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...

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 ...

The purpose of this paper is propose a simple de…nition of an interval-valued probability measure and to examine some of the implications of this de…nition. This de…nition provides a method for characterizing certain types of imprecise probabilities. We develop some properties of this de…nition and propose a de…nition of integration with respect to it. We show that this de…nition is a generaliz...

Different languages that are offered to model vague preferences are reviewed and an interval-valued language is proposed to resolve a particular difficulty encountered with other languages. It is shown that interval-valued languagesare well definedfor De Morgan triples constructedby continuoustriangular norms, conorms and a strong negation function. A new transitivity condition for vague prefer...

This paper introduces a new type of statistical model: the interval-valued linear model, which describes the linear relationship between an interval-valued output random variable and real-valued input variables. Firstly, we discuss the notions of variance and covariance of set-valued and interval-valued random variables. Then, we give the definition of the intervalvalued linear model and its le...

We define the Cartesian product, composition, union and join on interval-valued fuzzy graphs and investigate some of their properties. We also introduce the notion of interval-valued fuzzy complete graphs and present some properties of self complementary and self weak complementary interval-valued fuzzy complete graphs.

It was John Maynard Keynes [13] who first forcibly argued that probabilities cannot be simply ordered. There are cases, he argued, in which the probability of the hypothesis h can be regarded neither as greater than that of hypothesis k, nor less than that of hypothesis k, nor yet equal to that of hypothesis k. Although he did not provide a mathematical structure for his probability values, he ...