Solution sets of fuzzy relational equations on complete Brouwerian lattices

Authors:
Qing-quan Xiong;Xue-ping Wang
Affiliations:
Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610066, People's Republic of China;Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610066, People's Republic of China
Venue:
Information Sciences: an International Journal
Year:
2007

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Abstract

This work studies the problem of solving a fuzzy relational equation with composition on a complete Brouwerian lattice, where is a pseudo-t-norm. Two necessary and sufficient conditions that solution sets are nonempty are obtained. When is normal and the solution set of the equation is nonempty, a sufficient condition that there exists maximal solutions is given. Further, the solution set of the equation is presented.