Generalization of Fuzzy Connectives

Abstract

This paper is centered around the creation of new fuzzy connectives using automorphism functions. The fuzzy connectives theory has been implemented in many problems and fields. In particular, the N-negations, t-norms, S-conorms and I-implications concepts played crucial roles in forming the theory and applications of the fuzzy sets. Thus far, there are multiple strategies for producing fuzzy connectives. The purpose of this paper is to provide a new strategy that is more flexible and fast in comparison with the rest. In order to create this method, automorphism and additive generator functions were utilized. The general formulas created with this method can provide new fuzzy connectives. The main conclusion is that new fuzzy connectives can be created faster and with more flexibility with our strategy.

Keywords

• fuzzy connectives
• fuzzy negations
• t-norms
• S-conorms
• fuzzy implications
• automorphisms