Fuzzy processes |
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Authors: | Abraham Kandel William J Byatt |
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Institution: | Department of Mathematics, Computer Science Division, The Florida State University, Tallahassee, Florida 32306, USA;EECS Department, The University of New Mexico, Albuquerque, New Mexico 87131, USA |
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Abstract: | In this paper, contributions to fuzzy probability and to differential equations with fuzzy parameters are made.After an introductory section, a review of fuzzy sets and fuzzy algebra is given in Section 2. The main new results of the investigation are contained in Section 3.In Section 3, Zadeh's definition of the probability of a ‘fuzzy event’ the average value of a fuzzy function are extended into the time domain. It is then shown that not only grades of membership, but also probabilistic processes with notions of fuzziness contained, can be defined which obey ordinary, matric, or integro-differential equations. Applications are also given in Section 3. |
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Keywords: | Fuzzy probability Fuzzy differential equations Average value of a fuzzy function Fuzzy event Fuzzy sets |
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