In this paper we consider some properties of intuitionistic fuzzy preference relations. We pay attention to preservation of intuitionistic fuzzy preference relations by aggregation operations. In particular, we know, that a special kind of aggregation operations (lattice operations) do not preserve intuitionistic fuzzy preference relations. We describe the operations which preserve intuitionist...

In this paper, we study modal operator F α,β in intuitionistic fuzzy subgroup of a group and derive some results. 1. Introduction The idea of intuitionistic fuzzy sets (IFSs) was given by [1, 2] to generalize the notion of fuzzy sets (FSs). Intuitionistic fuzzy modal operator was defined by Atanassov in [3]. The modal operators have been known to be important tools for IFSs where the operators ...

The concepts of fuzzy θ-open (θ-closed)sets and fuzzy θ-closure operator are introduced and discussed in intuitionistic fuzzy topological spaces. As applications of these concepts, certain functions are characterized in terms of intuitionistic fuzzy θ-closure operator.

The Heronian mean provides an aggregation operator that considers the inter-dependent phenomena among the aggregated arguments. Nevertheless, it seems that the existing literatures only consider the HM for aggregating crisp numbers rather than any other types of arguments. In this paper, the HM under interval-valued intuitionistic fuzzy environments is studied. First, a generalized interval-val...

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems for for evaluating the information security risk with intuitionistic fuzzy information. We utilize the induced intuitionistic fuzzy ordered weighted averaging (I-IFOWA) operator and intuitionistic fuzzy weighted averaging (IFWA) operator to aggregate the intuitionistic fuzzy information corresponding to ...

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with hesitant fuzzy linguistic information. Then, motivated by the idea of traditional arithmetic operation, we have developed some aggregation operators for aggregating hesitant fuzzy linguistic information: hesitant fuzzy linguistic weighted average (...

Intuitionistic Fuzzy numbers each of which is characterized by the degree of membership and the degree of non-membership of an element are a very useful means to depict the decision information in the process of decision making. The aim of this article is to investigate the approach to multiple attribute group decision making with intuitionistic trapezoidal fuzzy numbers, some operational laws ...

In this paper, the Multiple Attribute Group Decision Making (MAGDM) problems is based on the attribute weights calculated from completely unknown information using the Maximal Entropy OWA weights. The interval-valued intuitionistic fuzzy ordered weighted averaging (IIFOWA) operator is utilized to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the dec...

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 use the Choquet integrals to define some induced fuzzy number intuitionistic fuzzy aggregating operators, including induced fuzzy number intuitionistic fuzzy correlated averaging(I-FIFCA) operator, induced fuzzy number intuitionistic fuzzy correlated geometric(I-FIFCG) operator. We also establish various properties of these operators, such as commutativity, idempotency and mon...