Additive-multiplicative generator of logical connectives in fuzzy systems

Abstract

The basic sets of logical connectives of fuzzy systems are analyzed. It is shown that triangular norms are the basis for constructing the operators for logical connectives. Two main classes are distinguished – conditional and algebraic. The known generators of operators of triangular norms are described. It is shown that they have limited functional characteristics. To expand them, a parameterized additive-multiplicative generator is proposed for constructing the logical operators of fuzzy systems. It is proved that this generator satisfies the requirements of the necessary axioms. Examples of construction of fuzzy system operators, which are generally known, are presented. The introduction of parameterized coefficient provides the obtaining of triangular norms of a new type.