (j)}), ({\overset{&OverBar;}{the s}}_{π (j)}, {\overset{&OverBar;}{a}}_{π (j)})]$ is the weighted set of binary semantic variables $({\tilde{μ}}_{1}, {\tilde{μ}}_{2}, ..., {\tilde{μ}}_{no}) ({\tilde{μ}}_{j} = {nω}_{j} {({the s}_{j}, a_{j})}^{~})$ The jth largest element, and n is a balance factor, then Φ_ω,w is called an interval binary semantic hybrid weighting (IT-WHA) operator.

定义7：设在语言评价集下得到的区间语言评价矩阵为 $\tilde{R} = {([{\underset{&OverBar;}{r}}_{i j}, {\overset{&OverBar;}{r}}_{i j}])}_{m \times n},$ 其中为属性值。设定基本语言评价集为 $S^{T} = {s_{i}^{T} | i &Element; {0, 1, ..., T - 1}},$ 采用转换函数ζ将转换为以基本语言评价集S^T表示下的区间二元语义评价矩阵Definition 7: Set in the language evaluation set The interval language evaluation matrix obtained from the following is $\tilde{R} = {([{\underset{&OverBar;}{r}}_{i j}, {\overset{&OverBar;}{r}}_{i j}])}_{m \times no},$ in for the attribute value. Set the base language evaluation set to $S^{T} = {{the s}_{i}^{T} | i &Element; {0, 1, ..., T - 1}},$ Using the transfer function ζ will Converted to an interval binary semantic evaluation matrix represented by the basic language evaluation set S^T

式中a_ij， ${\overset{&OverBar;}{a}}_{i j} &Element; [- 0.5, 0.5) .$ In the formulaa_ij , ${\overset{&OverBar;}{a}}_{i j} &Element; [- 0.5, 0.5) .$

a)：决策者集合为D＝{d₁,d₂,…,d_k,…,d_t}，共t位决策者。每位决策者d_k(k＝1,2,…,t)分别给出人、机能力优势对待分配功能的区间语言评估值和并得到评估矩阵 ${\tilde{H}}_{k} = {([{\underset{&OverBar;}{h}}_{i j}^{k}, {\overset{&OverBar;}{h}}_{i j}^{k}])}_{n \times m}, {\tilde{Q}}_{k} = {([{\underset{&OverBar;}{q}}_{i j}^{k}, {\overset{&OverBar;}{q}}_{i j}^{k}])}_{n \times l} .$ a): The set of decision makers is D={d₁ ,d₂ ,...,d_k ,...,d_t }, with t decision makers in total. Each decision maker d_k (k=1,2,...,t) respectively gives the interval language evaluation value of human and machine ability superiority treatment allocation function and and get the evaluation matrix ${\tilde{h}}_{k} = {([{\underset{&OverBar;}{h}}_{i j}^{k}, {\overset{&OverBar;}{h}}_{i j}^{k}])}_{no \times m}, {\tilde{Q}}_{k} = {([{\underset{&OverBar;}{q}}_{i j}^{k}, {\overset{&OverBar;}{q}}_{i j}^{k}])}_{no \times l} .$

b)：设定基本语言评价集S^T，根据(6)式将和转化成基于S^T表示的一致化区间二元语义评价矩阵和利用IT-WAA算子将和集结为群区间二元语义评价矩阵和b): Set the basic language evaluation set S^T , according to formula (6) and Transformed into a consistent interval binary semantic evaluation matrix based on S^T representation and Use the IT-WAA operator to and Assembled into a binary semantic evaluation matrix between clusters and

c)：根据IT-WAA算子以及人、机能力优势权重和τ将和按行集结，计算出人、机方案区间二元语义综合评价值和利用(3)式，计算出人、机能力对待分配功能的综合评估结果和之间的可能度c): According to the IT-WAA operator and the weight of advantages of human and machine capabilities and τ will be and Gather by row to calculate the binary semantic comprehensive evaluation value of the man-machine scheme interval and Using formula (3), calculate the comprehensive evaluation result of human and machine capabilities for the assigned function and possibility between

d)：根据可能度结果p确定待分配功能的自动化等级(LevelOfAutomation，LOA)范围。d): Determine the range of the Level of Automation (LOA) of the function to be assigned according to the result p of the degree of possibility.

$\{\begin{matrix} c c e e i i l l ((p p \times \times 55)) - - 11 \leq \leq L L O o A A \leq \leq c c e e i i l l ((p p \times \times 55)) + + 11 \\ L L O o A A &Element; &Element; {{11,, 22,, ... ...,, 1010}} \end{matrix} - - - - - - ((77))$

其中，ceil(x)为上取整函数。Among them, ceil(x) is the upper integer function.

