Geodesic
Fuzzy Algebraic Systems
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 3, pp. 76-93

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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
Mots-clés : interval valuation. 
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     author = {D. E. Palchunov and G. E. Yakhyaeva},
     title = {Fuzzy {Algebraic} {Systems}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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     url = {http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a5/}
}
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D. E. Palchunov; G. E. Yakhyaeva. Fuzzy Algebraic Systems. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 3, pp. 76-93. http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a5/