Research Article
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Year 2018, Volume: 3 Issue: 1, 28 - 41, 30.04.2018

Abstract

References

  • [1] Schell E D 1955 Distribution of a product by several properties. In: Proceedings of 2nd Symposium in Linear Programing, DCS/comptroller, HQ US Air Force, Washington DC, 615- 642.
  • [2] Haley KB 1962 New methods in mathematical programming-The solid transportation problem. Operations Research 10(4): 448- 463.
  • [3] Dalman H, G¨uzel N and Sivri M (2016) A fuzzy set-based approach to multi-objective multi-item solid transportation problem under uncertainty. International Journal of Fuzzy Systems, 18(4), 716-729.
  • [4] Dalman H (2016) Uncertain programming model for multi-item solid transportation problem, Int. J. Mach. Learn. and Cyber., doi: 10.1007/s13042-016-0538-7.
  • [5] Dalman H and SivriM (2017) Multi-objective Solid Transportation Problem in Uncertain Environment. Iranian Journal of Science and Technology, Transactions A: Science, 41(2), 505-514.
  • [6] Liu L, Zhang B and Ma W (2017) Uncertain programming models for fixed charge multi-item solid transportation problem. Soft Computing, doi: 10.1007/s00500-017-2718-0.
  • [7] Chakraborty D, Jana DK and Roy TK (2016) Expected value of intuitionistic fuzzy number and its application to solve multiobjective multi-item solid transportation problem for damageable items in intuitionistic fuzzy environment. Journal of Intelligent and Fuzzy Systems, 30(2), 1109-1122.
  • [8] Rani D and Gulati TR (2016) Uncertain multi-objective multi-product solid transportation problems. Sdhan, 41(5), 531-539.
  • [9] Liu B (2012) Why is there a need for uncertainty theory? J Uncertain Syst 6(1):3-10.
  • [10] Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin.
  • [11] Liu B (2010) Uncertainty theory: A branch of mathematics for modeling human uncertainty, SpringerVerlag, Berlin.
  • [12] Yang X, Gao J (2013) Uncertain diffrential games with application to capitalism. J Uncertain Anal Appl 1:17.
  • [13] Yang X, Gao J (2016) Linear-quadratic uncertain diffrential games with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819-826.
  • [14] Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J IntellManuf 28(3):515-525.
  • [15] Gao J, Yang X, Liu D (2017) Uncertain Shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput 56:551-556.
  • [16] Liu B (2013) Toward uncertain fiance theory. J Uncertain Anal Appl 1:1.
  • [17] Guo C, Gao J (2017) Optimal dealer pricing under transaction uncertainty. J Intell Manuf 28(3):657-665.
  • [18] Xiao C, Zhang Y, Fu Z (2016) Valuing interest rate swap contracts in uncertain fiancial market. Sustainability 8(11):1186-1196.
  • [19] Yao K, Gao J, Gao Y (2013) Some stability theorems of uncertain differential equation. Fuzzy Optim Decis Mak 12(1):3-13.
  • [20] Yao K, Liu B (2017) Uncertain regression analysis: an approach for imprecise observations. Soft Comput. doi:10.1007/ s00500- 017-2521-y.
  • [21] Liu B and Chen X (2015) Uncertain multiobjective programming and uncertain goal programming. Journal of Uncertainty Analysis and Applications, 3(1), 10.
  • [22] Liu B (2009) Theory and practice of uncertain programming, 2nd edn. Springer, Berlin.
  • [23] Zhou J, Yang F and Wang K (2014) Multi-objective optimization in uncertain random environments. Fuzzy Optimization and Decision Making, 13(4), 397-413.
  • [24] Liu B. (2014) Uncertain random graph and uncertain random network. Journal of Uncertain Systems, 8(1), 3-12.
  • [25] Ding S (2014) Uncertain minimum cost flow problem. Soft Computing, 18(11), 2201-2207.
  • [26] Sheng Y, and Gao J (2014) Chance distribution of the maximum flow of uncertain random network. Journal of Uncertainty Analysis and Applications, 2(1), 15.
  • [27] Shi G, Sheng Y and Ralescu DA (2017) The maximum flow problem of uncertain random network. Journal of Ambient Intelligence and Humanized Computing, doi: 10.1007/s12652-017-0495-3.
  • [28] Cui Q, Sheng Y (2013) Uncertain programming model for solid transportation problem. Inf Int Interdiscip J 16(2):1207-1214.
  • [29] Zhang B, Peng J, Li S, and Chen L (2016) Fixed charge solid transportation problem in uncertain environment and its algorithm. Computers and Industrial Engineering, 102, 186-197.
  • [30] Chen L, Peng J, and Zhang B (2017) Uncertain goal programming models for bicriteria solid transportation problem. Applied Soft Computing, 51, 49-59.
  • [31] Chen B, Liu Y and Zhou T (2017) An entropy based solid transportation problem in uncertain environment. Journal of Ambient Intelligence and Humanized Computing, doi: 10.1007/s12652-017-0535-z.
  • [32] Shannon CE and Weaver W (1949) The mathematical theory of communication. University of Illinois press, Urbana.
  • [33] Zadeh LA (1968) Probability measures of fuzzy events. Journal of mathematical analysis and applications, 23(2), 421-427.
  • [34] Liu B (2009) Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3-10.
  • [35] Chen X and Dai W (2011) Maximum entropy principle for uncertain variables. International Journal of Fuzzy Systems, 13(3), 232-236.
  • [36] Dai W and Chen X (2012) Entropy of function of uncertain variables. Mathematical and Computer Modelling, 55(3), 754-760.
  • [37] Liu YH and Ha M (2010) Expected value of function of uncertain variables. Journal of uncertain Systems, 4(3), 181-186.