功能分配自动化等级范围确定以后，即给定了功能分配的不同方案，还需要根据功能分配评估准则从分配方案中选出最优方案，最终确定驾驶舱人机功能分配的自动化等级。针对某个功能多属性决策问题，设A＝{a₁,a₂,…,a_n′}是方案集，其元素表示自动化等级的n'种情况。给定功能分配评估准则(属性)集合G＝{g₁,g₂,…,g_m′}，其元素分别对应驾驶舱人机功能分配的五个主要评估准则，g₁—态势感知；g₂—脑力负荷；g₃—决策风险；g₄—可靠性；g₁—系统成本。属性权重的权重向量为η＝(η₁,η₂,…,η_m′)，且其向量为η_l≥0(l＝1,2,…,m′)，After the scope of the automation level of function allocation is determined, that is, given the different schemes of function allocation, it is necessary to select the optimal scheme from the allocation schemes according to the evaluation criteria of function allocation, and finally determine the automation level of the cockpit man-machine function allocation. Aiming at a functional multi-attribute decision-making problem, let A={a₁ ,a₂ ,…,a_n′ } be a solution set, whose elements represent n' cases of automation level. Given the set of function allocation evaluation criteria (attributes) G={g₁ ,g₂ ,…,g_m′ }, its elements correspond to the five main evaluation criteria for cockpit man-machine function allocation, g₁ —situational awareness; g₂ —brain load; g₃ —decision risk; g₄ —reliability; g₁ —system cost. The weight vector of attribute weight is η=(η₁ ,η₂ ,…,η_m′ ), and its vector is η_l ≥ 0(l=1,2,…,m′),

a)：t位决策者的权重向量为决策者d_k∈D给出方案a_i∈A在属性g_j∈G下的区间语言评估值并得到评估矩阵a): The weight vector of t decision makers is The decision maker d_k ∈ D gives the interval language evaluation value of the scheme a_i ∈ A under the attribute g_j ∈ G and get the evaluation matrix

b)：根据(6)式将转化成基于基本语言评价集S^T′表示的一致化区间二元语义评价矩阵利用IT-WAA算子对中第i行的语言评估信息进行集结，得到决策者d_k(k＝1,2,…,t)对方案a_i(i＝1,2,…，n′)的综合属性评估值b): according to formula (6) will Transformed into a consistent interval binary semantic evaluation matrix based on the basic language evaluation set S^T′ Using the IT-WAA operator pair The language evaluation information in the i-th row in is assembled to obtain the comprehensive attribute evaluation value of the decision maker d_k (k=1,2,…,t) for the scheme a_i (i=1,2,…,n′)

c)：利用IT-WHA算子对t位决策者的综合属性评估值进行集结，得到关于方案a_i的群体综合评估值γⁱ(λ,w)：c): Using the IT-WHA operator to evaluate the comprehensive attributes of t decision makers Gather together to get the group comprehensive evaluation value γⁱ (λ,w) of the scheme a_i :

${γ γ}^{i i} ((λ λ,, w w)) = = {w w}_{11} {\overset{~ ~}{v v}}_{11} &CirclePlus; &CirclePlus; {w w}_{22} {\overset{~ ~}{v v}}_{22} &CirclePlus; &CirclePlus; ... ... &CirclePlus; &CirclePlus; {w w}_{t t} {\overset{~ ~}{v v}}_{t t} - - - - - - ((88))$

其中，w＝(w₁,w₂,…,w_t)是IT-WHA算子的加权向量，w_k∈[0,1](k＝1,2,…,t)且 $Σ_{k = 1}^{t} w_{k} = 1.$ 是加权的二元语义变量组 $({\tilde{μ}}_{1}, {\tilde{μ}}_{2}, ..., {\tilde{μ}}_{t}) ({\tilde{μ}}_{k} = {tλ}_{k} γ_{k}^{i} (η))$ 第k大元素，λ＝(λ₁,λ₂,…,λ_t)^T为相应的权重，且λ_k∈[0,1]，且t为平衡因子。Among them, w=(w₁ ,w₂ ,…,w_t ) is the weight vector of IT-WHA operator, w_k ∈[0,1](k=1,2,…,t) and $Σ_{k = 1}^{t} w_{k} = 1.$ is the weighted set of binary semantic variables $({\tilde{μ}}_{1}, {\tilde{μ}}_{2}, ..., {\tilde{μ}}_{t}) ({\tilde{μ}}_{k} = {tλ}_{k} γ_{k}^{i} (η))$ The kth largest element, λ=(λ₁ ,λ₂ ,…,λ_t )^T is the corresponding weight, and λ_k ∈[0,1], And t is the balance factor.

d)：利用式(3)，计算出方案a_i(i＝1,2,…,n′)综合评估值γⁱ(λ,w)与a_j(j＝1,2,…,n′)综合评估值γ^j(λ,w)之间的可能度p′_ij＝p[γⁱ(λ,w)≥γ^j(λ,w)]，从而得到可能度矩阵 $p^{'} = {(p_{i j}^{'})}_{n^{'} \times n^{'}} .$ d): Using formula (3), calculate the comprehensive evaluation value γⁱ (λ, w) and a_j (j=1, 2, ..., n′) of the scheme a_i (i=1,2,…,n′) ) The possibility p′_ij ＝p[γⁱ (λ,w)≥γ^j (λ,w)] between comprehensive evaluation values γ^j (λ,w), so as to obtain the possibility matrix $p^{'} = {(p_{i j}^{'})}_{{no}^{'} \times {no}^{'}} .$

e)：求出可能度矩阵p′的排序向量v＝(v₁,v₂,…,v_n′)，并按其分量大小对方案进行排序，即得到最优方案。其中e): Calculate the sorting vector v=(v₁ ,v₂ ,…,v_n' ) of the possibility matrix p′, and sort the proposals according to their component sizes, that is, get the optimal proposal. in

${v v}_{i i} = = \frac{11}{{n no}^{' '} (({n no}^{' '} - - 11))} (({Σ Σ}_{j j = = 11}^{{n no}^{' '}} {p p}_{i i j j}^{' '} + + \frac{{n no}^{' '}}{22} - - 11)),, i i = = 11,, 22,, ... ...,, {n no}^{' '} - - - - - - ((99))$

最后按其分量大小对方案进行排序，即得到最优的功能分配方案。Finally, the schemes are sorted according to the size of their components, and the optimal function allocation scheme is obtained.

