In this paper, we present the induced generalized intuitionistic fuzzy ordered weighted averaging (IGIFOWA) operator. It is a new aggregation operator that generalized the IFOWA operator, including all the characteristics of both the generalized IFOWA and the induced IFOWA operators. It provides a very general formulation that includes as special cases a wide range of aggregation operators for ...

First, we prove that the set of intuitionistic fuzzy congruences on a semigroup satisfying the particular condition is a modular lattice [Theorem 2.9]. Secondly, we prove that the set of all intuitionistic fuzzy congruences on a regular semigroup contained in (χH, χHc) forms a modular lattice [Proposition 3.5]. And also we show that the set of all intuitionistic fuzzy idempotent separating cong...

We first propose a series of similarity measures for intuitionistic fuzzy values (IFVs) based on the intuitionistic fuzzy operators (Atanassov 1995). The parameters in the proposed similarity measures can control the degree of membership and the degree of non-membership of an IFV, which can reflect the decision maker’s risk preference. Moreover, we can obtain some known similarity measures when...

The problem of evaluating the building engineering quality with intuitionistic fuzzy information is the multiple attribute group decision making (MAGDM) problems. In this paper, we investigate the multiple attribute group decision making (MAGDM) problems for evaluating the building engineering quality with intuitionistic fuzzy information. We utilize the induced intuitionistic fuzzy ordered wei...

During years of research, there have been defined 153 intuitionistic fuzzy implications. In the paper, it is checked which of these implications satisfy which axioms of the intuitionistic logic, whether as (classical) tautologies or as intuitionistic fuzzy tautologies. Some open problems, related to the operations of intuitionistic fuzzy propositional calculus, are formulated.

Paraconsistent intuitionistic fuzzy set is an extension of intuitionistic fuzzy set or interval-valued fuzzy set. It relaxes the requirement that t + f ≤ 1, where t is grade of truth-membership and f is grade of false-membership. In paraconsistent intuitionistic fuzzy set, t, f ∈ [0, 1], 0 ≤ t + f ≤ 2. In this paper, we present a generalization of the relational model of data based on paraconsi...

In the present paper, based on the concept of fuzzy entropy, an exponential intuitionistic fuzzy entropy measure is proposed in the setting of Atanassov’s intuitionistic fuzzy set theory. This measure is a generalized version of exponential fuzzy entropy proposed by Pal and Pal. A connection between exponential fuzzy entropy and exponential intuitionistic fuzzy entropy is also established. Some...

Intuitionistic fuzzy relations on finite universes can be represent by intuitionistic fuzzy matrices and the limiting behavior of the power matrices depends on the algebraic operation employed on the matrices. In this paper, the power of intuitionistic fuzzy matrices with maxarithmetic mean-minarithmetic mean operation have been studied. Here it is shown that the power of intuitionistic fuzzy m...

Park et al. (2011) introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, the concept of generalized intuitionistic fuzzy soft equality is introduced and some related properties are derived. It is proved that generalized intuitionistic fuzzy soft equality is congruence relation with res...

We establish relationships between the set of trapezoidal intuitionistic fuzzy numbers and the set of interval-valued trapezoidal fuzzy numbers and, on the other hand, between the set of triangular intuitionistic fuzzy numbers and the set of triangular fuzzy numbers. Based on these main results of the paper, the methods or procedures elaborated for interval-valued trapezoidal or triangular fuzz...