Possibilistic mean based defuzzification for fuzzy expert systems and fuzzy control—LSD for general fuzzy sets

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15210%2F24%3A73620457" target="_blank" >RIV/61989592:15210/24:73620457 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1016/j.cam.2023.115663" target="_blank" >https://doi.org/10.1016/j.cam.2023.115663</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cam.2023.115663" target="_blank" >10.1016/j.cam.2023.115663</a>

Result language

angličtina

Original language name

Possibilistic mean based defuzzification for fuzzy expert systems and fuzzy control—LSD for general fuzzy sets

Original language description

This paper introduces a new defuzzification technique derived as a generalization of the formula for the calculation of possibilistic mean originally proposed by Carlsson and Fullér in 2001 for fuzzy numbers. Unlike the possibilistic mean, the generalized formulation allows also for the defuzzification of subnormal convex fuzzy sets and also for non-convex fuzzy sets (e.g. the outputs of Mamdani- or Larsen-type fuzzy inference). The Luukka–Stoklasa–Collan transformation introduced in 2019 is applied to generalize the possibilistic mean formula. Using this transformation an algorithm for the calculation of the possibilistic-mean-based defuzzification of a general fuzzy set with a continuous membership function on the given interval is proposed. This way the Luukka–Stoklasa Defuzzification (LSD) inspired by the possibilistic mean construction is introduced - a defuzzification that can be calculated also for fuzzy sets in general (subnormal, non-convex), not only for fuzzy numbers. As such LSD is applicable also in fuzzy expert systems and fuzzy control settings where the outputs of the inference systems can be expected to be represented by subnormal and non-convex fuzzy sets. Fast-computation formulas for LSD of piece-wise linear fuzzy sets are also provided. The applicability of LSD in the ranking of fuzzy numbers and its ability to distinguish between fuzzy numbers where other frequently used defuzzification methods do not is shown. Two more case studies are presented where LSD outperforms the chosen frequently used defuzzification methods: a fuzzy expert system for inventory control and a fuzzy cruise controller problem.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

50202 - Applied Economics, Econometrics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Computational and Applied Mathematics

ISSN

0377-0427

e-ISSN

1879-1778

Volume of the periodical

441

Issue of the periodical within the volume

15 May 2024

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

20

Pages from-to

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UT code for WoS article

001112310000001

EID of the result in the Scopus database

2-s2.0-85176226785