Total views : 230

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


  • 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


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.


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

Full Text:

 |  (PDF views: 130)


  • Rouhi F, Effatnejad R. Unit Commitment in Power System by Combination of Dynamic Programming, Genetic Algorithm and Particle Swarm Optimization. Indian Journal of Science and Technology. 2015; 8(2):134–41.
  • Zadeh LA. Fuzzy Sets. Information and Control. 1965; 8:338–53.
  • Bellman RE, Zadeh LA. Decision-making in a fuzzy environment.Management Science. 1970; 17(4):B-14 – B-64.
  • Kacprzyk J. Fuzzy dynamic programming – basic issues.Fuzzy Optimization: Recent Advances. 1994; 321–31.
  • Kacprzyk J. Multistage Fuzzy control: A Model-Based Approach to Fuzzy Control and Decision Making, Wiley, New York, USA. 1997.
  • Kacprzyk J, Esogbue AO. Fuzzy dynamic programming: Main developments and applications. Fuzzy Sets and Systems.1996; 81(1):31–45.
  • EsogbueAO, Theologidu M, Guo K. On the application of fuzzy sets theory to the optimal Flood control problem arising in water resources systems. Fuzzy Sets and Systems.1992; 48(2):155–72.
  • Baldwin JF, Pilsworth BW. Dynamic programming for fuzzy systems with fuzz environment. Journal of Mathematical Analysis and Applications. 1982; 85(1):1–23.
  • Fodor JC, Roubens MR. Fuzzy Preference Modelling and Multi criteria Decision Support Kluwer Academic Publishers, Dordrecht. 1994.
  • Hojo T, Terano T, Masui S. Design of quasi-optimal fuzzy controller by fuzzy dynamic programming. Proceedings of 2nd IEEE International Conference on Fuzzy Systems.1993; 2. p. 1253–8.
  • Gluss B. Fuzzy multistage decision-making, fuzzy state and terminal regulators and their relationship to non-fuzzy quadratic state and terminal regulators. International Journal of Control. 1973; 17(1):177–92.
  • Hussein ML, Abo-Sinna MA. A fuzzy dynamic approach to the multicriterion resource allocation problem. Fuzzy Sets and Systems. 1995; 69(2):115–24.
  • Hussein ML, Abo-Sinna MA. Decomposition of multi objective programming problems by hybrid fuzzy-dynamic programming. Fuzzy Sets and Systems. 1993; 60(1):25–32.
  • Terano T, Sugeno M, Tsukamoto Y. Planning in management by fuzzy dynamic programming. IFAC Fuzzy Inform., Marseille, France. 1983; 381–6.
  • Malini P, Ananthanarayanan M. Solving Fuzzy Assignment Problem using Ranking of Generalized Trapezoidal Fuzzy Numbers. Indian Journals of Science and Technology. 2016; 9(20). DOI: 10.17485/ijst/2016/v9i20/88691.
  • Kumar A, Singh P, Kaur P, Amarpreetkaur. A new approach for ranking of GTrFN. International Journal of Computer, Electrical, Automation, Control and Information Engineering.2010; 4(8):1–11.


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.