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...

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in amedical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised...

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...

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...

It is firstly proved that the multi-input-single-output (MISO) fuzzy systems based on interval-valued $R$- and $S$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  A formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

On the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine...