In this paper, we study multidimensional integrals. We introduce a generalized fuzzy integral and we present a Fubini-like theorem for this generalized fuzzy integral. As this research was partly motivated by the definition of citation indices, we also describe how such multidimensional integrals can be used to define such indices. © 2008 Elsevier B.V. All rights reserved.

This paper introduces a method for mining multiple-choice assessment data for similarity of the concepts represented by the multiple choice responses. The resulting similarity matrix can be used to visualize the distance between concepts in a lower-dimensional space. This gives an instructor a visualization of the relative difficulty of concepts among the students in the class. It may also be u...

In 1974, the Japanese scholar Sugeno 1 presented a kind of typical nonadditive measure, Sugeno measure, which is an important generalization of probability measure 2–6 . As we all know, the definitions and properties of moment of random variable play an important role in probability theory 7–9 . Likewise, they are also very important for Sugenomeasure. In this paper we present the analogous def...

In [8], we introduced the concept of fuzzy r-minimal structure which is an extension of smooth fuzzy topological spaces and fuzzy topological spaces in Chang's sense. And we also introduced and studied the fuzzy r-M continuity. In this paper, we introduce the concepts of fuzzy r-minimal compactness, almost fuzzy r-minimal compactness and nearly fuzzy r-minimal compactness on fuzzy r-minimal spa...

We use a classical result of Gollinski and Ibragimov to prove an analog of the strong Szegő theorem for Jacobi matrices on l2(N). In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences and find necessary and sufficient conditions on the spectral measure such that ∑ ∞ k=n bk and ∑ ∞ k=n(a 2 k − 1) lie in l2 1, the linearly-weighted l2 space.

In the present paper, we study and investigate the properties of fuzzy soft α-connected sets, fuzzy soft α-separated sets and fuzzy soft α-s-connected sets and establish several interesting properties supported by examples. Moreover, we show that, a fuzzy soft α-disconnectedness is not an hereditary property in general. Finally, we show that the fuzzy α-irresolute surjective soft image of fuzzy...

This paper deals with the design of scalable, fuzzy adaptive, decision making systems constructed from sets of heterogeneous classifiers. We propose a multiclassifier architecture formed by sparsely connected coalitions of classifiers. Coalitions are defined by fuzzy integral operators on small, but not necessarily disjoint, subsets of classifiers. The small size constraint on individual coalit...

In a unified knowledge representation, data, information and knowledge are all represented in a single formalism as “items”. A unified knowledge representation is extended here to include two types of fuzzy measures of knowledge integrity. These integrity measures define a graduated integrity region for data, information and knowledge. This fuzzy region contains knowledge of increasingly questi...