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Selected topics in theory and applications of fuzzy relational equations. (English) Zbl 0559.04003

Large scale systems: theory and applications, Proc. IFAC/IFORS Symp., Warsaw/Pol. 1983, IFAC Proc. Ser. 10, 247-252 (1984).
[For the entire collection see Zbl 0547.00057.]
This paper describes the main theoretical and applicational aspects of the fuzzy relation equations. All the theorems are enunciated without proofs, which already appeared in the papers referred to. The authors recall the methods of solution of fuzzy equations with triangular norms introduced by W. Pedrycz [Busefal 11, 24-32 (1982; Zbl 0498.04004)], the methods of finding the boolean solutions of a fuzzy equation given by A. Di Nola and S. Sessa [Busefal 11, 14-23 (1982; Zbl 0516.94034)] and the solutions with minimal entropy measure given by the authors [Busefal 12, 60-71 (1983; Zbl 0525.04003)]. Further it is shown that problems of analysis and synthesis of nondeterministic systems and decision-making processes can be modelled via fuzzy systems. For related topics, see the papers of E. Czogała and W. Pedrycz [Fuzzy Sets Syst. 6, 73-83 (1981; Zbl 0473.93070) and ibid. 7, 257-273 (1982; Zbl 0506.93039)] and W. Pedrycz [Int. J. Control 34, 403-421 (1981; Zbl 0476.93011) and Fuzzy Sets Syst. 10, 185-201 (1983; Zbl 0525.04004)].

MSC:

03E20 Other classical set theory (including functions, relations, and set algebra)
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
08A02 Relational systems, laws of composition
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
93A99 General systems theory
91B06 Decision theory