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Multipollutant Air Quality Management Strategies: T-Sets Based Optimization Technique Under Imprecise Environment

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Abstract

In this paper, technique to find Pareto optimal solutions to multiple objective optimization problems under imprecise environment is discussed. In 1976, Zimmermann described optimization technique under fuzzy environment. Jiménez and Bilbao (Fuzzy Sets Syst 150:2714–2721, 2009) showed that fuzzy efficient solutions may not be Pareto optimal solutions to multiple objective optimization problems in case that one of the fuzzy goals is fully achieved. Wu et al. (Fuzzy Optim Decis Mak 14:43–55, 2015) redefined membership functions of fuzzy set theory and proposed two-phase approach. But under imprecise environment, it is observed that the prime intention of maximizing up-gradation of most misfortunate is better served by removing some constraints that are obtained by applying existing fuzzy optimization technique in mathematical models. Further in existing fuzzy optimization technique, it is observed that membership functions are not utilized as per their definitions. Moreover, some constraints in existing fuzzy optimization technique may make a model infeasible. Consequently, in this paper, one new function viz. T-characteristic function is introduced to supersede membership function of fuzzy set, and subsequently, one new set viz. T-set is introduced to supersede fuzzy set for representing uncertainty. Then, one general algorithm has been developed to find Pareto optimal solutions to multiple objective optimization problems by applying newly introduced T-sets. One model on multipollutant air quality management strategies under imprecise environment illustrates the limitations of existing fuzzy optimization technique as well as advantages of using proposed algorithm. Finally, conclusions are drawn.

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References

  1. Bellman, R.E., Zadeh, L.A.: Decision making in a fuzzy environment. Manag. Sci. 17, 141–164 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bowman, V.J.: On the relationship of the Tchebycheff norm and the efficient frontier of multiple-criteria objectives. Lect. Notes Econ. Math. Syst. 135, 76–85 (1976)

    Article  Google Scholar 

  3. Chakraborty, D., Jana, D.K., Roy, T.K.: A new approach to solve multi-objective multi-choice multi-item Atanassov’s intuitionistic fuzzy transportation problem using chance operator. J. Intell. Fuzzy Syst. 28(2), 843–865 (2015)

    MathSciNet  MATH  Google Scholar 

  4. Chow, J.C.: Critical review introduction: multipollutant air quality management. J. Air Waste Manag. Assoc. 60(6), 642–644 (2010)

    Article  Google Scholar 

  5. Dubois, D., Fortemps, P.: Computing improved optimal solutions to max–min flexible constraint satisfaction problems. Eur. J. Oper. Res. 118, 95–126 (1999)

    Article  MATH  Google Scholar 

  6. Ebrahimnejad, A., Verdegay, J.L.: A novel approach for sensitivity analysis in linear programs with trapezoidal fuzzy numbers. J. Intell. Fuzzy Syst. 27(1), 173–185 (2014)

    MathSciNet  MATH  Google Scholar 

  7. Fujita, H., Su, S.-F.: New trends on system science and engineering. In: Proceedings of ICSSE 2015, IOS Press (2015)

  8. Garai, A., Mandal, P., Roy, T.K.: Intuitionistic fuzzy T-sets based solution technique for multiple objective linear programming problems under imprecise environment. Notes Intuit. Fuzzy Sets 21(4), 104–123 (2015)

    Google Scholar 

  9. Garai, A., Mandal, P., Roy, T.K.: Pareto optimal solutions to multi objective linear programming problem with fuzzy goals using trade off ratios. Int. J. Math. Arch. 6(5), 52–65 (2015)

    Google Scholar 

  10. Garai, A., Roy, T.K.: Intuitionistic fuzzy Delphi method: more realistic and interactive forecasting tool. Notes Intuit. Fuzzy Sets. 18(2), 37–50 (2012)

    Google Scholar 

  11. Garai, A., Mandal, P., Roy, T.K.: Intuitionistic fuzzy T-sets based optimization technique for production-distribution planning in supply chain management. OPSEARCH 53(4), 950–975 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Garai, A., Mandal, P., Roy, T.K.: Interactive intuitionistic fuzzy technique in multi-objective optimisation. Int. J. Fuzzy Comput. Model. 2(1), 14 (2016)

    Article  Google Scholar 

  13. Garg, H., Rani, M., Sharma, S.P., Vishwakarma, Y.: Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment. Expert Syst. Appl. 41(7), 3157–3167 (2014)

