Remarks on minimal solutions of a system of fuzzy relation equations over complete infinitely distributive lattices |
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Authors: | Feng Sun Xiao-bing Qu Xue-ping Wang |
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Affiliation: | 1.College of Mathematics and Software Science,Sichuan Normal University,Chengdu,People’s Republic of China;2.College of Mathematics and Information Science,Leshan Normal University,Leshan,People’s Republic of China |
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Abstract: | In Section 3.6 of Fuzzy relation equations and their applications to knowledge engineering. Kluwer Academic Publishers, Boston (1989), Di Nola et al. presented a procedure to find a minimal solution from a fixed solution of a system of fuzzy relation equations over complete infinitely distributive lattices, and put the question: is the minimal solution found by the procedure unique or not? In this paper, we give a negative answer to the question and make some further remarks. We not only give a necessary and sufficient condition for the uniqueness of such minimal solutions, but also characterize the existence of the least solution and a unique solution of a system of fuzzy relation equations over complete infinitely distributive lattices. |
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