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Algebraic structure of centered M-fuzzy numbers. (English) Zbl 0724.04006
Fuzzy numbers are important and interesting in fuzzy systems and mathematics and this topic is being researched by many scholars such as D. Dubois, H. Prade, J. J. Buckley and some Chinese. Since the parameters in fuzzy numbers are of uncertainty, the degree to what a parameter may be considered acceptable depends on some subjective factors. This paper tries to answer the above problem by investigating the algebraic structure of fuzzy numbers: they are generated by a subset of the mappings from the real numbers to a lattice-ordered monoid. I feel that the method is effective.

MSC:
03E72 Theory of fuzzy sets, etc.
06F05 Ordered semigroups and monoids
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