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{...

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 Multiple Attribute Group Decision Making (MAGDM) problems are investigated in which all the information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices, and the information about attribute weights is partially known. Three different models are utilized for calculating the completely unknown attribute weights which are then used for aggr...

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{...

In this paper, associated with dominance relation, lattice theory and intuitionistic fuzzy sets theory, the lattice-valued information systems with interval-valued intuitionistic fuzzy decision are proposed and some of its properties are investigated carefully. And, an approach to knowledge reduction based on discernibility matrix in consistent latticevalued information systems with interval-va...

In this paper, the notions of (T, S)-composition matrix and (T, S)interval-valued intuitionistic fuzzy equivalence matrix are introduced where (T, S) is a dual pair of triangular module. They are the generalization of composition matrix and interval-valued intuitionistic fuzzy equivalence matrix. Furthermore, their properties and characterizations are presented. Then a new method based on α̃−mat...

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 relationship between the intuitionistic fuzzy sets and the algebraic hyperstructures is described in this paper. The concept of the quasi-coincidence of an intuitionistic fuzzy interval valued with an interval-valued intuitionistic fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of an intuitionistic fuzzy point in intuitionistic fuzzy sets. By using thi...

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 paper is to define the productoperation on a family of interval valued events and the notion ofjoint interval valued observable. We show the connection betweenproduct operations for interval valued events and intuitionisticfuzzy events, too. We display the relation between joint intervalvalued observable and joint intuitionistic fuzzy observable. We...