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2011•Unpublished venueOpen access

On the transitive closure of reciprocal [0, 1]-valued relations

Steven Freson, Hans De Meyer, Bernard De Baets

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Abstract

We build a theoretical framework that enables to extend the concept of transitive closure to the class of complete crisp relations, the class of reciprocal 3-valued relations and the class of reciprocal [0, 1]valued relations.We present algorithms to compute the transitive closure of reciprocal [0, 1]-valued relations, where the type of transitivity is either weak stochastic transitivity or strong stochastic transitivity.

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What this paper is about

We build a theoretical framework that enables to extend the concept of transitive closure to the class of complete crisp relations, the class of reciprocal 3-valued relations and the class of reciprocal [0, 1]valued relations.We present algorithms to compute the transitive closure of reciprocal [0, 1]-valued relations, where the type of transitivity is either weak stochastic transitivity or strong stochastic transitivity.

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Available abstract

We build a theoretical framework that enables to extend the concept of transitive closure to the class of complete crisp relations, the class of reciprocal 3-valued relations and the class of reciprocal [0, 1]valued relations.We present algorithms to compute the transitive closure of reciprocal [0, 1]-valued relations, where the type of transitivity is either weak stochastic transitivity or strong stochastic transitivity.

Key concepts: Transitive relation, Transitive closure, Reciprocal, Closure (psychology), Transitive reduction, Mathematics, Class (philosophy), Pure mathematics

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