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Fuzzy number

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Real numbers with a multi-valued logical classification

This article is about the mathematical generalization of a real number as a connected set of possible values. For for a game value which is incomparable with zero, seeFuzzy game.

Afuzzy number is a generalization of a regularreal number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1.^[1] This weight is called themembership function. A fuzzy number is thus a special case of a convex, normalizedfuzzy set of thereal line.^[2] Just likefuzzy logic is an extension ofBoolean logic (which uses absolute truth and falsehood only, and nothing in between), fuzzy numbers are an extension of real numbers. Calculations with fuzzy numbers allow the incorporation ofuncertainty on parameters, properties, geometry, initial conditions, etc. The arithmetic calculations on fuzzy numbers are implemented using fuzzy arithmetic operations, which can be done by two different approaches: (1)interval arithmetic approach;^[3] and (2) the extension principle approach.^[4]

A fuzzy number is equal to a fuzzy interval.^[5] The degree of fuzziness is determined by the a-cut which is also called the fuzzy spread.^{[citation needed]}

References

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^Dijkman, J.G; Haeringen, H van; Lange, S.J de (1983)."Fuzzy numbers".Journal of Mathematical Analysis and Applications.92 (2):301–341.doi:10.1016/0022-247x(83)90253-6.
^Michael Hanss, 2005.Applied Fuzzy Arithmetic, An Introduction with Engineering Applications. Springer,ISBN 3-540-24201-5
^Alavidoost, M.H.; Mosahar Tarimoradi, M.H.; Zarandi, F. (2015). "Fuzzy adaptive genetic algorithm for multi-objective assembly line balancing problems".Applied Soft Computing.34:655–677.doi:10.1016/j.asoc.2015.06.001.
^Gerami Seresht, N.;Fayek, A.R. (2019)."Computational method for fuzzy arithmetic operations on triangular fuzzy numbers by extension principle".International Journal of Approximate Reasoning.106:172–193.doi:10.1016/j.ijar.2019.01.005.S2CID 67868081.
^Kwang Hyung Lee (30 November 2006).First Course on Fuzzy Theory and Applications. Springer Science & Business Media. pp. 130–.ISBN 978-3-540-32366-2. Retrieved23 August 2020.

External links

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Fuzzy Logic Tutorial

v t e Number systems
Sets ofdefinable numbers	Natural numbers ( $\mathbb {N}$ ) Integers ( $\mathbb {Z}$ ) Rational numbers ( $\mathbb {Q}$ ) Constructible numbers Algebraic numbers ( $\mathbb {A}$ ) Closed-form numbers Periods ( ${\mathcal {P}}$ ) Computable numbers Arithmetical numbers Set-theoretically definable numbers Gaussian integers Gaussian rationals Eisenstein integers
Composition algebras	Division algebras:Real numbers ( $\mathbb {R}$ ) Complex numbers ( $\mathbb {C}$ ) Quaternions ( $\mathbb {H}$ ) Octonions ( $\mathbb {O}$ )
Split types	Over $\mathbb {R}$ : Split-complex numbers Split-quaternions Split-octonions Over $\mathbb {C}$ : Bicomplex numbers Biquaternions Bioctonions
Otherhypercomplex	Dual numbers Dual quaternions Dual-complex numbers Hyperbolic quaternions Sedenions ( $\mathbb {S}$ ) Trigintaduonions ( $\mathbb {T}$ ) Split-biquaternions Multicomplex numbers Geometric algebra/Clifford algebra Algebra of physical space Spacetime algebra Plane-based geometric algebra
Infinities andinfinitesimals	Cardinal numbers Extended natural numbers Extended real numbers Projective Extended complex numbers Hyperreal numbers Levi-Civita field Ordinal numbers Supernatural numbers Surreal numbers Superreal numbers
Other types	Irrational numbers Fuzzy numbers Transcendental numbers p-adic numbers (p-adic solenoids) Profinite integers Normal numbers
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