Theory of fuzzy integrals and its applications

Aggregation Functions: Aggregation on ordinal scales

Publisher Summary This chapter focuses on the concept of Galois connexions. The researches in algebraic linguistics have been performed in the frame of a particular Galois connexion, in which the objects are the words of a vocabulary, V, and the set of the properties is the set of the contexts that accept these words. Vocabulary V is, however, formed by a finite of words. The chapter highlights that if A is a generating kernel for the closed set φ ( X ), then the set formed by taking one element of every family contained in A is also a generator for φ ( X ). Such a generator is called the minimal generator of the set φ( X ) with respect to the kernel A . The chapter also discusses the properties of the operators G , ω , and φ .

On Galois Connexions

Bipolar fuzzy graph representation of concept lattice

Survey of the main existing techniques for concept lattices reduction.Classification of techniques in three classes based on seven dimensions.Analyzing reduction techniques with formal concept analysis.Considerations are carried out about computational complexity and feasibility. Formal concept analysis (FCA) is currently considered an important formalism for knowledge representation, extraction and analysis with applications in different areas. A problem identified in several applications is the computational cost due to the large number of formal concepts generated. Even when that number is not very large, the essential aspects, those effectively needed, can be immersed in a maze of irrelevant details. In fact, the problem of obtaining a concept lattice of appropriate complexity and size is one of the most important problems of FCA. In literature, several different approaches to control the complexity and size of a concept lattice have been described, but so far they have not been properly analyzed, compared and classified. We propose the classification of techniques for concept lattice reduction in three groups: redundant information removal, simplification, and selection. The main techniques to reduce concept lattice are analyzed and classified based on seven dimensions, each one composed of a set of characteristics. Considerations are made about the applicability and computational complexity of approaches of different classes.

Concept lattices reduction

Note on generating fuzzy concept lattices via Galois connections

On equivalence of conceptual scaling and generalized one-sided concept lattices

On possible generalization of fuzzy concept lattices using dually isomorphic retracts

We introduce a new property of the discrete Sugeno integrals which can be seen as their characterization, too. This property, compatibility with respect to congruences on $[0,1]$, stresses the importance of the Sugeno integrals in multicriteria decision support as well.

Jozef Pócs

Papers

Note on generating fuzzy concept lattices via Galois connections

On equivalence of conceptual scaling and generalized one-sided concept lattices

On possible generalization of fuzzy concept lattices using dually isomorphic retracts

A new characterization of the discrete Sugeno integral.

A new characterization of the discrete Sugeno integral