On a new kind of ordered fuzzy group

Abstract

This paper aims to further study the new kind of ordered fuzzy group named ordered L-group, which is put forward in literature [20]. Some algebraic properties of ordered L-groups, such as the relationship between elements, the equivalent characterizations and the products of these groups are discussed. Following that, the properties of substructures including characterization theorems, the convexity, the products of (normal) subgroups maintain the original substructure, along with the properties of ordered L-group homomorphisms are explored. The discussion of ordered fuzzy groups in this paper is from the perspective of fuzzy binary operation, which is different from the commonly method that just discuss the fuzzification of substructures in the research of fuzzy algebra. It can better reflect the essence of fuzzy groups logically just like that of classical groups.</jats:p