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Based on credibility theory, this paper studies the convergent properties about the sum of fuzzy variables. We first propose several convergence theorems in credibility and in expectation on the sum of fuzzy variables, and then we establish a strong law of large numbers for fuzzy variables, finally, a theorem similar to the law of large numbers for random variables is also obtained.
This paper discusses a renewal process in credibility theory, in which interarrival times are characterized as positive T-independent fuzzy variables. A fuzzy elementary renewal theorem shows that the expected average rate of fuzzy renewals converges to the reciprocal of the long-run expected value of the average time each renewal cost. The result obtained in this paper coincide with classical stochastic...
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