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Aggregation operators and fuzzy systems modeling. (English) Zbl 0845.93047
Summary: A general class of aggregation operators called MICA having the properties of monotonicity, symmetry and an identity element are introduced. We stress the significance of the choice of identity in characterizing the operator. We show that the \(t\)-norm and \(t\)-conorm are special cases of these operators. Other classes of these operators are introduced, notably an additive class which is very much in the spirit of the kind of aggregation used in neural networks. It is shown how a general description of the fuzzy systems modeling technique can be obtained using these operators.

93C42 Fuzzy control/observation systems
93A30 Mathematical modelling of systems (MSC2010)
Full Text: DOI
[1] Alsina, C.; Trillas, E.; Valverde, L., On some logical connectives for fuzzy set theory, J. math anal. appl., 93, 15-26, (1983) · Zbl 0522.03012
[2] Baldwin, J.F.; Pilsworth, B.W., Axiomatic approach to implication for approximate reasoning with fuzzy logic, Fuzzy sets and systems, 3, 193-219, (1980) · Zbl 0434.03021
[3] Driankov, D.; Hellendoorn, H.; Reinfrank, M., An introduction to fuzzy logic control, (1993), Springer Berlin
[4] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic Press New York · Zbl 0444.94049
[5] Dubois, D.; Prade, H., A review of fuzzy sets aggregation connectives, Inform. sci., 36, 85-121, (1985) · Zbl 0582.03040
[6] Dubois, D.; Prade, H., Fuzzy sets in approximate reasoning part I. inference with possibility distributions, Fuzzy sets and systems, 40, 143-202, (1991) · Zbl 0722.03017
[7] Kandel, A.; Langholz, G., Fuzzy control systems, (1993), CRC Press Boca Raton, FL
[8] Kosko, B., Neural networks and fuzzy systems, (1991), Prentice-Hall Englewood Cliffs, NJ
[9] Mamdani, E.H.; Assilian, S., An experiment in linguistic synthesis with a fuzzy logic controller, Internat. J. man-machine studies, 7, 1-13, (1975) · Zbl 0301.68076
[10] Yager, R.R., On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE trans. systems man cybernetics, 18, 183-190, (1988) · Zbl 0637.90057
[11] Yager, R.R., Connectives and quantifiers in fuzzy sets, Fuzzy sets and systems, 40, 39-76, (1991) · Zbl 0725.03033
[12] Yager, R.R., MAM and MOM operators for aggregation, Inform. sci., 69, 259-273, (1993) · Zbl 0783.04007
[13] Yager, R.R., Toward a unified approach to aggregation in fuzzy and neural systems, (), 619-622
[14] Yager, R.R., A unified approach to aggregation based upon MOM and MAM operators, () · Zbl 0783.04007
[15] Yager, R.R.; Filev, D.P., On the issue of defuzzification and selection based on a fuzzy set, Fuzzy sets and systems, 55, 255-272, (1993) · Zbl 0785.93060
[16] R.R. Yager and D.P. Filev, Essentials of Fuzzy Modeling and Control (Wiley, New York), to appear. · Zbl 0785.93060
[17] Yager, R.R.; Ovchinnikov, S.; Tong, R.; Nguyen, H., Fuzzy sets and applications: selected papers by L.A. zadeh, (1987), Wiley New York
[18] Zadeh, L.A., Approximate reasoning based on fuzzy logic, (), 1004-1010
[19] Zadeh, L.A., A computational approach to fuzzy quantifiers in natural languages, Comput. math. appl., 9, 149-184, (1983) · Zbl 0517.94028
[20] Zaruda, J.M., Introduction to artificial neural systems, (1992), West Publishing St. Paul, MN
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