Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decision-making preference. Hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (G-GIVIFSS) which conta...

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...

We investigate multiple attribute group decision making (MAGDM) problems with arguments taking the form of interval-valued intuitionistic fuzzy numbers. In order to relieve influence of unfair arguments, a Gaussian distribution-based argument-dependent weighting method and a hybrid support-function-based argument-dependent weighting method are devised by, respectively, measuring support degrees...

interval-valued intuitionistic fuzzy sets (ivifss) are widely used to handle uncertainty and imprecision in decision making. however, in more complicated environment, it is difficult to express the uncertain information by an ivifs with considering the decision-making preference. hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (g-givifss) which conta...

The aim of this manuscript is to present a new concept of hesitant q-rung orthopair fuzzy sets (Hq-ROFSs) by combining the concept of the q-ROFSs as well as Hesitant fuzzy sets. The proposed concept is the generalization of the fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and Pythagorean fuzzy sets as well as intuitionistic hesitant fuzzy sets (IHFSs) and hesitant Pythagorean fuz...

Intuitionistic fuzzy sets (IFSs) have attracted more and more scholars’ attention due to their powerfulness in expressing vagueness and uncertainty. In the course of decision making with IFSs, aggregation operators play a very important role since they can be used to synthesize multidimensional evaluation values represented as intuitionistic fuzzy values into collective values. This paper propo...

In this paper, we define the notion of a bipolar general fuzzy automaton, then we construct some closure operators on the set of states of a bipolar general fuzzy automaton. Also, we construct some topologies on the set of states of a bipolar general fuzzy automaton. Then we obtain some relationships between them.

The idea of bipolar complex fuzzy (BCF) sets, as a genuine modification both sets and gives massive valuable framework for representing evaluating ambiguous information. In intelligence decision making based on BCF it is critical dilemma to compare or rank positive negative membership grades. this framework, we deliberated various techniques aggregating the collection information into singleton...

In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define extended union, intersection of two bipolar fuzzy soft set. We also give an application of bipolar fuzzy soft set into decision making problem. We give a general algorithm...