The aim of this paper is to study some binary operations in approximate reasoning. In the first part we summarize a former practical investigation of the applicability of the implication function based on the nilpotent minimum in that framework [1]. We also present some numerical examples to illustrate the results. In the second part we recall a constructive approach to the axiomatics of generalized modus ponens (GMP) published in [5]. As a consequence, a system of functional equations is obtained. Idempotent as well as non-idempotent conjunctions fulfilling this system are studied. The obtained results support the use of noncommutative and non-associative conjunctions and the corresponding implications in approximate reasoning.
Approximate reasoning; generalized modus ponens; nilpotent minimum, and the related implication; conjunctions; Rand S-implications.
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