Fuzzy membership functions are considered as a key element in fuzzy systems. In order to generate a fuzzy membership function, there are two potential sources: expert knowledge and real data. However expert knowledge acquisition is a difficult issue, on the other hand using real data needs a methodology to translate real data to membership function. Most previous approaches considered membership function design highly dependent of fuzzy rule base and require the specification of membership functions' number. This paper attempts to overcome these problems and proposes an automatic membership function generation method. Our approach is based on a clustering technique and a density function for deriving cores of fuzzy sets. Experimental results show that our approach generates large core region which is more preferable than small core region in the context of membership function generation for neuro-fuzzy systems.

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The majority of existing information systems deals with crisp data through crisp database systems. Traditional Database Management Systems (DBMS) have not taken into account imprecision so one can say there is some sort of lack of flexibility. The reason is that queries retrieve only elements which precisely match to the given Boolean query. That is, an element belongs to the result if the query is true for this element; otherwise, no answers are returned to the user. The aim of this paper is to present a cooperative approach to handling empty answers of fuzzy conjunctive queries by referring to the Formal Concept Analysis (FCA) theory and fuzzy logic. We present an architecture which combines FCA and databases. The processing of fuzzy queries allows detecting the minimal reasons of empty answers. We also use concept lattice in order to provide the user with the nearest answers in the case of a query failure.

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