New measures of similarity based on fuzzy implications

Abstract

Abstract. An important problem in fuzzy theory is how to determine if two elements are similar or not. There are different definitions to measure how similar or close are elements. One of the most important concepts in this context is that one of similarity. This paper aims at studying fuzzy similarities defined by fuzzy implications, logical equivalences expressed by fuzzy bi-implication operators and aggregation operators. We propose a definition of proximity between two fuzzy finite sets by using the previous operators and we study when this type of operators satisfy the formal definition of similarity.