The interval-valued intuitionistic fuzzy set (IVIFS) which is an extension of the Atanassov’s intuitionistic fuzzy set is a powerful tool for modeling real life decision making problems. In this paper, we propose the emph{generalized interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral} (GIVIFHGSCI) and the emph{interval-valued intuitionistic fuzzy Hamacher general...

The aim of this paper is investigate the notion of a generalized interval valued intuitionistic fuzzy number (GIVIFN), which extends the interval valuedintuitionistic fuzzy number. Firstly, the concept of GIVIFNBs is introduced.Arithmetic operations and cut sets over GIVIFNBBs are investigated. Then the values and ambiguities of the membership degree and the non-membership degree and the value ...

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...

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...

* Correspondence author. Abstract The fuzzy multi-attribute decision making problems are investigated, in which the attribute values are given as intervalvalued intuitionistic fuzzy numbers and the attribute weight information is incomplete. Some operational laws of interval-valued intuitionistic fuzzy numbers, score function and accuracy function of interval-valued intuitionistic fuzzy numbers...

in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...

Interval-valued intuitionistic fuzzy number uses membership degree and non-member ship degree to express a decision-maker’s hesitation, which make decision-maker express his/her opinion in uncertainty decision-making environment easily. The comparison between some intervalvalued intuitionistic fuzzy numbers can not be undertaken because of its limitation. In application such as weak consistency...

In this paper, we propose a method to calculate the correlation coefficient of generalized intuitionistic fuzzy sets by means of "centroid". The value which obtained from this method tell us the strength of relationship between the generalized intuitionistic fuzzy sets [11] and the whether the generalized intuitionistic fuzzy sets are positively or negatively related. This method looks better t...

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...

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...