On solvability of systems of partial fuzzy relational equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA230259L" target="_blank" >RIV/61988987:17610/22:A230259L - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0165011422002937" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011422002937</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2022.06.014" target="_blank" >10.1016/j.fss.2022.06.014</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On solvability of systems of partial fuzzy relational equations

Popis výsledku v původním jazyce

Systems of fuzzy relational equations belong to key mathematical problems related to the correct behavior of fuzzy systems, especially of fuzzy inference systems. Indeed, if we find a fuzzy relation that solves a given system of fuzzy relational equations, we found a model of a fuzzy rule base related to the given system that will behave correctly in the sense that it will preserve the fundamental modus ponens property. This problem with numerous results becomes absolutely unexplored as soon as we allow partiality in the system. Partial fuzzy sets have only partially defined membership degrees, i.e., for some elements, the membership degree is undefined, i.e., partial propositions have only partially defined truth-values. There are many origins from which we may obtain propositions with undefined truth-values, e.g., non-denoting or irrelevant terms, inconsistent (both true and false) propositions, or truth-values are simply unknown. Partial logics belong to classical topics in logic so, the extensions to partial fuzzy logic in recent years were not surprising. However, we should not dare to deal with partial fuzzy sets in fuzzy systems without any guarantee of the preservation of fundamental properties such as modus ponens. This article is focusing on filling this gap.

Název v anglickém jazyce

On solvability of systems of partial fuzzy relational equations

Popis výsledku anglicky

Systems of fuzzy relational equations belong to key mathematical problems related to the correct behavior of fuzzy systems, especially of fuzzy inference systems. Indeed, if we find a fuzzy relation that solves a given system of fuzzy relational equations, we found a model of a fuzzy rule base related to the given system that will behave correctly in the sense that it will preserve the fundamental modus ponens property. This problem with numerous results becomes absolutely unexplored as soon as we allow partiality in the system. Partial fuzzy sets have only partially defined membership degrees, i.e., for some elements, the membership degree is undefined, i.e., partial propositions have only partially defined truth-values. There are many origins from which we may obtain propositions with undefined truth-values, e.g., non-denoting or irrelevant terms, inconsistent (both true and false) propositions, or truth-values are simply unknown. Partial logics belong to classical topics in logic so, the extensions to partial fuzzy logic in recent years were not surprising. However, we should not dare to deal with partial fuzzy sets in fuzzy systems without any guarantee of the preservation of fundamental properties such as modus ponens. This article is focusing on filling this gap.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA20-07851S" target="_blank" >GA20-07851S: Fuzzy relační struktury v přibližném usuzování</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

FUZZY SET SYST

ISSN

0165-0114

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

December

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

31

Strana od-do

87-117

Kód UT WoS článku

000884420700005

EID výsledku v databázi Scopus

2-s2.0-85133704927