ranking fuzzy numbers plays a very important role in linguistic decision making and other fuzzy application systems. in spite of many ranking methods, no one can rank fuzzy numbers with human intuition consistently in all cases. shortcoming are found in some of the convenient methods for ranking triangular fuzzy numbers such as the coefficient of variation (cv index), distance between fuzzy set...

Let D be a finite and simple digraph with the vertex set V (D), and let f : V (D) → {−1, 1} be a two-valued function. If∑ x∈N[v] f(x) ≥ 1 for each v ∈ V (D), where N[v] consists of v and all vertices of D from which arcs go into v, then f is a signed dominating function on D. The sum f(V (D)) is called the weight w(f) of f . The minimum of weights w(f), taken over all signed dominating function...

In this paper, we first use a fuzzy preference relation with a membership function representing preference degree forcomparing two interval-valued fuzzy numbers and then utilize a relative preference relation improved from the fuzzypreference relation to rank a set of interval-valued fuzzy numbers. Since the fuzzy preference relation is a total orderingrelation that satisfies reciprocal and tra...

In this Chapter, invoking the notion of signed fuzzy number valued measures on the fuzzy set, we attempt to study the Lebesgue decompositions of a signed fuzzy number valued measures. We introduce in this Chapter a new notion called singular complements to the domain of fuzzy number valued measures and derive some consequential properties. The contents of this chapter form the material of the p...

in this paper, we investigate the general fuzzy linear system of equations.  the  main aim of this paper is based on the embedding approach. we find the necessary and sufficient conditions for the existence of fuzzy solution of the mentioned systems.  finally, numerical examples are presented to more illustration of the proposed model.

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

ranking fuzzy numbers plays a very important role in decision making and some other fuzzy application systems. many different methods have been proposed to deal with ranking fuzzy numbers. constructing ranking indexes based on the centroid of fuzzy numbers is an important case. but some weaknesses are found in these indexes. the purpose of this paper is to give a new ranking index to rank vario...

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

Let $D$ be a finite simple digraph with vertex set $V(D)$ and arcset $A(D)$. A twin signed total Roman dominating function (TSTRDF) on thedigraph $D$ is a function $f:V(D)rightarrow{-1,1,2}$ satisfyingthe conditions that (i) $sum_{xin N^-(v)}f(x)ge 1$ and$sum_{xin N^+(v)}f(x)ge 1$ for each $vin V(D)$, where $N^-(v)$(resp. $N^+(v)$) consists of all in-neighbors (resp.out-neighbors) of $v$, and (...