    Article  Google Scholar 

  14. Guu, S.-M., Wu, Y.-K.: Weighted coefficients in two-phase approach for solving the multiple objective programming problems. Fuzzy Sets Syst. 85, 45–48 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  15. Guu, S.-M., Wu, Y.-K.: Two phase approach for solving the fuzzy linear programming problems. Fuzzy Sets Syst. 107, 191–195 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  16. Jerrettl, M., Burnett, R.T., Beckerman, B.S., Turner, M.C., Krewski, D., Thurston, G., Martin, R.V., Donkelaar, A.V., Hughes, E., Shi, Y., Gapstur, S.M., Thun, M.J., Pope III, C.A.: Spatial analysis of air pollution and mortality in California. Am. J. Respir. Crit. Care Med. 5, 593–599 (2013)

    Article  Google Scholar 

  17. Jiménez, M., Arenas, M., Bilbao, A., Rodríguez Uría, M.V.: Approximate resolution of an imprecise goal programming model with nonlinear membership functions. Fuzzy Sets Syst. 150, 129–145 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  18. Jiménez, M., Bilbao, A.: Pareto-optimal solutions in fuzzy multi-objective linear programming. Fuzzy Sets Syst. 150, 2714–2721 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Lai, Y.J., Hwang, C.L.: Fuzzy Multiple Objective Decision Making, vol. 404, pp. 139–262. Springer, Berlin (1994)

  20. Liao, K.-J., Hou, X.: Optimization of multipollutant air quality management strategies: a case study for five cities in the United States. J. Air Waste Manag. Assoc. 65(6), 732–742 (2015)

    Article  Google Scholar 

  21. Luhandjula, M.K.: Fuzzy optimization: milestones and perspectives. Fuzzy Sets Syst. 274(1), 4–11 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  22. Pechan, E.H.: Associates: AirControlNET version 4.1 document report. http://www.epa.gov/ttnecas1/models/DevelopmentReport.pdf (2015). Accessed 7 Jan 2015

  23. Sakawa, M., Yano, H.: Interactive decision making for multiple nonlinear programming using augmented minimax problems. Fuzzy Sets Syst. 20(1), 31–43 (1986)

    Article  MATH  Google Scholar 

  24. Sakawa, M., Yano H., Yumine, T.: An interactive fuzzy satisficing method for multiobjective linear-programming problems and its application. IEEE Trans. Syst. Man Cybern. 17(4), 654–661 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  25. Sakawa, M., Yano, H., Nishizaki, I.: Linear and Multi-Objective Programming with Fuzzy Stochastic Extensions. Springer, New York (2013)

    Book  MATH  Google Scholar 

  26. Su, S.-F., Chen, M.-C.: Enhanced fuzzy systems for type 2 fuzzy and their application in dynamic system identification. In: 16th World Congress of the International Fuzzy Systems Association, Atlantis Press (2015)

  27. Tanaka, H., Okuda, T., Asai, K.: On fuzzy mathematical programming. J. Cybern. 3, 37–46 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  28. Wei, G., Wang, H., Zhao, X., Lin, R.: Hesitant triangular fuzzy information aggregation in multiple attribute decision making. J. Intell. Fuzzy Syst. Appl. Eng. Technol. 26(3), 1201–1209 (2014)

    MathSciNet  MATH  Google Scholar 

  29. Werners, B.: An interactive fuzzy programming system. Fuzzy Sets Syst. 23, 131–147 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  30. Wu, Y., Liu, C., Lur, Y.: Pareto-optimal solution for multiple objective linear programming problems with fuzzy goals. Fuzzy Optim. Decis. Mak. 14(1), 43–55 (2015)

    Article  MathSciNet  Google Scholar 

  31. Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1(1), 45–55 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  32. Zimmermann, H.J.: Applications of fuzzy set theory to mathematical programming. Inf. Sci. 36, 29–58 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  33. Zimmermann, H.: Description and optimization of fuzzy systems. Int. J. Gen. Syst. 2(4), 209–215 (1976)

    Article  MATH  Google Scholar 

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Acknowledgements

This research work is supported by University Grants Commission (UGC), India, vide minor research project (PSW-071/13-14 (WC2-130) (S.N. 219630)). The first author sincerely acknowledges the contributions and is very grateful to University Grants Commission.

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Authors and Affiliations

  1. Department of Mathematics, Sonarpur Mahavidyalaya, Sonarpur, WB, 700149, India

    Arindam Garai

  2. Department of Mathematics, IIEST, Shibpur, WB, 711103, India

    Palash Mandal & Tapan Kumar Roy

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  1. Arindam Garai
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  2. Palash Mandal
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  3. Tapan Kumar Roy
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Correspondence to Arindam Garai.

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Garai, A., Mandal, P. & Roy, T.K. Multipollutant Air Quality Management Strategies: T-Sets Based Optimization Technique Under Imprecise Environment. Int. J. Fuzzy Syst. 19, 1927–1939 (2017). https://doi.org/10.1007/s40815-016-0286-6

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  • DOI: https://doi.org/10.1007/s40815-016-0286-6

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