and Applied Analysis 3 Conversely, if the pair of functions α and β satisfy the conditions 1 – 4 , then there exists a unique u ∈ E1 such that u λ α− λ , β λ for each λ ∈ 0, 1 , 9 . The fuzzy number u corresponding to the pair of functions α and β is defined by u : R → 0, 1 , u x sup{λ : α x ≤ λ ≤ β x }, 5 . A sequence u uk of fuzzy numbers is a function u from the set N, the set of all positiv...

In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal m...

Kripke frames (and models) provide a suitable semantics for sub-classical logics; for example Intuitionistic Logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive Kripke frames (with persistent satisfaction relations), and the Basic Logic (of Visser) axiomatizes transitive Kripke frames (with persistent satisfaction relations). Here, we investigate whether Kripke frames/models...

In this paper, we consider the fuzzy model-based designs for the complete synchronization of chaotic systems. T-S fuzzy model for chaotic systems are exactly derived. Based on the T-S fuzzy model, the fuzzy logic controllers for chaotic synchronization are designed via Linear Matrix Inequality (LMI). Lyapunov Exponent of lorenz system is calculated, one of them is positive which represents the ...

It is shown that, for any spatial frame L (i.e., L is a complete lattice generated by the set of all prime elements), both the specialization L-preorder of L-topological spaces introduced by Lai and Zhang [Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006) 1865–1885] and that of L-fuzzifying topological spaces introduced by Fang and Qiu [Fuzzy orders and fuzzifying topologies,...

The paper dealswith systems of fuzzy relation equations known in the literature as eigen fuzzy set equations, aswell aswith systems of related fuzzy relation inequalities.Ourmain results are algorithms for computing the greatest and the smallest solutions to the considered systems of fuzzy relation inequalities, and algorithms for computing the greatest solutions to the considered systems of fu...

By the development of Semantic Web, increasing demands for vague information representation have triggered a mass of theoretical and applied researches of fuzzy ontologies, whose main logical infrastructures are fuzzy description logics. However, current tableau algorithms can not supply complete reasoning support within fuzzy ontology: reasoning with general TBox is still a difficult problem i...

The system PICASSO 2 represents the latest version of software package, designed for a comparative evaluation of image processing algorithms. In this paper we discuss the part of the system which evaluates edge detectors and consider its fuzzy extension. Namely, we introduce the ground truth edge maps defined in the fuzzy way and complete the system with several fuzzy similarity measures. The p...

In this paper, a new method of fuzzy decision trees called soft decision trees (SDT) is presented. This method combines tree growing and pruning, to determine the structure of the soft decision tree, with re4tting and back4tting, to improve its generalization capabilities. The method is explained and motivated and its behavior is 4rst analyzed empirically on 3 large databases in terms of classi...

In this paper, we have dealt with the concept of fuzzy b-closed and fuzzy bcompact set, and we study the characterization of fuzzy b-compact set by using fuzzy filterbases. We consider some relations between the fuzzy b-compact space and fuzzy b-closed space. Finally, the concept of bounded and semi bounded operators between fuzzy normed space are studied and some immediate results are also pro...