下面以民机驾驶舱中近地告警系统(GroundProximityWarningSystem，GPWS)为例，详细说明基于区间二元语义的驾驶舱功能分配方法的具体实施过程，即采用所提出的方法确定GPWS的最优自动化等级。Taking the Ground Proximity Warning System (GPWS) in the civil aircraft cockpit as an example, the specific implementation process of the cockpit function allocation method based on interval binary semantics is described in detail, that is, the optimal automation level of GPWS is determined by the proposed method .

1.确定人、机优势能力集合H＝{h₁,h₂,h₃,h₄,h₅}和M＝{m₁,m₂,m₃,m₄,m₅}，各元素含义如表1所示。1. Determine the set of human and machine superior capabilities H={h₁ ,h₂ ,h₃ ,h₄ ,h₅ } and M={m₁ ,m₂ ,m₃ ,m₄ ,m₅ }, the meaning of each element As shown in Table 1.

2.利用模糊层次分析法得到H和M中元素的权重向量分别为：2. Using fuzzy analytic hierarchy process to get the weight vectors of the elements in H and M respectively:

τ＝(0.1425,0.1714,0.2873,0.1519,0.2469)。τ=(0.1425, 0.1714, 0.2873, 0.1519, 0.2469).

3.其GPWS功能划分为10个自动化级别，其自动化程度如表2所示。3. Its GPWS function is divided into 10 automation levels, and its automation degree is shown in Table 2.

4.确定功能的自动化等级范围4. Determine the scope of the automation level of the function

决策者集合为D＝{d₁,d₂,d₃}，三位决策者各自偏好的语言评价集为：The set of decision makers is D={d₁ ,d₂ ,d₃ }, and the preferred language evaluation sets of the three decision makers are:

三位决策者根据各自的语言偏好对人、机能力优势元素对GPWS功能影响程度的评估结果分别为：The evaluation results of the three decision makers on the impact of the superior elements of human and machine capabilities on the function of GPWS according to their respective language preferences are as follows:

${\tilde{H}}_{1} = {[s_{4}^{7}, s_{5}^{7}], [s_{3}^{7}, s_{4}^{7}], [s_{2}^{7}, s_{3}^{7}], [s_{3}^{7}, s_{6}^{7}], [s_{4}^{7}, s_{6}^{7}]},$ ${\tilde{h}}_{1} = {[{the s}_{4}^{7}, {the s}_{5}^{7}], [{the s}_{3}^{7}, {the s}_{4}^{7}], [{the s}_{2}^{7}, {the s}_{3}^{7}], [{the s}_{3}^{7}, {the s}_{6}^{7}], [{the s}_{4}^{7}, {the s}_{6}^{7}]},$

${\tilde{H}}_{2} = {[s_{2}^{5}, s_{4}^{5}], [s_{2}^{5}, s_{3}^{5}], [s_{1}^{5}, s_{2}^{5}], [s_{3}^{5}, s_{4}^{5}], [s_{1}^{5}, s_{3}^{5}]},$ ${\tilde{h}}_{2} = {[{the s}_{2}^{5}, {the s}_{4}^{5}], [{the s}_{2}^{5}, {the s}_{3}^{5}], [{the s}_{1}^{5}, {the s}_{2}^{5}], [{the s}_{3}^{5}, {the s}_{4}^{5}], [{the s}_{1}^{5}, {the s}_{3}^{5}]},$

${\overset{~ ~}{H h}}_{33} = = {{[[{s the s}_{66}^{1111},, {s the s}_{99}^{1111}]],, [[{s the s}_{33}^{1111},, {s the s}_{77}^{1111}]],, [[{s the s}_{22}^{1111},, {s the s}_{88}^{1111}]],, [[{s the s}_{55}^{1111},, {s the s}_{99}^{1111}]],, [[{s the s}_{66}^{1111},, {s the s}_{99}^{1111}]]}},, {\overset{~ ~}{Q Q}}_{33} = = {{[[{s the s}_{22}^{1111},, {s the s}_{88}^{1111}]],, [[{s the s}_{66}^{1111},, {s the s}_{99}^{1111}]],, [[{s the s}_{33}^{1111},, {s the s}_{88}^{1111}]],, [[{s the s}_{55}^{1111},, {s the s}_{77}^{1111}]],, [[{s the s}_{77}^{1111},, {s the s}_{99}^{1111}]]}} . .$

根据语言评价集粒度最大原则，选择作为基本语言评价集。根据(6)式将转化为由基本语言评价集表示的一致化区间二元语义评价向量According to the principle of the largest granularity of the language evaluation set, choose as a basic language evaluation set. According to formula (6) will into a basic language evaluation set Consistent Interval Binary Semantic Evaluation Vector

${\overset{&OverBar; &OverBar;}{\overset{~ ~}{H h}}}_{11} = = {{[[(({s the s}_{77}^{1111},, - - 0.33 0.33)),, (({s the s}_{88}^{1111},, 0.33 0.33))]],, [[(({s the s}_{55}^{1111},, 00)),, (({s the s}_{77}^{1111},, - - 0.33 0.33))]],, [[(({s the s}_{33}^{1111},, 0.33 0.33)),, (({s the s}_{55}^{1111},, 00))]],, [[(({s the s}_{55}^{1111},, 00)),, (({s the s}_{1010}^{1111},, 00))]],, [[(({s the s}_{77}^{1111},, - - 0.33 0.33)),, (({s the s}_{1010}^{1111},, - - 00))]]}}$

