On solvability of systems of partial fuzzy relational equations

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
On solvability of systems of partial fuzzy relational equations
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA20-07851S" target="_blank" >GA20-07851S: Fuzzy relational structures in approximate reasoning</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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