The notion of the interval-valued intuitionistic fuzzy set (IVIFS) is a generalization of that of the Atanassov’s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVIFSs. These operators are not monotone with respec...

In this paper, we define some results on generalized interval-valued intuitionistic fuzzy sets (GIVIFSs). In fact, all interval-valued intuitionistic fuzzy sets (IVIFSs) are GIVIFSs but all GIVIFSs are not IVIFSs. We define two composite relations, four types of reflexivity and irreflexivity of GIVIFSs with some of their properties. We define generalized interval-valued intuitionistic fuzzy rel...

Szmidt and Kacprzyk (Lecture Notes in Artificial Intelligence 3070:388– 393, 2004a) introduced a similarity measure, which takes into account not only a pure distance between intuitionistic fuzzy sets but also examines if the compared values are more similar or more dissimilar to each other. By analyzing this similarity measure, we find it somewhat inconvenient in some cases, and thus we develo...

In this paper, we have introduced the concept of Q-single value neutrosophic soft set, multi Qsingle valued neutrosophic set and defined some basic results and related properties. We have also defined the idea of Q-single valued neutrosophic soft set, which is the genralizations of Q-fuzzy set, Q-intuitionistic fuzzy set, multi Q-fuzzy set , Multi Q-intuitionistic fuzzy set, Q-fuzzy soft set, Q...

Cubic intuitionistic fuzzy (CIF) set is the hybrid set which can contain much more information to express an interval-valued intuitionistic fuzzy set and an intuitionistic fuzzy set simultaneously for handling the uncertainties in the data. Unfortunately, there has been no research on the aggregation operators on CIF sets so far. Since an aggregation operator is an important mathematical tool i...

Due to the increasing competition of globalization, selection of the most appropriate supplier is one of the key factors for asupply chain management’s success. Due to conflicting evaluations and insufficient information about the criteria, Intuitionisticfuzzy sets (IFSs) considered as animpressive tool and utilized to specify the relative importance of the criteria. The aim of this paper is to...

Research on soft set based decision making has received much attention in recent years. Feng et al. presented an adjustable approach to fuzzy soft sets based decision making by using level soft set, and subsequently extended the approach to interval-valued fuzzy soft set based decision making. Jiang et al. generalize the approach to solve intuitionistic fuzzy soft sets based decision making. In...

In this paper, the notion of an interval valued intuitionistic fuzzy subsemiring (ideal) of a semiring with respect to t−norm T and s−norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on semirings, new interval valued intuitionistic (S, T )−fuzzy subsemirings (ideals) ...

Abstract— This paper develops a solution procedure of multi-objective intuitionistic fuzzy optimization to solve a non-linear model with inexact co-efficient and resources. Interval approximation method is used here to convert the imprecise co-efficient which is a triangular fuzzy number to an interval number. We transform this interval number to a parametric interval valued functional form and...