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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.

03E72 Theory of fuzzy sets, etc.
06F05 Ordered semigroups and monoids
Full Text: DOI
[1] Birkhoff, G., Lattice theory, (1967), AMS Providence, RI · Zbl 0126.03801
[2] Buckley, J.J., Ranking alternatives using fuzzy numbers, Fuzzy sets and systems, 15, 21-31, (1985) · Zbl 0567.90057
[3] Dubois, D.; Prade, H., Operations on fuzzy numbers, Internat. J. system sci., 9, 613-626, (1978) · Zbl 0383.94045
[4] Dubois, D.; Prade, H., Ranking fuzzy numbers in the setting of possibility theory, Inform. sci., 30, 183-224, (1983) · Zbl 0569.94031
[5] Fuchs, L., Partially ordered algebraic systems, (1963), Pergamon Press New York · Zbl 0137.02001
[6] Menger, K., Statistical metrics, (), 535-537 · Zbl 0063.03886
[7] Nahmias, S., Fuzzy variables, Fuzzy sets and systems, 1, 97-110, (1978) · Zbl 0383.03038
[8] Ramik, J.; Rimanek, J., Inequality relation between fuzzy numbers and its use in fuzzy optimization, Fuzzy sets and systems, 16, 123-138, (1985) · Zbl 0574.04005
[9] Schweizer, B.; Sklar, A., Associative functions and statistical triangle inequalities, Publ. math. debrecen, 8, 169-186, (1967) · Zbl 0107.12203
[10] Wang, H.; Ma, J., On algebraic structures in the generalized fuzzy operation, Busefal, 26, 17-22, (1986)
[11] Zadeh, L.A.; Zadeh, L.A.; Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning III, Inform. sci., Inform. sci., Inform. sci., 9, 43-80, (1976) · Zbl 0404.68075
[12] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002
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