In crisp production inventory problem, let q, a, b, d, R and r be the quantity produced per cycle, the holding cost, production cost, production quantity per day, the total demand quantity and the demand quantity per day, respectively. We consider three fuzzification methods. Firstly, we fuzzify q, a, b, d, R and r to triangular fuzzy numbers. Secondly, we fuzzify d and r to triangular fuzzy nu...

The purpose of this study is to introduce a new regression model, based on the least squares method, when the available data of both explanatory variable(s) and response variable are interval-valued fuzzy (IVF) numbers. The proposed method is based on a new metric on the space of IVF numbers, which is an extended version of the signed distance introduced by Yao and Wu (2000). In order to evalua...

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...