Abstract
Control theory investigates the interaction between time-variant energy and physical systems. Interaction implies various operations to be carried out by means of certain rules. If the energy (mechanical, electrical, thermal, chemical, etc.) as well as the systems (or their mathematical models) are expressed in terms of sets, one must first determine the rules of interaction between sets in general. In as much as the rules of interaction affect the membership vectors of the respective sets, one must first establish the rules of combining membership vectors in general.
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References
CASTRO, JL: “Fuzzy Logic Controllers Are Universal Approximators”. Dep. Comp. Sci. Univ. Grenada, Artif.Int.Tech.Rep.DECSAI-93101, June, 1993
DUBOIS D, PRADE H: Fuzzy Sets and Systems, Chapter 2; 191–192, Academic Press, New York, 1980.
KANDEL, A, LEE, SC: Fuzzy Switching and Automata. John Wiley and Sons, 1982.
KAUFMANN A. Introduction to the Theory of Fuzzy Subsets, Vol I. Academic Press, 1975.
KOSKO, B: Neural Networks and Fuzzy Systems. Prentice Hall, 1992
LEE, CC: “Fuzzy Logic in Control Systems: Fuzzy Logic Controller, Parts I and II,” IEEE Trans.Sys., .Man.Cybern. 1990; 20; 2; 404–435.
PEDRYCZ, WS: Fuzzy Control and Fuzzy Systems. Report of Dept. of Math, Delft Univ.of Techn., Nederland, , 1982.
RAGADE, RK, GUPTA, MM: “Fuzzy Set Theory: An Introduction”. In: Fuzzy Automata and Decision Processes, Eds. Gupta, MM, Saridis, GN, Gaines BR. North Holland, 1976.
TONG, RM: “A Control Engineering Review of Fuzzy Systems.” Automatica, 1977; 13.
TONG, RM., BONISSONE, PP: A Linguistic Approach to Decisionmaking With Fuzzy Sets. IEEE Trans.Sys., Man, Cybern. 1980; SMC-10;11.
ZIMMERMANN HJ: Fuzzy Set Theory and Its Applications. Second Ed., Kluwer Academioc Publishers, Boston , Dordrecht, London, 1991.
ZADEH LA: “Outline Of a New Approach To the Analysis of Complex Systems and Decision Processes.” IEEE Trans. Sys, Man, Cybern., 1973; 3; 28–44
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© 1998 Springer Science+Business Media New York
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Shaw, I.S. (1998). Set Operations. In: Fuzzy Control of Industrial Systems. The Springer International Series in Engineering and Computer Science, vol 457. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2813-2_4
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DOI: https://doi.org/10.1007/978-1-4757-2813-2_4
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