In this paper, a hesitant fuzzy multiple attribute group decision making problem where there exists prioritization relationships over the attributes and decision makers is studied. First, some Einstein operations on hesitant fuzzy elements and their properties are presented. Then, several generalized hesitant fuzzy prioritized Einstein aggregation operators, including the generalized hesitant f...

The main result is to show that the space of nonmonotonic fuzzy measures on a measurable space (X,X) with total variation norm is separable if and only if the -algebra X is a finite set. Our result is related to fuzzy analysis, functional spaces and discrete mathematics. © 2007 Elsevier B.V. All rights reserved.

This chapter presents a new optimization method for clustering fuzzy data to generate Type-2 fuzzy system models. For this purpose, first, a new distance measure for calculating the (dis)similarity between fuzzy data is proposed. Then, based on the proposed distance measure, Fuzzy c-Mean (FCM) clustering algorithm is modified. Next, Xie-Beni cluster validity index is modified to be able to valu...

In sensory analysis a panel of assessors gives scores to blocks of sensory attributes for profiling products, thus yielding a three-way table crossing assessors, attributes and products. In this context, it is important to evaluate the panel performance as well as to synthesize the scores into a global assessment to investigate differences between products. Recently, a combined approach of fuzz...

[E ]u ⊂ L2(E∗, μ) ⊂ [E ]u, and to characterize white noise test function space [E ]u and generalized function space [E ]u in the series of papers [1],[2],[3],[4],[5]. The notion of Legendre transformation plays important roles to examine relationships between the growth order of holomorphic functions (S-transform) and the CKS-space of white noise test and generalized functions. It is well-known...

This paper presents a new biometric score fusion approach in an identification system using the upper integral with respect to Sugeno’s fuzzy measure. First, the proposed method considers each individual matcher as a fuzzy set in order to handle uncertainty and imperfection in matching scores. Then, the corresponding fuzzy entropy estimates the reliability of the information provided by each bi...

We consider the aggregation operators which are ⊕-additive for commonotone functions. The main result is that any operator is expressed by a kind of general fuzzy integral which uses a family of fuzzy measures connected by a ⊕-additive Cauchy’s equations. In particular, the family of fuzzy measures can be obtained by a ⊕-fitting pseudomultiplication. In this case, the aggregation operator is ex...