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A Fuzzy Approach in Finding an Optimal Solution of a Fuzzy Reliability Problem

Affiliations

  • Department of Mathematics, S.A. Engineering College. Chennai - 77, Tamil Nadu, India
  • P. G. and Research Department of Mathematics, Pachaiyappa’s College, Chennai - 30, Tamil Nadu, India

Abstract


Objectives: The mathematical technique of optimizing a sequence of interrelated decisions over a period of time with fuzzy parameters is called Fuzzy Dynamic Programming. A typical characteristic of this proposed approach is the ambiguity and vagueness in Reliability models is effectively eliminated by FDP. Methods/ Statistical Analysis: In this paper, a new fuzzy approach is made to find an optimal solution of a fuzzy reliability problem. The values of Reliability are assumed as GTrFNs (Generalized Trapezoidal Fuzzy Numbers). Findings: Fuzzy Forward recursive equations as well as Fuzzy Backward recursive equations are framed to solve the numerical example of a fuzzy reliability problem. Now-a-days, many problems arise in the real world which involve decision making in multi stages. Sometimes, the parameters will not be known exactly due to some unmanageable components. Or else, some important data would be lost if the obtained results are taken as crisp values. Classical mathematics has proved its inadequate in handling many optimization problems that involve large number of decision variables along with inequality constraints. FDP furnishes an orderly process to determine the synthesis of decisions in order to maximize the effectiveness on the whole. Hence it has wide range of applications in the future. Application/Improvement: The proposed approach to solve a fuzzy reliability problem by fuzzy dynamic programming can be made use in the field of problems which involves various decision making situations. This will assist researchers currently engaged in fuzzy optimization to stimulate new areas of research in other DP models. This also gives Decision makers new tools and ideas on how to make decisions in fuzzy environment in optimization problems in current real life situations.

Keywords

Fuzzy Dynamic Programming, Fuzzy Reliability Problem, Fuzzy Recursive Equations, Generalized Trapezoidal Fuzzy Numbers, Optimal Solution.

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