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Paper Information

Journal:   JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY)   WINTER 2010 , Volume - , Number 74/2 (MATHEMATICS ISSUE); Page(s) 79 To 88.
 
Paper: 

SOLVING FUZZY DIFFERENTIAL INCLUSIONS USING THE LV-REPRESENTATION OF FUZZY NUMBERS

 
 
Author(s):  ABBASBANDY S.*, PANAHI A., ROUHPARVAR H.
 
* MATHEMATICS DEPARTMENT, SCIENCE AND RESEARCH BRANCH, ISLAMICAZAD UNIVERSITY, TEHRAN, IRAN
 
Abstract: 
Introduction: In this paper, the solution of fuzzy differential inclusions (FDIs) with Lower-Upper Representation is established.
Aim: Finding an approximate solution of fuzzy differential inclusions.
Materials and Methods: Instead of a precise fuzzy number as an initial value, we have just some information in some a -cuts of it, which shows the value of initial value at the endpoints of a -cuts and also the slopes of the fuzzy number's membership function in the mentioned points.
Results: Using the intervals formed with the a -cut of initial value we apply the Euler method and solve the FDIs to find the same information for the solution of the given problem.
Also to determine the slopes of the estimated fuzzy solution again we use the Euler method and solve the fuzzy differential equations (FDEs). Finally with an specific interpolation polynomial we obtain the approximated solution.
Conclusion: The method presented in this paper is based on the LU-representation of fuzzy numbers with N=1. We find the solution set just in two a -cuts and then the approximate solution will introduce via interpolation polynomials.
 
Keyword(s): FUZZY DIFFERENTIAL EQUATIONS, FUZZY DIFFERENTIAL INCLUSIONS, LU-REPRESENTATION, FUZZY NUMBER, FUZZY CALCULUS
 
References: 
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