Interval valued $(\in,\ivq)$-fuzzy filters of pseudo $BL$-algebras

TL;DR

This paper introduces and studies a new class of interval valued fuzzy filters in pseudo $BL$-algebras, exploring their properties, characterizations, and relationships, with applications to fuzzy implicative filters and Lukasiewicz logic.

Contribution

It proposes the concept of quasi-coincidence for fuzzy interval values and develops the theory of interval valued $( in, vq)$-fuzzy filters in pseudo $BL$-algebras, including characterization theorems and implications.

Findings

Characterization theorems for the new fuzzy filters

Relationships among different types of fuzzy filters

Application to implication-based fuzzy implicative filters

Abstract

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued $(\in,\ivq)$-fuzzy filters of pseudo $BL$-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these generalized interval valued fuzzy filters of pseudo $BL$-algebras is considered. Finally, we consider the concept of implication-based interval valued fuzzy implicative filters of pseudo $BL$-algebras, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.