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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50202 - Applied Economics, Econometrics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Journal of Computational and Applied Mathematics

ISSN

0377-0427

e-ISSN

1879-1778

Svazek periodika

441

Číslo periodika v rámci svazku

15 May 2024

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

20

Strana od-do

—

Kód UT WoS článku

001112310000001

EID výsledku v databázi Scopus

2-s2.0-85176226785