Generating theorems for s-norms and t-norms

• Main Authors: Shawkat Mahmoud Rasheed Alkhazaleh, Abdul Razak Salleh
• Format: Article
• Published: Penerbit ukm 2008
• Online Access: http://journalarticle.ukm.my/1870/; http://www.ukm.my/~ppsmfst/jqma/index.html
• Institution: Universiti Kebangsaan Malaysia

The s-norm and t-norm operators are generalization of the union and intersection operators respectively for fuzzy sets. Thus various alternative operators have been proposed by several authors since the introduction of fuzzy sets by Zadeh in 1965. In this paper we give generating theorems for s-norms and t-norm, namely given an s-norm we can generate a class of s-norms and t-norms, and given a t-norm we can generate a class of t-norms and s-norms. We also give bijective generating theorems for s-norms and t-norms. Given two bijective functions on [0, 1] under certain conditions, from an s-norm, we generate an s-norm and a t-norm, and from a t-norm we generate a t-norm and an s-norm