Generating pseudo-t-norms and implication operators

Authors:
Zhudeng Wang
Affiliations:
Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, People's Republic of China and Department of Mathematics, Yancheng Teachers College, Jiangsu 224002, People's Republic of China
Venue:
Fuzzy Sets and Systems
Year:
2006

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Abstract

In this paper, we show that the set of all pseudo-t-norms, the set of all implications, the set of all infinitely @?-distributive pseudo-t-norms, and the set of all infinitely @?-distributive implications on a complete Brouwerian lattice are all complete lattices and lay bare the formulas for calculating the smallest pseudo-t-norm (the smallest infinitely @?-distributive pseudo-t-norm) that is stronger than a binary operation and the largest implication (the largest infinitely @?-distributive implication) that is weaker than a binary operation.