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Di Nola, Antonio; Lettieri, Ada; Perfilieva, Irina; Novák, Vilém

Algebraic analysis of fuzzy systems. (English) Zbl 1110.93012

Fuzzy Sets Syst. 158, No. 1, 1-22 (2007).
Summary: We have developed an algebraic theory, suitable for the analysis of fuzzy systems. We have used the notions of semiring and semimodule, introduced the notion of semilinear space, have given numerous examples of them and defined also the notions of linear dependence and independence. We have shown that the composition operation, which plays an essential role in the analysis of fuzzy systems because of its role in the compositional rule of inference, can be interpreted as a homomorphism between special semimodules. Consequently, this operation is, in a certain sense, a linear operation. This property formally explains why fuzzy systems are attractive for applications.

Cited in 1 Review
Cited in 33 Documents

MSC:

93B25 Algebraic methods
93C42 Fuzzy control/observation systems

Keywords:

fuzzy logic; MV-algebra; semimodule; semilinear space; semiring; fuzzy systems

Software:

LFLC 2000
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Full Text: DOI

References:

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