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.