The fuzzy extension principle has been widely used to extend the domain of mathematical functions and relations from elements of a referential set to fuzzy subsets of that referential set. However, there are restrictions associated with the fuzzy extension principle. This paper addresses the question how restricted is the family of “fuzzy set to fuzzy set mappings” obtained by the fuzzy extensi...

Lattice-valued up-sets and down-sets of a poset are investigated under the cutworthy approach. It is proved that the collections of all lattice valued up-sets and down-sets of a given poset are complete lattices under fuzzy inclusion. Properties of these are investigated. For a given collection of crisp up-sets of a poset, necessary and sufficient conditions are given under which the family rep...

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 aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...

In this paper, we introduce the concept of ε–generalized fuzzy filters (ideals) and δ–multiplication of fuzzy set μ, of BE–algebras and their basic properties are investigated. c ©2013 World Academic Press, UK. All rights reserved.

Lane changing manoeuvres of heavy vehicles have significant influence on surrounding traffic characteristics due to the physical effects that the heavy vehicles impose on surrounding vehicles. These effects are the result of heavy vehicles’ length, size, weight and the limitations in their manoeuvrability. Due to the importance of heavy vehicle lane changing manoeuvres, this paper presents an e...

In this paper, we start from this idea that the set of nonzero fuzzy subsets of a fuzzy hyperalgebra can be organized naturally as a universal algebra, and constructing the term functions over this algebra we can deduce some results on fuzzy hyperalgebras from some of the very known properties of the term functions of a universal algebra. Also, we present the form of the generated subfuzzy hype...

In this work, by Zadeh’s extension principle, we extend representable uninorms and their fuzzy implications (coimplications) to type-2 fuzzy sets. Emphatically, we investigate in which algebras of fuzzy truth values the extended operations are type-2 uninorms and type-2 fuzzy implications (coimplications), respectively.

This paper discusses fuzzification of crisp domains into fuzzy classes providing fuzzy domains. Relationship between two fuzzy domains, Xi and Xj , is represented by a matrix, wij . If Xi and Xj have n and m elements of fuzzy data, respectively, then wij is n × m matrix. Our primary goal in this paper is to generate and provide some formulas for predicting interval probability in the relation t...