In this paper, the researchers proposed a new method to rank fuzzy numbers by median value of fuzzy numbers. The median value can be used as a crisp approximation with respect to a fuzzy quantity. Therefore, a method for ordering the fuzzy numbers is defined accordingly. This method can effectively rank various fuzzy numbers, their images and overcome the shortcomings of the previous techniques.

Images of fuzzy relations provide powerful access to fuzzifications of properties of and/or relationships between fuzzy sets. As an important example, images of fuzzy orderings canonically lead to a concept of ordering of fuzzy sets. This contribution studies in which way the partial (i.e. componentwise) monotonicity of an n-ary mapping transfers to its extension to fuzzy sets.

Some special general aggregation operators are given with respect to different ordering relations on the set of all fuzzy subsets of a universe X, F(X ). The proof that pointwise extensions of aggregation operators are general aggregation operators with respect to the ordering fuzzy subset (⊆F ) is given. Also, we have proved that min–extensions of aggregation operators are general aggregation ...

Abstract This paper suggests a fuzzy MCDM (multiple criteria decision-making) approach, where ratings of alternatives versus criteria and weights of criteria are assessed in fuzzy numbers or linguistic values represented by fuzzy numbers. Criteria are classified into cost and benefit ones. In the proposed method, the ratings assigned by decision makers to each alternative versus each criterion ...

Recently, a novel hesitant fuzzy set (HFS) ranking technique based on the idea of lexicographical ordering is proposed and an example is presented to demonstrate that the proposed ranking method is invariant with multiple occurrences of any element of a hesitant fuzzy element (HFE). In this paper, we show by examples that the HFS lexicographical ordering method is sometimes invalid, and a modif...

in this paper, we propose the least-squares method for computing the positive solution of a m  n fully fuzzy linear system (ffls) of equations, where m > n, based on kaman's arithmetic operations on fuzzy numbers that introduced in [18]. first, we consider all elements of coecient matrix are non-negative or non-positive. also, we obtain 1-cut of the fuzzy number vector solution of the n...

We propose three methods for obtaining solutions in fuzzy constraint networks and study their application to the problem of ordering fuzzy numbers. The techniques proposed may be classified as defuzzification functions which are applicable to any set of mutually dependent fuzzy numbers in which the dependence relationships are represented by means of metric constraints. We suggest the use of th...

in this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group g and give four equivalent conditions each ofwhich characterizes this relation. we demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. moreover, we study the behavior of these equivalence classes under theaction of a...

The purpose of this paper is to introduce a general framework for comparing fuzzy sets with respect to fuzzy orderings in a gradual way. This approach is applicable to fuzzy subsets of any kind of universe for which a fuzzy ordering, no matter whether linear or not, is known.