Abstract
In modeling of an optimization problem, situations arise when the information about the objective functions and/or constraints are imprecise. One efficient approach to deal with such problems is considering the solution of such optimization problems in intuitionistic fuzzy environment. Here, we have considered the imprecise coefficients of objective functions and constraints as intuitionistic fuzzy numbers and are approximated by its expected interval value. Further, a goal programming approach is applied to solve such problems. The developed method has been illustrated by implementing on a multi objective programming problem of agricultural production management system.
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References
Adrian B (2008) Trapezoidal approximations of intuitionistic fuzzy numbers expressed by value, ambiguity, width and weighted expected value. NIFS 14:130–147
Adrian BK, Coroiann LC (2009) A method to obtain trapezoidal approximations of intuitionistic fuzzy numbers from trapezoidal approximations of fuzzy numbers. NIFS 15:113–125
Angelov PP (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst 86:299–306
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Bharati SK, Nishad AK, Singh SR (2014) Solution of multi-objective linear programming under intuitionistic fuzzy environment. In: Proceedings of the second international conference on soft computing for problem solving (Soc.Pros 2012). December 28–30, 2012, Advances in Intelligent Systems and Computing 236, doi: 10.1007/978-81-322-1602-5_18, © Springer
Biswas A, Pal BB (2005) Application of fuzzy goal programming technique to land use planning in agricultural system. Omega 33:391–398
Chakraborty M, Gupta S (2002) Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy Sets Syst 125:335–342
Charnes A, Cooper WW (1961) Management models of industrial applications of linear program. Wiley, New York
Cohon JL (1978) Multi objective programming and planning. Academic Press, New York
Dubois D, Prade H (1987) The mean value of a fuzzy number. Fuzzy Sets Syst 24:279–300
Dutta D, Tiwari RN, Rao JR (1992) Multiple objective linear fractional programming-a fuzzy set theoric approach. Fuzzy Sets Syst 52:39–45
Grzegorzewski P (2003) Distances and orderings in a family of intuitionistic fuzzy numbers. In: Proceedings of the third conference on fuzzy logic and technology (Eusflat03), pp. 223–227
Hassan MN (2010) A new ranking method for intuitionistic fuzzy numbers. Int J Fuzzy Syst 12(1):80–86
Heilpern S (1992) The expected value of a fuzzy number. Fuzzy Sets Syst 47:81–86
Ignizio JP (1976) Goal programming and extensions. D.C.Heath, Lexington, Mass
Inuiguchi M, Kume Y (1991) A goal programming problems with interval coefficients and target intervals. Eur J Oper Res 52:345–360
Inuiguchi H, Tanaka H (1990) Multi-objective programming in optimization of the interval objective function. Eur J Oper Res 48:219–225
Kuwano H (1996) On the fuzzy multi-objective linear programming problems: goal programming approach. Fuzzy Sets Syst 82:57–64
Lai YJ, Hwang CL (1994) Fuzzy multiple objective decision making. Springer, New york
Luhandjula MK (1984) Fuzzy approaches for multiple objective linear fractional optimization. Fuzzy Sets Syst 13:11–23
Mishra B, Singh SR (2013) Linear fractional programming procedure for multi objective linear programming problem in agriculture system. Int J Comput Appl 61(20):45–52
Mohamed RH (1997) The relationship between goal programming and fuzzy programming. Fuzzy Sets Syst 89:215–222
Mohanty BK, Vijayaraghawan TAS (1995) A multiobjective programming problem and its equivalent goal programming problem with approprite priorities and aspiration levels: a fuzzy approach. Comput Oper Res 22(8):771–778
Narasimhan R (1981) On fuzzy goal programming-some comments. Decis Sci 12:532–538
Nishad A K, Bharati S K, Singh S R (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), December 28–30, 2012, Advances in Intelligent Systems and Computing 236, doi: 10.1007/978-81-322-1602-5_17, © Springer India
Pal BB, Sen S (2008) A goal programming procedure for solving interval valued multi-objective fractional programming problems. 978-1-4244-2963-9/08/$25.00© 2008 IEEE
Pal BB, Moitra BN, Maulik U (2003) A goal programming procedure for fuzzy multiobjective linear fractional programming problem. Fuzzy Sets Syst 139:395–405
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Zeng X, Kang S, Li F, Zhang L, Guo P (2010) Fuzzy multiobjective linear programming applying to crop area planning. Agric Water Manag 98:134–142
Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1:45–55
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Authors are thankful to University Grants Commission, New Delhi, India for providing financial assistance to carry out this research work.
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Nishad, A.K., Singh, S.R. Solving multi-objective decision making problem in intuitionistic fuzzy environment. Int J Syst Assur Eng Manag 6, 206–215 (2015). https://doi.org/10.1007/s13198-014-0331-5
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DOI: https://doi.org/10.1007/s13198-014-0331-5