We give de nitions for fuzzy subalgebras, for fuzzy relations on fuzzy sets, and for fuzzy compatibility, which generalize, improve and correct the existing ones. The unit interval is replaced here by a partially ordered algebra. Then we study their connection with the corresponding crisp concepts through their newly de ned Q-cuts.

The notion of a linear space is generalized to the case where the underlying algebra is a commutative monoid and the set of scalars is a semiring reduct of a BL-algebra or an MValgebra. The notions of linear dependence and independence are also introduced and necessary and sufficient conditions when vectors form a basis of a semi-linear space are given. A linear mapping between two semilinear s...

This paper one of the series of papers in which we lay down the foundations for design of trustworthy computing systems. We propose here a methodology to perform behavior-based intrusion detection on security protocols using fuzzy relational methods. Fuzzified Allen temporal algebra plays an important role in capturing the time dimension of concurrent activites of principals as well as of intru...

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.

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...

We present a fuzzy version of the notion relational Galois connection between transitive directed graphs (fuzzy T-digraphs) on specific setting in which underlying algebra truth values is complete Heyting algebra. The components such are relations satisfying certain reasonable properties expressed terms so-called full powering. Moreover, we provide necessary and sufficient condition under it po...

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...