NUMERICAL SOLUTION OF THE IMPROPER FUZZY INTEGRALS USING THE STOCHASTIC ARITHMETIC

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FARIBORZI ARAGHI M.A.

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Journal: JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY) Year:2006 | Volume:16 | Issue:58/1 (MATHEMATICS ISSUE) Page(s): 6-14

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Title

NUMERICAL SOLUTION OF THE IMPROPER FUZZY INTEGRALS USING THE STOCHASTIC ARITHMETIC

Author(s)

FARIBORZI ARAGHI M.A. | Issue Writer Certificate

Keywords

FUZZY NUMBERSQ3

IMPROPER INTEGRALSQ4

(ALPHA) A -LEVEL SETSQ4

SIMPSON RULEQ4

STOCHASTIC ARITHMETICQ4

CESTAC METHODQ4

Abstract

In this paper, the numerical solution of the improper fuzzy integral ~I=ò+¥~a ~¦(~x)~dx is proposed where, ~¦(~x) is a bounded and closed fuzzy valued function defined on the closed fuzzy real number system and a is ~a fuzzy number with triangular or bell-shape membership function. For this purpose, the a -level sets of the fuzzy number ~I, -Ia and -Ia, 0£a£1, are evaluated whose end points are the crisp IMPROPER INTEGRALS. Then, a reliable method is introduced to estimate -Ia and -Ia by using the STOCHASTIC ARITHMETIC. In this case, an algorithm is presented which evaluates these integrals by using the SIMPSON RULE. By using the CESTAC METHOD, we find the optimal natural numbers -ma and -ma such that these IMPROPER INTEGRALS are estimated by definite integrals. Also, for a given r, we evaluate the approximate value of the membership function m~I (r) and determine the accuracy of the results. At last, two fuzzy integrals are computed using the given algorithm to show the results of the research.

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APA: Copy

FARIBORZI ARAGHI, M.A.. (2006). NUMERICAL SOLUTION OF THE IMPROPER FUZZY INTEGRALS USING THE STOCHASTIC ARITHMETIC. JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY), 16(58/1 (MATHEMATICS ISSUE)), 6-14. SID. https://sid.ir/paper/70624/en

Vancouver: Copy

FARIBORZI ARAGHI M.A.. NUMERICAL SOLUTION OF THE IMPROPER FUZZY INTEGRALS USING THE STOCHASTIC ARITHMETIC. JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY)[Internet]. 2006;16(58/1 (MATHEMATICS ISSUE)):6-14. Available from: https://sid.ir/paper/70624/en

IEEE: Copy

M.A. FARIBORZI ARAGHI, “NUMERICAL SOLUTION OF THE IMPROPER FUZZY INTEGRALS USING THE STOCHASTIC ARITHMETIC,” JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY), vol. 16, no. 58/1 (MATHEMATICS ISSUE), pp. 6–14, 2006, [Online]. Available: https://sid.ir/paper/70624/en

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