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Solution of multiobjective linear programming problems in interval-valued intuitionistic fuzzy environment

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Abstract

The present paper gives a new computational algorithm for the solution of multiobjective linear programming (MOLP) problem in interval-valued intuitionistic fuzzy (IV-IF) environment. In MOLP problem which occurs in agricultural production planning, industrial planning and waste management. The parameters involved in real-life MOLP problems are impure, and several pioneer works have been done based on fuzzy or intuitionistic fuzzy sets for its compromise solutions. But many times the degree of membership and non-membership for certain element is not defined in exact numbers, so we observe another important kind of uncertainty. Thus fixed values of membership and non-membership cannot handle such uncertainty involved in real-life MOLP problem. Atanassov and Gargov first identified it and presented concept of IV-IF sets which is characterized by sub-intervals of unit interval. In this paper, we study IV-IF sets and develop a new computational method for the solution of real-life MOLP problems based on IV-IF sets. Further, the developed method has been presented in the form of a computational algorithm and implemented on a production problem, and solutions are compared with other existing methods.

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References

  • Angelov PP (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst 86:299–306

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov T (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  MATH  Google Scholar 

  • Atanassov KT, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343–349

    Article  MathSciNet  MATH  Google Scholar 

  • Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 14:141–164

    Article  MathSciNet  MATH  Google Scholar 

  • Bharati SK, Malhotra R (2017) Two stage intuitionistic fuzzy time minimizing transportation problem based on generalized Zadeh’s extension principle. Int J Syst Assur Eng Manag 8:1–8

    Article  Google Scholar 

  • Bharati SK, Singh SR (2014) Solving multi objective linear programming problems using intuitionistic fuzzy optimization method: a comparative study. Int J Model Optim 4:10

    Article  Google Scholar 

  • Bharati SK, Singh SR (2015) A note on solving a fully intuitionistic fuzzy linear programming problem based on sign distance. Int J Comput Appl 119:30–35

    Google Scholar 

  • Bharati SK, Nishad AK, Singh SR (2014) Solution of multi-objective linear programming problems in intuitionistic fuzzy environment. In: Proceedings of the second international conference on soft computing for problem solving (SocProS 2012), vol 236. Advances in Intelligent Systems and Computing, pp 161–171

  • Bharati, SK, Abhishekh, Singh SR (2017) A computational algorithm for the solution of fully fuzzy multi-objective linear programming problem. Int J Dyn Control. https://doi.org/10.1007/s40435-017-0355-1

  • Chanas S, Kuchta D (1996) A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy Sets Syst 82:299–305

    Article  MathSciNet  Google Scholar 

  • Chinneck JW, Ramadan K (2000) Linear programming with interval coefficients. J Oper Res Soc 5:209–220

    Article  MATH  Google Scholar 

  • De SK, Biswas RA, Ray R (2000) Some operations on intuitionistic fuzzy sets. Fuzzy Sets Syst 114:474–487

    Article  MathSciNet  Google Scholar 

  • Dubey D, Mehra A (2011) Linear programming with triangular intuitionistic fuzzy number, EUSFLAT-LFA 2011, vol 1. Advances in Intelligent Systems Research, Atlantis Press, pp 563–569

  • Dubey D, Chandra S, Mehra A (2012) Fuzzy linear programming under interval uncertainty based on IFS representation. Fuzzy Sets Syst 188:68–87

    Article  MathSciNet  MATH  Google Scholar 

  • Garg A, Singh SR (2010) Optimization under uncertainty in agricultural production planning. iconcept Pocket J Comput Intell Financ Eng 1:1–12

    Google Scholar 

  • Hwang CL, Chen SJ (1992) Fuzzy multiple attribute decision making: methods and applications. Springer, Berlin

    MATH  Google Scholar 

  • Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48:219–225

    Article  MATH  Google Scholar 

  • Itoh T, Ishii H, Nanseki T (2003) Fuzzy crop planning problem under uncertainty in agriculture management. Int J Prod Econ 81–82:555–558

    Article  Google Scholar 

  • Jana, B, Roy TK (2007) Multiobjective intuitionistic fuzzy linear programming and its application in transportation model. NIFS-13-1-34-51, pp 1–18

  • Jiuping X (2011) A kind of fuzzy multi-objective linear programming problems based on interval valued fuzzy sets. J Syst Sci Complex 14:149–158

    MathSciNet  MATH  Google Scholar 

  • Lee ES, Li RJ (1993) Fuzzy multi objective programming and compromise programming with Pareto-Optimum. Fuzzy Sets Syst 53:275–288

    Article  MATH  Google Scholar 

  • Li DF (2010) Linear programming method for MADM with interval valued intuitionistic fuzzy sets. Expert Syst Appl 37:5939–5945

    Article  Google Scholar 

  • Malhotra R, Bharati SK (2016) Intuitionistic fuzzy two stage multiobjective transportation problems. Adv Theor Appl Math 11:305–316

    Google Scholar 

  • Mondal TK, Samanta SK (2012) Generalized intuitionistic fuzzy set. J Fuzzy Math 10:839–861

    MathSciNet  MATH  Google Scholar 

  • Nishad AK, Bharati SK, Singh SR (2014) A new centroid method of ranking for intuitionistic fuzzy numbers. In: Proceedings of the second international conference on soft computing for problem solving (SocProS 2012), vol 236. Advances in Intelligent Systems and Computing, pp 151–159

  • Parvathi R, Malathi C (2012) Intuitionistic fuzzy linear optimization. Notes Intuit Fuzzy Sets 18:48–56

    MATH  Google Scholar 

  • Parvathi R, Parvathi CM (2011) Intuitionistic fuzzy linear programming problems. World Appl Sci J 17:1802–1807

    MATH  Google Scholar 

  • Shaocheng T (1994) Interval number and fuzzy number linear programming. Fuzzy Sets Syst 66:301–306

    Article  MathSciNet  Google Scholar 

  • Su JS (2007) Fuzzy linear programming with interval valued fuzzy set and ranking. Int J Contemp Math Sci 2:393–410

    Article  MathSciNet  MATH  Google Scholar 

  • Tanaka HK, Asai K (1984) Fuzzy linear programming problems with fuzzy numbers. Fuzzy Sets Syst 139:1–10

    Article  MathSciNet  MATH  Google Scholar 

  • Zangiababdi M, Maleki HR (2013) Fuzzy goal programming technique to solve multiobjective transportation problem with some nonlinear membership functions. Iran J Fuzzy Syst 10:61–74

    MathSciNet  MATH  Google Scholar 

  • Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1:45–55

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Kamala Nehru College, University of Delhi, Delhi, 110049, India

    S. K. Bharati

  2. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    S. R. Singh

Authors
  1. S. K. Bharati
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  2. S. R. Singh
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Correspondence to S. K. Bharati.

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Communicated by V. Loia.

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Bharati, S.K., Singh, S.R. Solution of multiobjective linear programming problems in interval-valued intuitionistic fuzzy environment. Soft Comput 23, 77–84 (2019). https://doi.org/10.1007/s00500-018-3100-6

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