Relations between Proto-fuzzy concepts, Crisply Generated Fuzzy Concepts, and Interval Pattern Structures
نویسندگان
چکیده
Relationships between proto-fuzzy concepts, crisply generated fuzzy concepts, and pattern structures are considered. It is shown that proto-fuzzy concepts are closely related to crisply generated fuzzy concepts in the sense that the mappings involved in the definitions coincide for crisp subsets of attributes. Moreover, a proto-fuzzy concept determines a crisp subset of attributes, which generates a (crisply generated) fuzzy concept. However, the reverse is true only in part: given a crisp subset of attributes, one can find a proto-fuzzy concept whose intent includes (but not necessarily coincides with) the given subset of attributes. Interval pattern concepts are shown to be related to crisply generated formal concepts. In particular, every crisply closed subset of objects is an extent of an interval pattern concept.
منابع مشابه
Concept Lattices and Their Applications
Preface This special issue contains extended versions of selected papers presented at the International Con-(FCA) a forum to share innovative theories, methodologies, and applications in FCA and areas closely related to FCA such as data mining, information retrieval, knowledge management, data and knowledge engineering, logic, algebra, and lattice theory. The conference program included present...
متن کاملCrisply Generated Fuzzy Concepts
In formal concept analysis of data with fuzzy attributes, both the extent and the intent of a formal (fuzzy) concept may be fuzzy sets. In this paper we focus on so-called crisply generated formal concepts. A concept 〈A,B〉 ∈ B (X,Y, I) is crisply generated if A = D↓ (and so B = D↓↑) for some crisp (i.e., ordinary) set D ⊆ Y of attributes (generator). Considering only crisply generated concepts ...
متن کاملSome classes of statistically convergent sequences of fuzzy numbers generated by a modulus function
The purpose of this paper is to generalize the concepts of statisticalconvergence of sequences of fuzzy numbers defined by a modulus functionusing difference operator $Delta$ and give some inclusion relations.
متن کاملReducing the size of fuzzy concept lattices by fuzzy closure operators
The paper presents a general method of imposing constraints in formal concept analysis of tabular data with fuzzy attributes. The constraints represent a user-defined requirements which are supplied along with the input data table. The main effect is to filter-out conceptual clusters (outputs of the analysis) which are not compatible with the constraint, in a computationally efficient way. Our ...
متن کاملSimilarity relations in concept lattices 1 RADIM BĚLOHLÁVEK
Abstract. Studied is the issue of similarity relations in fuzzy concept lattices. Fuzzy concepts and fuzzy concept lattices represent a formal approach to the modeling of non-sharp (fuzzy) concepts and conceptual structures in the sense of traditional (PortRoyal) logic. Applications of concept lattices are in representation of conceptual knowledge and in conceptual analysis of (fuzzy) data. Sim...
متن کامل