Modelling and optimization of multi-item solid transportation problems with uncertain variables and uncertain entropy function

Year 2018, Volume: 3 Issue: 1, 28 - 41, 30.04.2018

Abstract

This paper concentrates on modeling of the uncertain entropy multi item solid transportation problem, in which the supply


capacities, demands, conveyances and transportation capacities are thought to be uncertain variables due to the obvious uncertainty of


information. In general, the transportation cost in the transportation problem is employed by the optimization aim, while the dispersals


of trips among sources, destinations, and conveyances are often ignored. In order to minimize both transportation penalties and


maximize entropy value which guarantees uniform transportation of products from sources to destinations via conveyances, this paper


holds entropy function of dispersals of trips among sources, destinations, and conveyances as a second objective function. Inside the


construction of uncertainty theory, the uncertain entropy function for transportation models is first proposed here. Thus the model is


turned into its crisp equivalent by using uncertainty theory, which can be solved by applying minimizing distance optimization


method. Finally, a numerical experiment is given to illustrate the models.


References

  • [1] Schell E D 1955 Distribution of a product by several properties. In: Proceedings of 2nd Symposium in Linear Programing, DCS/comptroller, HQ US Air Force, Washington DC, 615- 642.
  • [2] Haley KB 1962 New methods in mathematical programming-The solid transportation problem. Operations Research 10(4): 448- 463.
  • [3] Dalman H, G¨uzel N and Sivri M (2016) A fuzzy set-based approach to multi-objective multi-item solid transportation problem under uncertainty. International Journal of Fuzzy Systems, 18(4), 716-729.
  • [4] Dalman H (2016) Uncertain programming model for multi-item solid transportation problem, Int. J. Mach. Learn. and Cyber., doi: 10.1007/s13042-016-0538-7.
  • [5] Dalman H and SivriM (2017) Multi-objective Solid Transportation Problem in Uncertain Environment. Iranian Journal of Science and Technology, Transactions A: Science, 41(2), 505-514.
  • [6] Liu L, Zhang B and Ma W (2017) Uncertain programming models for fixed charge multi-item solid transportation problem. Soft Computing, doi: 10.1007/s00500-017-2718-0.
  • [7] Chakraborty D, Jana DK and Roy TK (2016) Expected value of intuitionistic fuzzy number and its application to solve multiobjective multi-item solid transportation problem for damageable items in intuitionistic fuzzy environment. Journal of Intelligent and Fuzzy Systems, 30(2), 1109-1122.
  • [8] Rani D and Gulati TR (2016) Uncertain multi-objective multi-product solid transportation problems. Sdhan, 41(5), 531-539.
  • [9] Liu B (2012) Why is there a need for uncertainty theory? J Uncertain Syst 6(1):3-10.
  • [10] Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin.
  • [11] Liu B (2010) Uncertainty theory: A branch of mathematics for modeling human uncertainty, SpringerVerlag, Berlin.
  • [12] Yang X, Gao J (2013) Uncertain diffrential games with application to capitalism. J Uncertain Anal Appl 1:17.
  • [13] Yang X, Gao J (2016) Linear-quadratic uncertain diffrential games with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819-826.
  • [14] Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J IntellManuf 28(3):515-525.
  • [15] Gao J, Yang X, Liu D (2017) Uncertain Shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput 56:551-556.
  • [16] Liu B (2013) Toward uncertain fiance theory. J Uncertain Anal Appl 1:1.
  • [17] Guo C, Gao J (2017) Optimal dealer pricing under transaction uncertainty. J Intell Manuf 28(3):657-665.
  • [18] Xiao C, Zhang Y, Fu Z (2016) Valuing interest rate swap contracts in uncertain fiancial market. Sustainability 8(11):1186-1196.
  • [19] Yao K, Gao J, Gao Y (2013) Some stability theorems of uncertain differential equation. Fuzzy Optim Decis Mak 12(1):3-13.
  • [20] Yao K, Liu B (2017) Uncertain regression analysis: an approach for imprecise observations. Soft Comput. doi:10.1007/ s00500- 017-2521-y.
  • [21] Liu B and Chen X (2015) Uncertain multiobjective programming and uncertain goal programming. Journal of Uncertainty Analysis and Applications, 3(1), 10.
