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Fuzzy Optimization and Decision Making
Published in: Fuzzy Optimization and Decision Making 1/2019

06-02-2018

A method to solve linear programming problem with interval type-2 fuzzy parameters

Authors: Pradip Kundu, Saibal Majumder, Samarjit Kar, Manoranjan Maiti

Published in: Fuzzy Optimization and Decision Making | Issue 1/2019

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Abstract

In this paper, we propose a method to solve linear programming network problems with constraints using interval type-2 fuzzy variables. The method is developed using generalized credibility measure, and lower and upper membership functions of an interval type-2 fuzzy variable. This method has been applied to solve a solid transportation problem with availabilities and demands of a product, and conveyance capacities, which are represented by trapezoidal interval type-2 fuzzy variables. Moreover, we have also shown that different types of problems with objective function having interval type-2 fuzzy parameters can be solved using the proposed method. Apart from a solid transportation problem, we demonstrate its applicability by solving two different network problems: (i) a shortest path problem and (ii) a minimum spanning tree problem. Suitable numerical examples are provided to illustrate the proposed method
previous article Optimal incentive contracts under loss aversion and inequity aversion

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Literature
Aliev, R. A., Pedrycz, W., Guirimov, B., Aliev, R. R., Ilhan, U., Babagil, M., et al. (2011). Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization. Information Sciences, 181(9), 1591–1608.MathSciNetCrossRef
Chen, T. Y. (2013). An interactive method for multiple criteria group decision analysis based on interval type-2 fuzzy sets and its application to medical decision making. Fuzzy Optimization and Decision Making, 12(3), 323–356.MathSciNetCrossRefMATH
Dubois, D., & Prade, H. (1998). Possibility theory: An approach to computerized processing of uncertainty. New York: Plenum.
Figueroa-García, J. C., & Hernández, G. (2012). A transportation model with interval type-2 fuzzy demands and supplies. Lecture Notes in Computer Science, 7389, 610–617.CrossRef
Figueroa-García, J. C., & Hernández, G. (2014). A method for solving linear programming models with interval type-2 fuzzy constraints. Pesquisa Operacional, 34(1), 73–89.CrossRef
Jiménez, F., & Verdegay, J. L. (1999). Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach. European Journal of Operational Research, 117, 485–510.CrossRefMATH
Kundu, P., Kar, S., & Maiti, M. (2014a). Multi-objective solid transportation problems with budget constraint in uncertain environment. International Journal of Systems Science, 45(8), 1668–1682.MathSciNetCrossRefMATH
Kundu, P., Kar, S., & Maiti, M. (2014b). Fixed charge transportation problem with type-2 fuzzy variables. Information Sciences, 255, 170–186.MathSciNetCrossRefMATH
Kundu, P., Kar, S., & Maiti, M. (2015). Multi-item solid transportation problem with type-2 fuzzy parameters. Applied Soft Computing, 31, 61–80.CrossRef
Lee, S., & Lee, K. H. (2001). Shortest path problem in a type-2 weighted graph. Journal of Korea Fuzzy and Intelligent Systems Society, 11(6), 528–531.
Liu, P., Yang, L., Wang, L., & Li, S. (2014). A solid transportation problem with type-2 fuzzy variables. Applied Soft Computing, 24, 543–558.CrossRef
Liu, Z. Q., & Liu, Y. K. (2010). Type-2 fuzzy variables and their arithmetic. Soft Computing, 14, 729–747.CrossRefMATH
Maali, Y., & Mahdavi-Amiri, N. (2014). A triangular type-2 multi-objective linear programming model and a solution strategy. Information Sciences, 279, 816–826.MathSciNetCrossRefMATH
Mendel, J. M. (2007). Computing with words: Zadeh, turing, popper and occam. IEEE Computational Intelligence Magazine, 2(4), 10–17.CrossRef
Mendel, J. M., & John, R. I. (2002). Type-2 fuzzy sets made simple. IEEE Transactions on Fuzzy Systems, 10(2), 307–315.CrossRef
Mendel, J. M., John, R. I., & Liu, F. L. (2006). Interval type-2 fuzzy logical systems made simple. IEEE Transactions on Fuzzy Systems, 14(6), 808–821.CrossRef
Pramanik, S., Jana, D. K., Mondal, S. K., & Maiti, M. (2015). A fixed-charge transportation problem in two-stage supply chain network in Gaussian type-2 fuzzy environments. Information Sciences, 325, 190–214.MathSciNetCrossRefMATH
Qin, R., Liu, Y. K., & Liu, Z. Q. (2011). Methods of critical value reduction for type-2 fuzzy variables and their applications. Journal of Computational and Applied Mathematics, 235, 1454–1481.MathSciNetCrossRefMATH
Vasant, P. (2013). Hybrid linear search, genetic algorithms, and simulated annealing for fuzzy non-linear industrial production planning problems. In P. Vasant (Ed.), Meta-heuristics optimization algorithms in engineering, business, economics, and finance (pp. 87–109). Hershey, PA: IGI Global.CrossRef
Wu, X. L., & Liu, Y. K. (2012). Optimizing fuzzy portfolio selection problems by parametric quadratic programming. Fuzzy Optimization and Decision Making, 11(4), 411–449.MathSciNetCrossRefMATH
Yang, L., & Liu, L. (2007). Fuzzy fixed charge solid transportation problem and algorithm. Applied Soft Computing, 7, 879–889.CrossRef
Metadata
Title
A method to solve linear programming problem with interval type-2 fuzzy parameters
Authors
Pradip Kundu
Saibal Majumder
Samarjit Kar
Manoranjan Maiti
Publication date
06-02-2018
Publisher
Springer US
Published in
Fuzzy Optimization and Decision Making / Issue 1/2019
Print ISSN: 1568-4539
Electronic ISSN: 1573-2908
DOI
https://doi.org/10.1007/s10700-018-9287-2

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