We propose a method for ranking alternatives represented by Atanassov’s intuitionistic fuzzy sets (A-IFSs) which takes into account not only the amount of information related to an alternative (expressed by a distance from the ideal positive alternative) but also the reliability of information (how sure the information is). We stress (like in our previous papers) that taking into account all th...

In this paper, we introduce four kinds of rough approximations for a given intuitionistic fuzzy set.

As an extension of the intuitionistic fuzzy set, intuitionistic trapezoidal fuzzy set is an invaluable mathematical theory to express uncertain phenomenon in our real word. In this article, the aggregation methods of the intuitionistic trapezoidal fuzzy information are chief researched. Firstly, the generalized aggregation operator is introduced for aggregating intuitionistic trapezoidal fuzzy ...

In this paper, we consider the intuitionistic fuzzification of the concept of p-ideals in BCI-algebras and investigate some of their properties. Intuitionistic fuzzy p-ideals are connected with intuitionistic fuzzy ideals and intuitionistic fuzzy subalgebras. Moreover, intuitionistic fuzzy p-ideals are characterized using level subsets, homomorphic pre-images, and intuitionistic fuzzy ideal ext...

This paper is a continuation of our previous works on geometric similarity measures between Atanassov’s intuitionistic fuzzy sets (A-IFSs for short). We consider some traps of the straightforward approach in the case of A-ISs while similarity is understood as a dual concept of a distance. The difficulties are a result of, first, the symmetry of the three terms (the membership, nonmembership and...

With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of fuzzy number intuitionistic fuzzy numbers, a new group decision making analysis method is developed. Firstly, some operational laws of fuzzy number intuitionistic fuzzy numbers, score function and ac...

In this work we present a method for constructing an Atanassov’s intuitionistic fuzzy preference relation from a fuzzy preference relation that takes into account the ignorance of the expert when evaluating the preferences in the latter. Moreover, we present two algorithms that make use of this method for extending the weighted voting method to the Atanassov’s intuitionistic fuzzy setting in de...

Abstract. In this paper, intuitionistic fuzzy h-bi-ideals and intuitionistic fuzzy hquasi-ideals of hemirings are studied and some related properties are investigated. We characterize fully idempotent hemirings by the properties of their intuitionistic fuzzy h-ideals.We also characterize h-hemiregularity, h-intra-hemiregularity and h-quasi-hemiregularity in hemirings by the properties of their ...

Taking into account the notion of BL-general fuzzy automaton, in the present study we define the notation of BL-intuitionistic general L-fuzzy automaton and I-bisimulation for BL-intuitionistic general L-fuzzy automaton.Then for a given BL-intuitionistic general L-fuzzy automaton, we obtain the greatest I-bisimulation. According to this notion, we give the structure of quotient BL-intuiti...

Intuitionistic fuzzy logic IF was introduced by Takeuti and Titani. This logic coincides with the first-order Gödel logic based on the real unit interval [0, 1] as set of truth-values. We present a natural deduction system NIF for IF . NIF is defined by suitably translating a first-order extension of Avron’s hypersequent calculus for Gödel logic. Soundness, completeness and normal form theorems...