The word Interpretability is becoming more and more frequent in the fuzzy literature. It is admitted as the main advantage of fuzzy systems and it should be given a main role in fuzzy modeling. However, although researchers talk a lot about Interpretability, it is even not clear what it really means. Understanding of fuzzy systems is a subjective task which strongly depends on the person (exper...

This paper studies the issue of similarity relations in fuzzy concept lattices. Fuzzy concepts and fuzzy concept lattices represent a formal approach to the modelling of non-sharp (fuzzy) concepts and conceptual structures in the sense of traditional (Port-Royal) logic. Applications of concept lattices are in representation of conceptual knowledge and in conceptual analysis of (fuzzy) data. Sim...

To each fuzzy subgroup a fuzzy equivalence relation is associated and it is proved that a fuzzy subgroup is normal if and only if the operation of the group is compatible with its associated fuzzy equivalence relation. In the de-nition of fuzzy subgroup only the subset is fuzzy whilst the group operation remains crisp. In an opposite direction, another structure can be constructed maintaining c...

To improve the effectiveness of the fuzzy identification, a structure identification method based on moving rate is proposed for T-S fuzzy model. The proposed method is called " T-S modeling (or T-S fuzzy identification method) based on moving rate ". First, to improve the shortcomings of existing fuzzy reasoning methods based on matching degree, the moving rates for s-type, z-type and trapezoi...

The contents and meanings of mapping relationships between physical domain and function domain in different design stages, such as conceptual design, detail design and enhancement design, were analyzed. According to the analysis results, the fuzzy mapping between physical domain and function domain in different design stages was established by integrating objective information and subjective in...

The paper describes a fuzzy decisionmalung approach to controlling thermal comfort in the occupied zones of an airconditioned building. The control objective is defined in terms of fuzzy goals and fuzzy cost functions and a fuzzy decision-maker is used to find the most appropriate control action. Simulation results are presented that demonstrate the performance of the comfort control scheme whe...

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyhv-ideal of an hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy hv-ideals is an important and ...

In this paper we present a method for early identification of students who would have serious difficulties in studying a particular subject due to lack of preliminary knowledge. Methods from formal concept analysis are applied for finding relationships between results from a test on students’ preliminary knowledge and the outcome of learning new knowledge within the same subject. Fuzzy logic ru...

Moved by the need increased for modeling of the fuzzy data, the success of the systems of exact generation of summary of data, we propose in this paper, a new approach of generation of summary from fuzzy data called “FuzzySaintEtiQ”. This approach is an extension of the SaintEtiQ model to support the fuzzy data. It presents the following optimizations such as 1) the minimization of the expert r...