${\overset{&OverBar; &OverBar;}{\overset{~ ~}{H h}}}_{22} = = {{[[(({s the s}_{55}^{1111},, 00)),, (({s the s}_{1010}^{1111},, 00))]],, [[(({s the s}_{55}^{1111},, 00)),, (({s the s}_{88}^{1111},, - - 0.5 0.5))]],, [[(({s the s}_{33}^{1111},, - - 0.5 0.5)),, (({s the s}_{55}^{1111},, 00))]],, [[(({s the s}_{88}^{1111},, - - 0.5 0.5)),, (({s the s}_{1010}^{1111},, 00))]],, [[(({s the s}_{33}^{1111},, - - 0.5 0.5)),, (({s the s}_{88}^{1111},, - - 0.5 0.5))]]}}$

${\overset{&OverBar; &OverBar;}{\overset{~ ~}{H h}}}_{33} = = {{[[(({s the s}_{66}^{1111},, 00)),, (({s the s}_{99}^{1111},, 00))]],, [[(({s the s}_{33}^{1111},, 00)),, (({s the s}_{77}^{1111},, 00))]],, [[(({s the s}_{22}^{1111},, 00)),, (({s the s}_{88}^{1111},, 00))]],, [[(({s the s}_{55}^{1111},, 00)),, (({s the s}_{99}^{1111},, 00))]],, [[(({s the s}_{66}^{1111},, 00)),, (({s the s}_{99}^{1111},, 00))]]}}$

${\overset{&OverBar; &OverBar;}{\overset{~ ~}{Q Q}}}_{11} = = {{[[(({s the s}_{33}^{1111},, 0.33 0.33)),, (({s the s}_{55}^{1111},, 00))]],, [[(({s the s}_{77}^{1111},, - - 0.33 0.33)),, (({s the s}_{1010}^{1111},, 00))]],, [[(({s the s}_{33}^{1111},, 0.33 0.33)),, (({s the s}_{77}^{1111},, - - 0.33 0.33))]],, [[(({s the s}_{22}^{1111},, - - 0.33 0.33)),, (({s the s}_{55}^{1111},, 00))]],, [[(({s the s}_{88}^{1111},, 0.33 0.33)),, (({s the s}_{1010}^{1111},, 00))]]}}$

${\overset{&OverBar; &OverBar;}{\overset{~ ~}{Q Q}}}_{22} = = {{[[(({s the s}_{33}^{1111},, - - 0.5 0.5)),, (({s the s}_{55}^{1111},, 00))]],, [[(({s the s}_{88}^{1111},, - - 0.5 0.5)),, (({s the s}_{1010}^{1111},, 00))]],, [[(({s the s}_{55}^{1111},, 00)),, (({s the s}_{1010}^{1111},, 00))]],, [[(({s the s}_{33}^{1111},, - - 0.5 0.5)),, (({s the s}_{55}^{1111},, 00))]],, [[(({s the s}_{55}^{1111},, 00)),, (({s the s}_{88}^{1111},, - - 0.5 0.5))]]}}$

利用IT-WAA算子对三个决策者评估结果进行集结，得到人、机能力各个元素对GPWS功能的评估结果：The IT-WAA operator is used to gather the evaluation results of the three decision makers, and the evaluation results of each element of human and machine capabilities on the GPWS function are obtained:

$\begin{matrix} \overset{&OverBar; &OverBar;}{\overset{~ ~}{H h}} = = {{[[(({s the s}_{66}^{1111},, - - 0.1089 0.1089)),, (({s the s}_{99}^{1111},, 0.1089 0.1089))]],, [[(({s the s}_{44}^{1111},, 0.32 0.32)),, (({s the s}_{77}^{1111},, 0.0561 0.0561))]],, [[(({s the s}_{33}^{1111},, - - 0.3961 0.3961)),, \\ (({s the s}_{66}^{1111},, - - 0.02 0.02))]],, [[(({s the s}_{66}^{1111},, - - 0.175 0.175)),, (({s the s}_{1010}^{1111},, - - 0.34 0.34))]],, [[(({s the s}_{55}^{1111},, 0.0661 0.0661)),, (({s the s}_{99}^{1111},, - - 0.165 0.165))]]}} \end{matrix}$

$\begin{matrix} \overset{~ ~}{Q Q} = = {{[(s {[(s}_{33}^{1111},-0,-0 {.3961),(s .3961),(s}_{66}^{1111},0,0 {.02)],[(s .02)],[(s}_{77}^{1111},-0,-0 {.2839),(s .2839),(s}_{1010}^{1111},-0,-0 {.34)],[(s .34)],[(s}_{44}^{1111},-0,-0 .2311), .2311), \\ {(s (s}_{88}^{1111},0,0 {.2211)],[(s .2211)],[(s}_{33}^{1111},0,0 {.0761),(s .0761),(s}_{66}^{1111},-0,-0 {.32)],[(s .32)],[(s}_{77}^{1111},-0,-0 {.2211),(s .2211),(s}_{99}^{1111},-0,-0 .165)]} .165)]} \end{matrix}$

根据人、机能力优势权重和τ，利用IT-WAA算子集结得到人、机能力对GPWS功能的评估综合结果：According to the weight of human and machine ability advantages and τ, using IT-WAA operator aggregation to obtain the comprehensive results of the evaluation of human and machine capabilities on GPWS functions:

$\overset{~ ~}{L L} ((\overset{&OverBar; &OverBar;}{\overset{~ ~}{Q Q}},, τ τ)) = = [[(({s the s}_{55}^{1111},, 0.1249 0.1249)),, (({s the s}_{88}^{1111},, - - 0.0804 0.0804))]] . .$

利用(3)式计算可得的可能度为再根据(7)式可得GPWS的自动化等级范围为2≤LOA≤4。Using formula (3), we can get The probability of According to formula (7), the range of automation level of GPWS is 2≤LOA≤4.

