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Two families of fuzzy integrals. (English) Zbl 0595.28011

Summary: In this paper we present two definitions of fuzzy integrals arising from the t-seminorm and the t-semiconorm concepts. We show that Sugeno’s fuzzy integral is a particular case of them and we study their principal properties. Finally we suggest some applications of these results.

MSC:

28A99 Classical measure theory
28A10 Real- or complex-valued set functions
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[1] Batle, N.; Trillas, E., Entropy and fuzzy integral, J. Math. Anal. Appl., 69, 469-474 (1979) · Zbl 0421.28015
[2] Dubois, D.; Prade, H., Additions of interactive fuzzy numbers, IEEE. Trans. Automat. Control, 26, 926-936 (1981) · Zbl 1457.68262
[3] Kandel, A., On fuzzy statistics, (Gupta, M. M.; Ragade, R. K.; Yager, R. R., Advances in Fuzzy Set Theory and Applications (1979), North-Holland: North-Holland Amsterdam), 181-199 · Zbl 0434.94026
[4] Mizumoto, M., Fuzzy sets and their operations II, Inform. and Control, 50, 160-174 (1981) · Zbl 0488.04004
[5] Ralescu, D.; Adams, G., The fuzzy integral, J. Math. Anal. Appl., 75, 562-570 (1980) · Zbl 0438.28007
[6] Schweizer, B.; Sklar, A., Associative functions and abstract semi-groups, Pub. Math. Debrecen, 10, 69-81 (1963) · Zbl 0119.14001
[7] Sugeno, M., Theory of fuzzy integral and its applications, (Ph.D. Thesis (1974), Tokyo Inst. of Technol) · Zbl 0733.28014
[8] Sugeno, M., Fuzzy measures and fuzzy integrals: A survey, (Gupta, M. M.; Saridis, G. N.; Gaines, B. R., Fuzzy Automata and Decision Processes (1977), North-Holland: North-Holland Amsterdam), 89-102
[9] Vila, M. A.; Delgado, M., Problems of classification in a fuzzy environment, Fuzzy Sets and Systems, 9, 229-239 (1983) · Zbl 0532.62037
[10] Weber, S., Measures of fuzzy sets and measures of fuzziness, Fuzzy Sets and Systems, 13, 247-271 (1984) · Zbl 0576.28011
[11] Yager, R., On a general class of fuzzy connectives, Fuzzy Sets and Systems, 4, 235-242 (1980) · Zbl 0443.04008
[12] Zadeh, L. A., Theory of fuzzy sets, Memo UCB/ERL M77/1 Berkeley (1977) · Zbl 0382.03017
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