Generalizations to the constructions of t-norms: Rotation(-annihilation) construction

Authors:
Zhi-Hong Yi;Feng Qin;Wei-Cai Li
Affiliations:
College of Mathematics and Information Science, Jiangxi Normal University, 330022 Nanchang, PR China;College of Mathematics and Information Science, Jiangxi Normal University, 330022 Nanchang, PR China;College of Mathematics and Information Science, Jiangxi Normal University, 330022 Nanchang, PR China
Venue:
Fuzzy Sets and Systems
Year:
2008

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Abstract

In this paper, the constructions of triangular norms are investigated. Specially, based on weak negations which are not necessarily involutive, the rotation and the rotation-annihilation constructions are extended. By means of these methods, we can get new families of left-continuous t-norms compatible with weak negations given. However, not all weak negations are suitable for those generalized constructions. To highlight it, some counterexamples are given.