5.建立功能分配评估准则(属性)集合5. Establish a set of function allocation evaluation criteria (attributes)

确定了GPWS功能的自动化等级范围以后，相当于给定了3种不同的分配方案，设GPWS分配方案集合A＝{a₂,a₃,a₄}，其元素表示GPWS功能分配方案采用的是2、3、4级自动化的三种情况。设分配评估准则(属性)集合G＝{g₁,g₂,g₃,g₄,g₅}，其代表着人、机功能分配的五个重要评估准则：g₁—态势感知；g₂—脑力负荷；g₃—决策风险；g₄—可靠性；g₁—系统成本。同样利用模糊层次分析法获得属性的权重向量η＝(0.2447,0.3581,0.1423,0.1869，0.068)。After determining the range of automation levels of GPWS functions, it is equivalent to giving three different allocation schemes. Let the GPWS allocation scheme set A={a₂ ,a₃ ,a₄ }, and its elements indicate that the GPWS function allocation scheme adopts Three cases of automation at levels 2, 3, and 4. Assume that the allocation evaluation criteria (attributes) set G={g₁ , g₂ , g₃ , g₄ , g₅ }, which represent five important evaluation criteria for the allocation of human and machine functions: g₁ — situational awareness; g₂ —brain load; g₃ —decision risk; g₄ —reliability; g₁ —system cost. Also use fuzzy analytic hierarchy process to obtain attribute weight vector η=(0.2447, 0.3581, 0.1423, 0.1869, 0.068).

针对三个方案a_i(i＝2,3,4)关于五个属性g_j(j＝1,2,3,4,5)的测度，三位决策者给出的区间语言评估信息分别为For the measurement of the five attributes g_j (j=1,2,3,4,5) of the three schemes a_i (i=2,3,4), the interval language evaluation information given by the three decision makers are respectively

${\overset{~ ~}{R R}}_{11} = = [\begin{matrix} [[{s the s}_{33}^{77},, {s the s}_{44}^{77}]] & [[{s the s}_{11}^{77},, {s the s}_{22}^{77}]] & [[{s the s}_{00}^{77},, {s the s}_{11}^{77}]] & [[{s the s}_{55}^{77},, {s the s}_{66}^{77}]] & [[{s the s}_{44}^{77},, {s the s}_{66}^{77}]] \\ [[{s the s}_{55}^{77},, {s the s}_{66}^{77}]] & [[{s the s}_{33}^{77},, {s the s}_{44}^{77}]] & [[{s the s}_{22}^{77},, {s the s}_{33}^{77}]] & [[{s the s}_{11}^{77},, {s the s}_{33}^{77}]] & [[{s the s}_{33}^{77},, {s the s}_{55}^{77}]] \\ [[{s the s}_{22}^{77},, {s the s}_{33}^{77}]] & [[{s the s}_{55}^{77},, {s the s}_{66}^{77}]] & [[{s the s}_{22}^{77},, {s the s}_{44}^{77}]] & [[{s the s}_{22}^{77},, {s the s}_{44}^{77}]] & [[{s the s}_{33}^{77},, {s the s}_{44}^{77}]] \end{matrix}]$

${\overset{~ ~}{R R}}_{22} = = [\begin{matrix} [[{s the s}_{22}^{55},, {s the s}_{33}^{55}]] & [[{s the s}_{11}^{55},, {s the s}_{22}^{55}]] & [[{s the s}_{00}^{55},, {s the s}_{11}^{55}]] & [[{s the s}_{22}^{55},, {s the s}_{44}^{55}]] & [[{s the s}_{22}^{55},, {s the s}_{44}^{55}]] \\ [[{s the s}_{33}^{55},, {s the s}_{44}^{55}]] & [[{s the s}_{22}^{55},, {s the s}_{33}^{55}]] & [[{s the s}_{11}^{55},, {s the s}_{44}^{55}]] & [[{s the s}_{11}^{55},, {s the s}_{33}^{55}]] & [[{s the s}_{11}^{55},, {s the s}_{33}^{55}]] \\ [[{s the s}_{11}^{55},, {s the s}_{33}^{55}]] & [[{s the s}_{22}^{55},, {s the s}_{44}^{55}]] & [[{s the s}_{22}^{55},, {s the s}_{33}^{55}]] & [[{s the s}_{22}^{55},, {s the s}_{44}^{55}]] & [[{s the s}_{11}^{55},, {s the s}_{22}^{55}]] \end{matrix}]$

