In this paper, we present a new security risk assessment method of website based on generalized fuzzy numbers. First, we present a new similarity measure between generalized fuzzy numbers. We also prove some properties of the proposed similarity measure and make an experiment to use 18 sets of generalized fuzzy numbers to compare the experimental results of the proposed method with the existing...

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...

The L-decomposable and the bi-decomposable models are two families of distributions on the set Sn of all permutations of the first n positive integers. Both of these models are characterized by collections of conditional independence relations. We first compute a Markov basis for the L-decomposable model, then give partial results about the Markov basis of the bi-decomposable model. Using these...