Based on the Choquet integral and the generalized Shapley function, two new induced Atanassov’s interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov’s interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov’s interval-val...

As an special intuitionistic fuzzy set defined on the real number set, triangular intuitionistic fuzzy number (TIFN) is a fundamental tool for quantifying an ill-known quantity. In order to model the decision maker's overall preference with mandatory requirements, it is necessary to develop some Bonferroni harmonic mean operators for TIFNs which can be used to effectively intergrate the informa...

A fuzzy number intuitionistic fuzzy set (FNIFS) is a generalization of intuitionistic fuzzy set. The fundamental characteristic of FNIFS is that the values of its membership function and non-membership function are trigonometric fuzzy numbers rather than exact numbers. In this paper, we define some operational laws of fuzzy number intuitionistic fuzzy numbers, and, based on these operational la...

Trapezoidal intuitionistic fuzzy numbers (TrIFNs) express abundant and flexible information in a suitable manner and  are very useful to depict the decision information in the procedure of decision making. In this paper, some new aggregation operators, such as, trapezoidal intuitionistic fuzzy weighted power harmonic mean (TrIFWPHM) operator, trapezoidal intuitionistic fuzzy ordered weighted po...

The notion of intuitionistic fuzzy ideals with thresholds of an ordered semigroup is considered and some of its properties are given. An embedding theorem of the set of all intuitionistic fuzzy ideals with thresholds is presented and the homomorphic images and inverse images of intuitionistic fuzzy ideals with thresholds are studied too. 2010 Mathematics Subject Classification: 06F05

In this paper we define intuitionistic fuzzy quasi-ideals of ordered semigroups. The main result of the paper is a characterization of quasi-ideals in terms of intuitionistic fuzzy quasi-ideals. We also characterize left simple, right simple, and completely regular ordered semigroups in terms of intuitionistic fuzzy quasi-ideals. We study the decomposition of left and right simple ordered semig...

Intuitionistic fuzzy information aggregation plays an important part in Atanassov’s intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we first introduce some operations on intuitionistic fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc., and further develop some new ...

The objective of this work is to present a triangular interval type-2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws. Furthermore, based on these operators, an approach to mul...

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...

The dominance–based rough set approach plays an important role in the development of the rough set theory. It can be used to express the inconsistencies coming from consideration of the preference–ordered domains of the attributes. The purpose of this paper is to further generalize the dominance–based rough set model to fuzzy environment. The constructive approach is used to define the intuitio...