${\overset{~ ~}{R R}}_{33} = = [\begin{matrix} [[{s the s}_{55}^{1111},, {s the s}_{77}^{1111}]] & [[{s the s}_{77}^{1111},, {s the s}_{99}^{1111}]] & [[{s the s}_{22}^{1111},, {s the s}_{44}^{1111}]] & [[{s the s}_{44}^{1111},, {s the s}_{55}^{1111}]] & [[{s the s}_{66}^{1111},, {s the s}_{1010}^{1111}]] \\ [[{s the s}_{11}^{1111},, {s the s}_{44}^{1111}]] & [[{s the s}_{33}^{1111},, {s the s}_{55}^{1111}]] & [[{s the s}_{33}^{1111},, {s the s}_{55}^{1111}]] & [[{s the s}_{66}^{1111},, {s the s}_{77}^{1111}]] & [[{s the s}_{55}^{1111},, {s the s}_{99}^{1111}]] \\ [[{s the s}_{33}^{1111},, {s the s}_{66}^{1111}]] & [[{s the s}_{44}^{1111},, {s the s}_{66}^{1111}]] & [[{s the s}_{99}^{1111},, {s the s}_{1010}^{1111}]] & [[{s the s}_{33}^{1111},, {s the s}_{77}^{1111}]] & [[{s the s}_{33}^{1111},, {s the s}_{88}^{1111}]] \end{matrix}]$

根据(6)式将转化为由基本语言评价集表示的一致化区间二元语义评价向量According to formula (6) will into a basic language evaluation set Consistent Interval Binary Semantic Evaluation Vector

$\begin{matrix} {\overset{&OverBar; &OverBar;}{\overset{~ ~}{R R}}}_{11} = = [\begin{matrix} [[(\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix}),, (({s the s}_{77}^{1111},, - - 0.33 0.33))]] & [[(\begin{matrix} {s the s}_{22}^{1111},, & 0.33 0.33 \end{matrix}),, (\begin{matrix} {s the s}_{33}^{1111},, & 0.33 0.33 \end{matrix})]] & [[(\begin{matrix} {s the s}_{00}^{1111},, & 00 \end{matrix}),, \\ [[(({s the s}_{88}^{1111},, 0.33 0.33)),, (\begin{matrix} {s the s}_{1010}^{1111},, & 00 \end{matrix})]] & [[(\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix}),, (({s the s}_{77}^{1111},, - - 0.33 0.33))]] & [[(({s the s}_{33}^{1111},, 0.33 0.33)),, \\ [[(({s the s}_{33}^{1111},, 0.33 0.33)),, (\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix})]] & [[((\begin{matrix} {s the s}_{88}^{1111},, & 00 \end{matrix} .33 .33)),, (\begin{matrix} {s the s}_{1010}^{1111},, & 00 \end{matrix})]] & [[(({s the s}_{33}^{1111},, 0.33 0.33)),, \end{matrix} \\ \begin{matrix} (({s the s}_{22}^{1111},, - - 0.33 0.33))]] & [[((\begin{matrix} {s the s}_{88}^{1111},, & 00 \end{matrix} .33 .33)),, (\begin{matrix} {s the s}_{1010}^{1111},, & 00 \end{matrix})]] & [[(({s the s}_{77}^{1111},, - - 0.33 0.33)),, (\begin{matrix} {s the s}_{1010}^{1111},, & 00 \end{matrix})]] \\ ((\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix}))]] & [[(({s the s}_{22}^{1111},, - - 0.33 0.33)),, (\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix})]] & [[(\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix}),, (\begin{matrix} {s the s}_{88}^{1111},, & 0.33 0.33 \end{matrix})]] \\ (({s the s}_{77}^{1111},, - - 0.33 0.33))]] & [[(\begin{matrix} {s the s}_{33}^{1111},, & 0.33 0.33 \end{matrix}),, (({s the s}_{77}^{1111},, - - 0.33 0.33))]] & [[(\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix}),, (({s the s}_{77}^{1111},, - - 0.33 0.33))]] \end{matrix}] \end{matrix}$

$\begin{matrix} {\overset{&OverBar; &OverBar;}{\overset{~ ~}{R R}}}_{22} = = [\begin{matrix} [[(\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix}) (({s the s}_{88}^{1111},, - - 0.5 0.5))]] & [[(({s the s}_{33}^{1111},, - - 0.5 0.5)),, (\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix})]] & [[(\begin{matrix} {s the s}_{00}^{1111},, & 00 \end{matrix}),, \\ [[(({s the s}_{88}^{1111},, - - 0.5 0.5)),, (\begin{matrix} {s the s}_{1010}^{1111},, & 00 \end{matrix})]] & [[(\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix}),, (({s the s}_{88}^{1111},, - - 0.5 0.5))]] & [[(({s the s}_{33}^{1111},, - - 0.5 0.5)),, \\ [[(({s the s}_{33}^{1111},, - - 0.5 0.5)),, (({s the s}_{88}^{1111},, - - 0.5 0.5))]] & [[(\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix}),, (\begin{matrix} {s the s}_{1010}^{1111},, & 00 \end{matrix})]] & [[(\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix}),, \end{matrix} \\ \begin{matrix} (({s the s}_{33}^{1111},, - - 0.5 0.5))]] & [[(\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix}),, (\begin{matrix} {s the s}_{1010}^{1111},, & 00 \end{matrix})]] & [[(\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix}),, (\begin{matrix} {s the s}_{1010}^{1111},, & 00 \end{matrix})]] \\ ((\begin{matrix} {s the s}_{1010}^{1111},, & 00 \end{matrix}))]] & [[(({s the s}_{33}^{1111},, - - 0.5 0.5)),, (({s the s}_{88}^{1111},, - - 0.5 0.5))]] & [[(({s the s}_{33}^{1111},, - - 0.5 0.5)),, (({s the s}_{88}^{1111},, - - 0.5 0.5))]] \\ (({s the s}_{88}^{1111},, - - 0.5 0.5))]] & [[(\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix}),, (\begin{matrix} {s the s}_{1010}^{1111},, & 00 \end{matrix})]] & [[(({s the s}_{33}^{1111},, - - 0.5 0.5)),, (\begin{matrix} {s the s}_{55}^{1111},, & 00 \end{matrix})]] \end{matrix}] \end{matrix}$

