Minimal join decompositions and their applications to fuzzy relation equations over complete Brouwerian lattices

Authors:
Feng Sun;Xue-Ping Wang;Xiao-Bing Qu
Affiliations:
College of Mathematics and Information Science, Leshan Normal University, Leshan, Sichuan 614004, People's Republic of China;College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, People's Republic of China;College of Mathematics and Information Science, Leshan Normal University, Leshan, Sichuan 614004, People's Republic of China
Venue:
Information Sciences: an International Journal
Year:
2013

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Abstract

This paper deals with the existence of minimal solutions of fuzzy relation equations over complete Brouwerian lattices from the viewpoint of join decompositions. First, the concept of a minimal join decomposition is introduced. Then the existence conditions and properties of such decomposition are discussed. As their applications, the conditions for the existence of minimal solutions of fuzzy relation equations over complete Brouwerian lattices and complete lattices are given, respectively.