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Transitive closure and betweenness relations
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DOI：10.1016/S0165-0114(99)00133-5.png)
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Abstract
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Indistinguishability operators fuzzify the concept of equivalence relation and have been proved a useful tool in theoretical studies as well as in different applications such as fuzzy control or approximate reasoning. One interesting problem is their construction. There are different ways depending on how the data are given and on their future use. In this paper, the length of an indistinguishability operator is defined and it is used to relate its generation via max-T product and via the representation theorem when T is an Archimedean t-norm. The link is obtained taking into account that indistinguishability operators generate betweenness relations. The study is also extended to decomposable operators. (C) 2001 Elsevier Science B.V. All rights reserved.
Keywords:
indistinguishability
dimension
Archimedean t-norm
betweenness relation
transitive closure
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