Generator of Fuzzy Implications

Abstract

In this research paper, a generator of fuzzy methods based on theorems and axioms of fuzzy logic is derived, analyzed and applied. The family presented generates fuzzy implications according to the value of a selected parameter. The obtained fuzzy implications should satisfy a number of axioms, and the conditions of satisfying the maximum number of axioms are denoted. New theorems are stated and proven based on the rule that the fuzzy function of fuzzy implication, which is strong, leads to fuzzy negation. In this work, the data taken were fuzzified for the application of the new formulae. The fuzzification of the data was undertaken using four kinds of membership degree functions. The new fuzzy functions were compared based on the results obtained after a number of repetitions. The new proposed methodology presents a new family of fuzzy implications, and also an algorithm is shown that produces fuzzy implications so as to be able to select the optimal method of the generator according to the value of a free parameter.