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 ...

a new approach to define the similarity measure betweeninterval-valued fuzzy sets is presented. the proposed approach isbased on a weighted measure in which the normalized similaritiesbetween lower functions and also between upper functions arecombined by a weight parameter. the properties of this similaritymeasure are investigated. it is shown that, the proposed measurehas some advantages in c...

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K.Atanassov, the notion of interval valued intuitionistic fuzzyHv-submodules of anHv-module with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated.In particular, the connections between interval valued in...

In this paper, we study in-depth certain properties of interval-valued fuzzy sets and Atanassov’s intuitionistic fuzzy sets (A-IFSs). In particular, we study the manner in which to construct different interval-valued fuzzy connectives (or Atanassov’s intuitionistic fuzzy connectives) starting from an operator. We further study the law of contradiction and the law of excluded middle for these se...

Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a useful tool allowing several possible degrees of membership of an element to a set. Recently, another suitable means were defined by Zhiming Zhang [1], called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and vagueness, and which is more powerful than the h...

In this communication, we study decision influence diagrams using fuzzy sets and fuzzy random variables t,o model problems in which assessing real-valued ~t i l i t~ies , and employing real-valued random variables t o model random magnit,udes, are considered to be too restrictive. We propose conditions allowing us to solve decision influence diagrams when uncertainty magnitudes are formalized b...

We present a new approach for handling fuzzy triadic data in the setting of Formal Concept Analysis. The starting point is a fuzzyvalued triadic context (K1,K2,K3, Y ), where K1,K2 and K3 are sets and Y is a ternary fuzzy relation between these sets. First, we generalise the methods of Triadic Concept Analysis to our setting and show how they fit other approaches to Fuzzy Triadic Concept Analys...

Interval-valued fuzzy sets involve more uncertainties than ordinary fuzzy sets and can be used to capture imprecise or uncertain decision information in fields that require multiple-criteria decision analysis (MCDA). This paper takes the simple additive weighting (SAW) method and the technique for order preference by similarity to an ideal solution (TOPSIS) as the main structure to deal with in...

We reformulate Mesiar’s hypothesis [Possibility measures, integration and fuzzy possibility measures, Fuzzy Sets and Systems 92 (1997) 191196], which as such was shown to be untrue by Murofushi [Two-valued possibility measures induced by σ-finite σ-additive measures, Fuzzy Sets and Systems 126 (2002) 265268]. We prove that a two-valued σ-maxitive measure can be induced by a σ-additive measure u...