Relations in Fuzzy Class Theory
Fuzzy Sets and Systems
I-Fuzzy equivalence relations and I-fuzzy partitions
Information Sciences: an International Journal
Approximate fuzzy preorders and equivalences
FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
Finite-valued indistinguishability operators
International Journal of Approximate Reasoning
Permutable indistinguishability operators, perfect vague groups and fuzzy subgroups
Information Sciences: an International Journal
Structural analysis of indistinguishability operators and related concepts
Information Sciences: an International Journal
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Fuzzy transitivity is a key property for many fuzzy relational structures, such as fuzzy preorders and equivalences. Theoretical models for practical problems which are based on fuzzy relations make use of continuous scales, mostly the unit interval [0,1]. Practical implementation of these models though, involves their discretization into finite scales, which generally results in some loss of transitivity. In this paper we study if there are any transitivity preserving discretization strategies. Also, we evaluate the loss of transitivity in some commonly used discretization approaches.