Abstract
In the present paper, we deal two types of uncertainties involved in transportation problem (TP). First one comes due to objective functions of TP depending on various uncertain situations such as road conditions, traffic conditions, variation in diesel prices, and dense fog, while other one is due to decision maker face difficulties about degrees of membership and non-membership of cost of transportation, profit of transportation, time of transportation, loss during transportation present in the problem. Several models for TP-based fuzzy and intuitionistic fuzzy sets with first uncertainty are proposed in the literature, but TP with second type of uncertainty is not dealt yet. We use interval-valued intuitionistic fuzzy (IVIF) set tool to capture second type of uncertainty. The present iterative method based on the score and accuracy functions of IVIF set captures both kinds of uncertainty involved in TP with multiple objectives. The implementation of method shows the superiority of the presented approach over those of the literature from the results quality.
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References
Ammar EE, Youness EA (2005) Study on multiobjective transportation problem with fuzzy parameters. Appl Math Comput 166:241–253
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Atanassov K, Gargov G (1989) Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343–349
Atony RJP, Savarimuthu SJ, Pathinathan T (2014) Method for solving the transporation problem using triangular intutitionistic fuzzy number. Int J Comput Algorithm 03:590–605
Angelov PP (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst 86:299–306
Bellman RE, Zadeh LA (1970) Decision making in a fuzzy environment. Manag Sci 17:B141–B164
Bharati SK, Malhotra R. Two stage intuitionistic fuzzy time minimizing transportation problem based on generalized Zadeh extension principle. Int J Syst Assur Eng Manag. 2017;1–8.
Bharati SK, Singh SR (2014a) Solving multi-objective linear programming problems using intuitionistic fuzzy optimization method: a comparative study. Int J Model Optim 4:10–16
Bharati SK, Nishad AK, Singh SR (2014) Solution of multi-objective linear programming problems in intuitionistic fuzzy environment. Adv Intell Syst Comput 236:161–171
Bharati SK, Singh SR (2014b) Intuitionistic fuzzy optimization technique in agricultural production planning: a small farm holder perspective. Int J Comput Appl 89:25–31
Bharati SK (2019) Trapezoidal intuitionistic fuzzy fractional transportation problem. In: Bansal J, Das K, Nagar A, Deep K, Ojha A (eds) Soft computing for problem solving. Advances in intelligent systems and computing, vol 817. Springer, Singapore
Bit AK, Biswas MP, Alam SS (1992) Fuzzy programming approach to multicriteria decision making transportation problem. Fuzzy Sets Syst 50:35–41
Chen SM, Tan JM (1994) Handling multicriteria fuzzy decision making problems based on vague set theory. Fuzzy Sets Syst 67:163–172
Das SK, Goswami A, Alam SS (1997) Multiobjective transportation problem with interval cost, source and destination parameters. Eur J Oper Res 117:100–112
Ebrahimnejad A (2016) Fuzzy linear programming approach for solving transportation problems with interval-valued trapezoidal fuzzy numbers. Sadhana 41(3):299–316
Ebrahimnejad A (2016) New method for solving fuzzy transportation problems with LR flat fuzzy numbers. Inf Sci 357:108–124
Ebrahimnejad A, Verdegay JL (2016) An efficient computational approach for solving type-2 intuitionistic fuzzy numbers based transportation problems. Int J Comput Intell Syst 9(6):1154–1173
Gupta A, Kumar A (2012) A new method for solving linear multiobjective transportation problems with fuzzy parameters. Appl Math Model 36:1421–1430
Hong DH, Choi C-H (2000) Multicriteria fuzzy decision making problems besed on vague set theory. Fuzzy Sets Syst 114:103–113
Hitchcock FL (1941) The distribution of a product from several sources to numerous localities. J Math Phys 20:224–230
Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48:219–225
Jana B, Roy TK (2007) Multi-objective intuitionistic fuzzy linear programming and its application in transportation model. Notes Intuit Fuzzy Sets 13:34–51
Kumar PS, Hussain RJ (2015) Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems. Int J Syst Assur Eng Manag 1:1–12
Li L, Lai KK (2000) A fuzzy approach to the multiobjective transportation problem. Comput Oper Res 27:43–57
Li DF (2005) Multiattribute decision making models and methods using Intuitionistic fuzzy sets. J Comput Syst Sci 70:73–85
Li DF (2010) Linear programming method for MADM with interval-valued intuitionistic fuzzy sets. Expert Syst Appl 37:5939–5945
Liu S-T (2003) The total cost bounds of the transportation problem with varying demand and supply. Omega 31:247–251
Liu S-T, Kao C (2004) Solving fuzzy transportation problems based on extension principle. Eur J Oper Res 153:661–674
Mahato SK, Bhunia AK. Interval-arithmetic-oriented interval computing technique for global optimization. Appl Math Res Express. 2006;1–19.
