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Paper Information

Journal:   JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY)   WINTER 2006 , Volume 16 , Number 58/1 (MATHEMATICS ISSUE); Page(s) 6 To 14.
 
Paper: 

NUMERICAL SOLUTION OF THE IMPROPER FUZZY INTEGRALS USING THE STOCHASTIC ARITHMETIC

 
 
Author(s):  FARIBORZI ARAGHI M.A.*
 
* DEPARTMENT OF MATHEMATICS, CENTRAL TEHRAN BRANCH, ISLAMIC AZAD UNIVERSITY
 
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.

 
Keyword(s): FUZZY NUMBERS, IMPROPER INTEGRALS,(ALPHA) A -LEVEL SETS, SIMPSON RULE, STOCHASTIC ARITHMETIC, CESTAC METHOD
 
References: 
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