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A MAP CHARACTERIZING THE FUZZY POINTS AND COLUMNS OF A T-INDISTINGUISHABILITY OPERATOR

Secció Matemàtiques i Informàtica, ETS Arquitectura del Vallès, Universitat Politècnica de Catalunya, Pere Serra 1-15, 08190 Sant Cugat del Vallès, Spain

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D. BOIXADER

Secció Matemàtiques i Informàtica, ETS Arquitectura del Vallès, Universitat Politècnica de Catalunya, Pere Serra 1-15, 08190 Sant Cugat del Vallès, Spain

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https://doi.org/10.1142/S0218488508005108Cited by:2 (Source: Crossref)

Abstract

A new map (Λ_E) between fuzzy subsets of a universe X endowed with a T-indistinguishability operator E is introduced. The main feature of Λ_E is that it has the columns of E as fixed points, and thus it provides us with a new criterion to decide whether a generator is a column. Two well known maps (φ_E and ψ_E) are also reviewed, in order to compare them with Λ_E. Interesting properties of the fixed points of φ_E and are studied. Among others, the fixed points of Λ_E (Fix(Λ_E)) are proved to be the maximal fuzzy points of (X, E) and the fixed points of coincide with the Image of Λ_E. An isometric embedding of X into Fix(Λ_E) is established and studied.

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