Nagoor Gani A, Razak Abdul K (2006) Two stage fuzzy transportation problem. J Phys Sci 10:63–69
Mahapatra GS, Mitra M, Roy TK (2010) Intuitionistic fuzzy multiobjective mathematical programming on reliability optimization model. Int J Fuzzy Syst 12:259–266
Peidro D, Vasant P (2011) Transportation planning with modified S-curve membership functions using an interactive fuzzy multi-objective approach. Appl Soft Comput 11:2656–2663
Ritha W, Vinotha JM (2009) Multi-objective two stage fuzzy transportation problem. J Phys Sci 13:107–120
Ringuest JL, Rinks DB (1987) Interactive solution for linear multiobjective transportation problems. Eur J Oper Res 32:96–106
Sonia MR (2003) A polynomial algorithm for a two stage time minimising transportation problem. Opsearch 39:251–266
Singh SK, Yadav SP (2014) A new approach for solving intutionistic fuzzy transporation problem of type-2. Annu Oper Res. https://doi.org/10.1007/s10479-014-1724-1
Tan CQ (2011) A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS. Expert Syst Appl 38(4):3023–3033
Verma R, Biswal MP, Biswal A (1997) Fuzzy programming technique to solve multi-objective transportation problems with some non-linear membership functions. Fuzzy Sets Syst 91:37–43
Waiel WAF (2001) A multi-objective transportation problem under fuzziness. Fuzzy Sets Syst 177:27–33
Wang H, Zhang C, Dong D (2013) Fuzzy multi-objective decision making based on interval-valued intuitionstic fuzzy sets. J Comput Appl 33:967–970
Wang ZJ, Li KW (2012) An interval-valued intuitionistic fuzzy multiattribute group decision making framework with incomplete preference over alternatives. Expert Syst 39(12):13509–13516
Wan SP, Dong JY (2015) Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees. Inf Fusion 26:49–65
Xu ZS, Chen J (2007a) An approach to group decision making based on interval-valued intuitionistic fuzzy judgement metrices. Syst Eng Theory Pract 27:126–133
Xu ZS (2007) Method for aggregating interval-valued intutionistic fuzzy information and their appliaction to decision making. Control Decis 22:215–219
Xu ZS, Chen J (2007b) On geometric aggregation over interval-valued intuitionistic fuzzy information. FSKD 2:466–471
Zangiabadi M, Maleki HR (2007) Fuzzy goal programming for multiobjective transportation problems. J Appl Math Comput 24:449–460
Zadeh LA. Fuzzy sets, information and control. 1965;8:338–353.
Zhang QS, Jiang SY, Jia BG, Luo SH (2010) Some information measures for interval-valued intuitionistic fuzzy sets. Inf Sci 180:5130–5145
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Bharati, S.K. Detailed study of uncertainty and hesitation in transportation problem. Life Cycle Reliab Saf Eng 8, 357–364 (2019). https://doi.org/10.1007/s41872-019-00095-y
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DOI: https://doi.org/10.1007/s41872-019-00095-y