Abstract
In this paper, we proposed the problem of optimizing the reliability of a series–parallel system in fuzzy environment and also consider entropy as an additional objective function. Taking into account the resources (such as weight, volume, cost etc.) as generalized trapezoidal fuzzy number and considering vagueness of judgements of the decision maker, an Interactive fuzzy multiple-objective decision making method is presented to solve the above mentioned reliability optimization problem based on entropy. An important characteristics of the Interactive approach is that, it provides a learning process about the system, whereby the decision maker can learn to recognize good solutions, relative importance of factors in the system and then, design a high productivity system instead of optimizing a given system. The object of this study is to find the optimum number of redundant components of the proposed entropy based reliability optimization problem to produce highly reliable system as well as maximize the entropy amount of the system subject to the available resources of each component. Here total integral value of fuzzy number is used to transform the fuzzy problem into crisp multi-objective problem. The effectiveness of additional entropy to this model and the performance of this solution approach are evaluated by comparing its result with the other method at the end of this paper.
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References
Misra, K.B.: A method of solving redundancy optimization problems. IEEE Trans. Reliab. R–20, 117–120 (1971)
Misra, K.B.: Reliability optimization of a series–parallel system. IEEE Trans. Reliab. R–21, 230–238 (1972)
Sakawa, M.: Multiobjective relibility and redundancy optimization of a series–parallel system by the surrogate worth trade off methods. Microelectron. Reliab. 17, 465–467 (1978)
Chern, M.S., Jan, R.H.: Parametric programming applied to reliability optimization problems. IEEE Trans. Reliab. R–34, 165–170 (1985)
kuo, W., Prasad, V.R.: An annotated overview of system-reliability optimization. IEEE Trans. Reliab. 49(2), 176–187 (2000)
Kuo, W., Prasad, V.R., Tillman, F.A., Hwang, C.: Optimal Reliability Design: Fundamentals and Applications. Cambridge University Press, Cambridge (2001)
Wang, G.B., Huang, H.Z., Liu, Y., Zhang, X., Wang, Z.: Uncertainty estimation of reliability redundancy in complex system based on the cross-entropy method. J. Mech. Sci. Technol. 23, 2612–2623 (2009)
Caserta, M., Nodar”, M.C.: A cross-entropy based algorithm for reliability problems. J. Heuristics 15, 479–501 (2009)
Kang, H.Y., Kwak, B.M.: Application of maximum entropy principle for reliability-based design optimization. Struct. Multidiscip. Optim. 38, 331–346 (2009)
Mahapatra, G.S., Roy, T.K.: Fuzzy multi-objective mathematical programming on reliability optimization model. Appl. Math. Comput. 174(1), 643–659 (2006)
Park, K.S.: Fuzzy apportionment of system reliability. IEEE Trans. Reliab. R–36, 129–132 (1987)
Islam, S., Roy, T.K.: Multi-objective transportation problem with an additional entropy objective function in fuzzy environment. J. Fuzzy Math. 18(2), 1–24 (2010)
Gong, B., Chen, X., Hu, C.: Fuzzy entropy clustering approach to evaluate the reliability of emergancy logistic system. Energy Procedia 16, 278–283 (2012). Elsevier
Grag, H.: Fuzzy multi-objective reliability optimization problem of industrial system using particle swarm optimization. J. Ind. Math. Article ID: 872450 (2013)
Mahaptra, B.S., Mahapatra, G.S.: Reliability and cost analysis of series system models using fuzzy parametric geometric programming. Fuzzy Inf. Eng. 2(4), 399–411 (2010)
Dancese, M., Abbas, F., Ghamry, E.: Reliability and cost analysis of a series system model using fuzzy parametric geometric programming. Int. J. Innov. Sci. Eng. Technol. 1(8), 18–23 (2014)
Sakawa, M., Matsui, T.: An interactive satisficing method for multi-objective stochastic integer programming with simple resource. Appl. Math. 3, 1245–1251 (2012)
Lai, Y.J., Hwang, C.L.: Fuzzy Multiple Objective Decision Making—Methods and Application. Springer, Berlin (1994)
Hwang, C.L., Lee, H.B.: Non-linear integer goal programming applied to optimal system reliability. IEEE Trans. Reliab. R–33, 431–438 (2004)
Zangiabadi, M., Maleki, H.R.: Fuzzy goal programming for multi-objective transportation problem. J. Appl. Math. Comput. 24, 449–460 (2007)
Kapur, J.N.: Maximum-Entropy Models in Science and Engineering. Wiley, New Delhi (1993)
Shannon, C.E.: A mathematical theory of communication. Bell Syst Tech J 27, 379–423, 623–656 (1948)
Mahapatra, G.S.: Reliability optimization of entropy based series–parallel system using global criterion method. Intell. Inf. Manag. 1, 145–149 (2009)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Zimmermann, H.J.: Fuzzy Set Theory—and its Applications. Allied Publishers Limited, New Delhi (1996)
Chen, S.H.: Operations on fuzzy members with function principal. Tamkang J. Manag. Sci. 6(1), 13–25 (1985)
Liou, T.S., Wang, M.J.J.: Ranking fuzzy numbers with integral value. Fuzzy Sets Syst. 50, 247–255 (1992)
Bellman, R.E., Zadeh, L.A.: Decision making in a fuzzy environment. Manag. Sci. 17(4), B141–B164 (1970)
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Kundu, T., Islam, S. A new interactive approach to solve entropy based fuzzy reliability optimization model. Int J Interact Des Manuf 13, 137–146 (2019). https://doi.org/10.1007/s12008-018-0484-6
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DOI: https://doi.org/10.1007/s12008-018-0484-6