${\overset{&OverBar; &OverBar;}{\overset{~ ~}{R R}}}_{33} = = [\begin{matrix} [[(({s the s}_{55}^{1111},, 00)),, (({s the s}_{77}^{1111},, 00))]] & [[(({s the s}_{77}^{1111},, 00)),, (({s the s}_{99}^{1111},, 00))]] & [[(({s the s}_{22}^{1111},, 00)),, (({s the s}_{44}^{1111},, 00))]] & [[(({s the s}_{44}^{1111},, 00)),, (({s the s}_{55}^{1111},, 00))]] & [[(({s the s}_{66}^{1111},, 00)),, (({s the s}_{1010}^{1111},, 00))]] \\ [[(({s the s}_{11}^{1111},, 00)),, (({s the s}_{44}^{1111},, 00))]] & [[(({s the s}_{33}^{1111},, 00)),, (({s the s}_{55}^{1111},, 00))]] & [[(({s the s}_{33}^{1111},, 00)),, (({s the s}_{55}^{1111},, 00))]] & [[(({s the s}_{66}^{1111},, 00)),, (({s the s}_{77}^{1111},, 00))]] & [[(({s the s}_{55}^{1111},, 00)),, (({s the s}_{99}^{1111},, 00))]] \\ [[(({s the s}_{33}^{1111},, 00)),, (({s the s}_{66}^{1111},, 00))]] & [[(({s the s}_{44}^{1111},, 00)),, (({s the s}_{66}^{1111},, 00))]] & [[(({s the s}_{99}^{1111},, 00)),, (({s the s}_{1010}^{1111},, 00))]] & [[(({s the s}_{33}^{1111},, 00)),, (({s the s}_{77}^{1111},, 00))]] & [[(({s the s}_{33}^{1111},, 00)),, (({s the s}_{88}^{1111},, 00))]] \end{matrix}]$

利用IT-WAA算子对中第i行的语言评估信息进行集结，得到决策者d_k(k＝1,2,3对)方案a_i(i＝2,3,4)的综合属性评估值Using the IT-WAA operator pair The language evaluation information in the i-th line of the group is assembled to obtain the comprehensive attribute evaluation value of the plan a_i (i=2,3,4) of the decision maker d_k (k=1,2,3 pairs)

${γ γ}_{11}^{22} ((η η)) = = [[(({s the s}_{44}^{1111},, - - 0.168 0.168)),, (({s the s}_{66}^{1111},, - - 0.3887 0.3887))]];;$

${γ γ}_{11}^{33} ((η η)) = = [[(({s the s}_{55}^{1111},, - - 0.0452 0.0452)),, (({s the s}_{77}^{1111},, 0.048 0.048))]];;$

${γ γ}_{11}^{44} ((η η)) = = [[(({s the s}_{55}^{1111},, 0.2341 0.2341)),, (({s the s}_{77}^{1111},, 0.4538 0.4538))]];;$

${γ γ}_{22}^{22} ((η η)) = = [[(({s the s}_{33}^{1111},, 0.3933 0.3933)),, (({s the s}_{77}^{1111},, - - 0.4695 0.4695))]];;$

${γ γ}_{22}^{33} ((η η)) = = [[(({s the s}_{55}^{1111},, - - 0.3812 0.3812)),, (({s the s}_{88}^{1111},, 0.4675 0.4675))]];;$

${γ γ}_{22}^{44} ((η η)) = = [[(({s the s}_{44}^{1111},, 0.2182 0.2182)),, (({s the s}_{99}^{1111},, - - 0.3075 0.3075))]];;$

${γ γ}_{33}^{22} ((η η)) = = [[(({s the s}_{55}^{1111},, 0.1704 0.1704)),, (({s the s}_{77}^{1111},, 0.1195 0.1195))]];;$

${γ γ}_{33}^{33} ((η η)) = = [[(({s the s}_{33}^{1111},, 0.2073 0.2073)),, (({s the s}_{55}^{1111},, 0.4011 0.4011))]];;$

${γ γ}_{33}^{44} ((η η)) = = [[(({s the s}_{44}^{1111},, 0.2119 0.2119)),, (({s the s}_{77}^{1111},, - - 0.1079 0.1079))]] . .$

由n＝3以及三位决策者的权重向量为得到：By n=3 and the weight vectors of the three decision makers are get:

$33 {λ λ}_{11} {γ γ}_{11}^{22} ((η η)) = = [[(({s the s}_{44}^{1111},, - - 0.2063 0.2063)),, (({s the s}_{66}^{1111},, - - 0.4448 0.4448))]];;$

$33 {λ λ}_{11} {γ γ}_{11}^{33} ((η η)) = = [[(({s the s}_{55}^{1111},, - - 0.0947 0.0947)),, (({s the s}_{77}^{1111},, - - 0.0225 0.0225))]];;$

