EXTENDED LATTICE-ORDERED STRUCTURES FOR L-FUZZY SETS AND L-FUZZY NUMBERS

Abstract

An L-fuzzy set A is a mapping of a set X into another set L. The set L is called the true set of A and X is called the universe of A. It has been discussed that a better structure for the truth set L is a complete lattice-ordered monoid. Then operations on L can be directly extended to operate on L(X) and a complete lattice-ordered monoid can be obtained. In this paper, we consider operations on L(X) which are extended from operations on X by the extension principle. We will obtain a similar complete lattice-ordered monoid constituted by extended operations. Moreover, a notion of L-fuzzy numbers is proposed. Then, extended operations on L-fuzzy numbers are discussed and a distributively lattice-ordered structure is developed for L-fuzzy numbers.