A theorem of renewal process for fuzzy random variables and its application. (English) Zbl 0966.60081
In the first part of the paper, the author describes briefly some properties of fuzzy numbers, fuzzy random variables, and the notions of expectation of fuzzy random variables. The theorem of the strong law of large numbers for fuzzy random variables [see R. Kruse, Inf. Sci. 28, 233-241 (1982; Zbl 0571.60039)] is also exposed. In the second part, there is considered a renewal process having inter-arrival times that are fuzzy random variables, and a theorem for the rate of the renewal process is proved. Two examples illustrate the usefulness of the obtained result.
Reviewer: Neculai Curteanu (Iaşi)
MSC:
| 60K05 | Renewal theory |
| 93C42 | Fuzzy control/observation systems |
| 94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |
Keywords:
fuzzy random variable; independent and identically distributed fuzzy random variable; expectation of fuzzy random variables; strong law of large numbers; fuzzy renewal processCitations:
Zbl 0571.60039References:
| [1] | Hirota, K., Concepts of probabilistic set, Fuzzy Sets and Systems, 5, 31-46 (1981) · Zbl 0442.60008 |
| [2] | Kruse, R., The strong law of large numbers for fuzzy random variables, Inform. Sci., 28, 233-241 (1982) · Zbl 0571.60039 |
| [3] | Kwakernaak, H., Fuzzy random variables. Part Idefinition and theorem, Inform. Sci., 15, 1-29 (1978) · Zbl 0438.60004 |
| [4] | Kwakernaak, H., Fuzzy random variables. Part IIalgorithms and examples for the discrete case, Inform. Sci., 17, 253-278 (1979) · Zbl 0438.60005 |
| [5] | S.M. Ross, Introduction to Probability Models, 4th ed., Academic Press, Boston; S.M. Ross, Introduction to Probability Models, 4th ed., Academic Press, Boston · Zbl 0255.60001 |
| [6] | Zadeh, L. A., Fuzzy Sets, Inform. and Control, 8, 338-353 (1965) · Zbl 0139.24606 |
| [7] | H.J. Zimmermann, Fuzzy Set Theory and its Applications, 2nd ed., Kluwer Academic Publishers, Boston; H.J. Zimmermann, Fuzzy Set Theory and its Applications, 2nd ed., Kluwer Academic Publishers, Boston · Zbl 0984.03042 |
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