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JOURNALS // Siberian Journal of Pure and Applied Mathematics // Archive

Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2010 Volume 10, Issue 3, Pages 76–93 (Mi vngu51)

This article is cited in 2 papers

Fuzzy Algebraic Systems

D. E. Palchunova, G. E. Yakhyaevab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: In the paper the problem of extrapolation of partial information on fuzzy truth values of first order formulas on an algebraic system is investigated. A semantic approach to fuzzy logic is presented. This approach is based on construction of fuzzy models and generalized fuzzy models with the help of fuzzyfication of Boolean-valued models.
The operation of product of Boolean-valued models is introduced. Properties of product of Boolean-valued models with a finite Boolean algebra are studied.
Generalized fuzzy models generated by interval valuations are investigated. It is proved that if a generalized fuzzy model is generated by an interval valuation of some set of sentences then the truth value of each sentence on this generalized fuzzy model is an interval.

Keywords: fuzzy logics, Fuzzy algebraic system, fuzzy model, Boolean-valued model, fuzzification of Boolean-valued model, generalized fuzzy model, interval valuation.

UDC: 004.82+510.64

Received: 19.12.2009



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