Why fuzzy T-equivalence relations do not resolve the Poincaré paradox, and related issues

Authors:
Martine De Cock;Etienne Kerre
Affiliations:
Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 291 (S9), B-9000 Gent, Belgium;Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 291 (S9), B-9000 Gent, Belgium
Venue:
Fuzzy Sets and Systems - Theme: Basic notions
Year:
2003

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Abstract

In this paper, which is a rejoinder on the comments (Fuzzy Sets and Systems, 133 (2) (2003)), we will answer the questions whether approximate equality should satisfy transitivity, and whether fuzzy T-equivalence relations resolve the Poincaré paradox. Furthermore, we will present an improved definition of resemblance relation and we will investigate its connection with nearness relations.