Abstract How to solve a multi-criterion decision-making (MCDM) problem with linguistic interval-valued intuitionistic fuzzy numbers (LIVIFNs) effectively is an important research topic. So far, number of methods for solving this have been presented within the academia. Each these can work well in specific situation. But they could produce undesirable results when information insufficient or acq...

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{...

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 ...

In this paper, we investigate the multiple attribute decision making(MADM) problems for evaluating the security of wireless sensor networks with interval-valued intuitionistic fuzzy information. We utilize the interval-valued intuitionistic fuzzy hybrid geometric (IVIFHG) operator to aggregate the interval-valued intuitionistic fuzzy numbers corresponding to each alternative and derive the over...

In this paper, we investigate the multiple attribute decision making (MADM) problems for for evaluating the computer network security with interval-valued intuitionistic fuzzy information. To determine the attribute weights, a model based on the information entropy, by which the attribute weights can be determined, is established. We utilize the interval-valued intuitionistic fuzzy weighted ave...

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 ...

In this paper, we define some results on generalized interval-valued intuitionistic fuzzy sets (GIVIFSs). In fact, all interval-valued intuitionistic fuzzy sets (IVIFSs) are GIVIFSs but all GIVIFSs are not IVIFSs. We define two composite relations, four types of reflexivity and irreflexivity of GIVIFSs with some of their properties. We define generalized interval-valued intuitionistic fuzzy rel...

10 This article proposes a framework to handle multiattribute group decision making 11 problems with incomplete pairwise comparison preference over decision alternatives 12 where qualitative and quantitative attribute values are furnished as linguistic variables 13 and crisp numbers, respectively. Attribute assessments are then converted to interval14 valued intuitionistic fuzzy numbers (IVIFNs...