On the convex combination of TD and continuous triangular norms

Authors:
Yao Ouyang;Jinxuan Fang;Guiling Li
Affiliations:
Department of Mathematics, Nanjing Normal University, Nanjing, Jiangsu 210097, People's Republic of China and Faculty of Science, Huzhou Teacher's College, Huzhou, Zhejiang 313000, People's Republ ...;Department of Mathematics, Nanjing Normal University, Nanjing, Jiangsu 210097, People's Republic of China;Science Department of Laiyang Agricultural College, Laiyang, Shandong 266109, People's Republic of China
Venue:
Information Sciences: an International Journal
Year:
2007

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Abstract

The problem of when T"@l@?(1-@l)T"D+@lT@l@?(0,1) is a triangular norm, where T"D is the drastic product and T is a continuous triangular norm, is studied. It is shown that T"@l cannot be a triangular norm when T is nilpotent. It is also shown that T"@l is a triangular norm if T is strict and its additive generator f satisfies f(@lx)=f(x)+f(@l) for all x@?[0,1]. The cases that T=T"M and T is the ordinal sum of continuous Archimedean summands are also discussed. Some left-continuous t-norms which can be combined with each other are given.