  • [22] Liu B (2009) Theory and practice of uncertain programming, 2nd edn. Springer, Berlin.
  • [23] Zhou J, Yang F and Wang K (2014) Multi-objective optimization in uncertain random environments. Fuzzy Optimization and Decision Making, 13(4), 397-413.
  • [24] Liu B. (2014) Uncertain random graph and uncertain random network. Journal of Uncertain Systems, 8(1), 3-12.
  • [25] Ding S (2014) Uncertain minimum cost flow problem. Soft Computing, 18(11), 2201-2207.
  • [26] Sheng Y, and Gao J (2014) Chance distribution of the maximum flow of uncertain random network. Journal of Uncertainty Analysis and Applications, 2(1), 15.
  • [27] Shi G, Sheng Y and Ralescu DA (2017) The maximum flow problem of uncertain random network. Journal of Ambient Intelligence and Humanized Computing, doi: 10.1007/s12652-017-0495-3.
  • [28] Cui Q, Sheng Y (2013) Uncertain programming model for solid transportation problem. Inf Int Interdiscip J 16(2):1207-1214.
  • [29] Zhang B, Peng J, Li S, and Chen L (2016) Fixed charge solid transportation problem in uncertain environment and its algorithm. Computers and Industrial Engineering, 102, 186-197.
  • [30] Chen L, Peng J, and Zhang B (2017) Uncertain goal programming models for bicriteria solid transportation problem. Applied Soft Computing, 51, 49-59.
  • [31] Chen B, Liu Y and Zhou T (2017) An entropy based solid transportation problem in uncertain environment. Journal of Ambient Intelligence and Humanized Computing, doi: 10.1007/s12652-017-0535-z.
  • [32] Shannon CE and Weaver W (1949) The mathematical theory of communication. University of Illinois press, Urbana.
  • [33] Zadeh LA (1968) Probability measures of fuzzy events. Journal of mathematical analysis and applications, 23(2), 421-427.
  • [34] Liu B (2009) Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3-10.
  • [35] Chen X and Dai W (2011) Maximum entropy principle for uncertain variables. International Journal of Fuzzy Systems, 13(3), 232-236.
  • [36] Dai W and Chen X (2012) Entropy of function of uncertain variables. Mathematical and Computer Modelling, 55(3), 754-760.
  • [37] Liu YH and Ha M (2010) Expected value of function of uncertain variables. Journal of uncertain Systems, 4(3), 181-186.
There are 37 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Hasan Dalman

Publication Date April 30, 2018
Published in Issue Year 2018 Volume: 3 Issue: 1

Cite

APA Dalman, H. (2018). Modelling and optimization of multi-item solid transportation problems with uncertain variables and uncertain entropy function. Communication in Mathematical Modeling and Applications, 3(1), 28-41.
AMA Dalman H. Modelling and optimization of multi-item solid transportation problems with uncertain variables and uncertain entropy function. CMMA. April 2018;3(1):28-41.
Chicago Dalman, Hasan. “Modelling and Optimization of Multi-Item Solid Transportation Problems With Uncertain Variables and Uncertain Entropy Function”. Communication in Mathematical Modeling and Applications 3, no. 1 (April 2018): 28-41.
EndNote Dalman H (April 1, 2018) Modelling and optimization of multi-item solid transportation problems with uncertain variables and uncertain entropy function. Communication in Mathematical Modeling and Applications 3 1 28–41.
IEEE H. Dalman, “Modelling and optimization of multi-item solid transportation problems with uncertain variables and uncertain entropy function”, CMMA, vol. 3, no. 1, pp. 28–41, 2018.
ISNAD Dalman, Hasan. “Modelling and Optimization of Multi-Item Solid Transportation Problems With Uncertain Variables and Uncertain Entropy Function”. Communication in Mathematical Modeling and Applications 3/1 (April 2018), 28-41.
JAMA Dalman H. Modelling and optimization of multi-item solid transportation problems with uncertain variables and uncertain entropy function. CMMA. 2018;3:28–41.
MLA Dalman, Hasan. “Modelling and Optimization of Multi-Item Solid Transportation Problems With Uncertain Variables and Uncertain Entropy Function”. Communication in Mathematical Modeling and Applications, vol. 3, no. 1, 2018, pp. 28-41.
Vancouver Dalman H. Modelling and optimization of multi-item solid transportation problems with uncertain variables and uncertain entropy function. CMMA. 2018;3(1):28-41.