$33 {λ λ}_{11} {γ γ}_{11}^{44} ((η η)) = = [[(({s the s}_{55}^{1111},, 0.1818 0.1818)),, (({s the s}_{77}^{1111},, 0.3793 0.3793))]];;$

$33 {λ λ}_{22} {γ γ}_{22}^{22} ((η η)) = = [[(({s the s}_{33}^{1111},, 0.3594 0.3594)),, (({s the s}_{66}^{1111},, 0.4652 0.4652))]];;$

$33 {λ λ}_{22} {γ γ}_{22}^{33} ((η η)) = = [[(({s the s}_{55}^{1111},, - - 0.4274 0.4274)),, (({s the s}_{88}^{1111},, 0.3828 0.3828))]];;$

$33 {λ λ}_{22} {γ γ}_{22}^{44} ((η η)) = = [[(({s the s}_{44}^{1111},, 0.1760 0.1760)),, (({s the s}_{99}^{1111},, - - 0.3944 0.3944))]];;$

$33 {λ λ}_{33} {γ γ}_{33}^{22} ((η η)) = = [[(({s the s}_{55}^{1111},, 0.2738 0.2738)),, (({s the s}_{77}^{1111},, 0.2619 0.2619))]];;$

$33 {λ λ}_{33} {γ γ}_{33}^{33} ((η η)) = = [[(({s the s}_{33}^{1111},, 0.2714 0.2714)),, (({s the s}_{66}^{1111},, - - 0.4909 0.4909))]];;$

$33 {λ λ}_{33} {γ γ}_{33}^{44} ((η η)) = = [[(({s the s}_{44}^{1111},, 0.2961 0.2961)),, (({s the s}_{77}^{1111},, 0.0299 0.0299))]] . .$

设IT-WHA算子的位置加权向量w＝(0.25,0.50,0.25)，利用IT-WHA算子对三位决策者给各个方案的综合评估值进行集结，得到γⁱ(λ,w)(i＝2,3,4)：Assuming the position weighting vector w=(0.25, 0.50, 0.25) of the IT-WHA operator, the IT-WHA operator is used to gather the comprehensive evaluation values given by the three decision makers to each scheme to obtain γⁱ (λ, w)( i=2,3,4):

$\begin{matrix} {γ γ}^{22} ((λ λ,, w w)) = = 0.25 0.25 \times \times [[(({s the s}_{55}^{1111},, 0.2738 0.2738)),, (({s the s}_{77}^{1111},, 0.2619 0.2619))]] &CirclePlus; &CirclePlus; 0.50 0.50 \times \times [[(({s the s}_{33}^{1111},, 0.3594 0.3594)),, (({s the s}_{66}^{1111},, 0.4652 0.4652))]] \\ &CirclePlus; &CirclePlus; 0.25 0.25 \times \times [[(({s the s}_{44}^{1111},, - - 0.2063 0.2063)),, (({s the s}_{66}^{1111},, - - 0.4448 0.4448))]] \\ = = [[(({s the s}_{44}^{1111},, - - 0.0534 0.0534)),, (({s the s}_{66}^{1111},, 0.4369 0.4369))]] \end{matrix}$

$\begin{matrix} {γ γ}^{33} ((λ λ,, w w)) = = 0.25 0.25 \times \times [[(({s the s}_{55}^{1111},, - - 0.4274 0.4274)),, (({s the s}_{88}^{1111},, 0.3828 0.3828))]] &CirclePlus; &CirclePlus; 0.50 0.50 \times \times (({s the s}_{55}^{1111},, - - 0.0947 0.0947)),, (({s the s}_{77}^{1111},, - - 0.0225 0.0225))]] \\ &CirclePlus; &CirclePlus; 0.25 0.25 \times \times [[(({s the s}_{33}^{1111},, 0.2714 0.2714)),, (({s the s}_{66}^{1111},, - - 0.4909 0.4909))]] \\ = = [[(({s the s}_{44}^{1111},, 0.4137 0.4137)),, (({s the s}_{77}^{1111},, - - 0.0383 0.0383))]] \end{matrix}$

利用(3)式，计算出方案a_i(i＝2,3,4)综合评估值γⁱ(λ,w)与a_j(j＝2,3,4)综合评估值γ^j(λ,w)之间的可能度从而得到可能度矩阵Using formula (3), calculate the comprehensive evaluation value γⁱ (λ, w) of the scheme a_i (^{i=2,3,4) and the comprehensive evaluation value γ j}₍ λ, w) the likelihood between to get the possibility matrix

${P P}^{' '} = = [\begin{matrix} 0.5000 0.5000 & 0.4016 0.4016 & 0.3212 0.3212 \\ 0.5984 0.5984 & 0.5000 0.5000 & 0.4176 0.4176 \\ 0.6788 0.6788 & 0.5824 0.5824 & 0.5000 0.5000 \end{matrix}]$

根据(9)式可得可能度矩阵P′的排序向量为According to formula (9), the sorting vector of the probability matrix P′ can be obtained as

v＝(0.2871,0.3360,0.3796)v=(0.2871,0.3360,0.3796)

由此可知a₄＞a₃＞a₂，方案a₄为最优方案，因此，GWPS功能的最终自动化等级为4。It can be known that a₄ >a₃ >a₂ , scheme a₄ is the optimal scheme, therefore, the final automation level of the GWPS function is 4.