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

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

[1]  J.M. Mendel,et al.  Computing with Words: Zadeh, Turing, Popper and Occam , 2007, IEEE Computational Intelligence Magazine.

[2]  Baoding Liu,et al.  Chance constrained programming with fuzzy parameters , 1998, Fuzzy Sets Syst..

[3]  P. Vasant,et al.  Hybrid Linear Search, Genetic Algorithms, and Simulated Annealing for Fuzzy Non-Linear Industrial Production Planning Problems , 2013 .

[4]  José L. Verdegay,et al.  Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach , 1999, Eur. J. Oper. Res..

[5]  Yashar Maali,et al.  A triangular type-2 multi-objective linear programming model and a solution strategy , 2014, Inf. Sci..

[6]  Samarjit Kar,et al.  Multi-item solid transportation problem with type-2 fuzzy parameters , 2015, Appl. Soft Comput..

[7]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[8]  Shyamal Kumar Mondal,et al.  A fixed-charge transportation problem in two-stage supply chain network in Gaussian type-2 fuzzy environments , 2015, Inf. Sci..

[9]  Jerry M. Mendel,et al.  Type-2 fuzzy sets made simple , 2002, IEEE Trans. Fuzzy Syst..

[10]  Yian-Kui Liu,et al.  Optimizing fuzzy portfolio selection problems by parametric quadratic programming , 2012, Fuzzy Optim. Decis. Mak..

[11]  Juan Carlos Figueroa–García,et al.  A method for solving linear programming models with Interval Type-2 fuzzy constraints , 2014 .

[12]  Witold Pedrycz,et al.  Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization , 2011, Inf. Sci..

[13]  Ting-Yu Chen,et al.  An interactive method for multiple criteria group decision analysis based on interval type-2 fuzzy sets and its application to medical decision making , 2013, Fuzzy Optim. Decis. Mak..

[14]  Didier Dubois,et al.  Possibility Theory - An Approach to Computerized Processing of Uncertainty , 1988 .

[15]  Jerry M. Mendel,et al.  Uncertainty measures for interval type-2 fuzzy sets , 2007, Inf. Sci..

[16]  Juan Carlos Figueroa García,et al.  A Transportation Model with Interval Type-2 Fuzzy Demands and Supplies , 2012, ICIC.

[17]  Yian-Kui Liu,et al.  Type-2 fuzzy variables and their arithmetic , 2010, Soft Comput..

[18]  Pei Liu,et al.  A solid transportation problem with type-2 fuzzy variables , 2014, Appl. Soft Comput..

[19]  Manoranjan Maiti,et al.  Fixed charge transportation problem with type-2 fuzzy variables , 2014, Inf. Sci..

[20]  Lixing Yang,et al.  Fuzzy fixed charge solid transportation problem and algorithm , 2007, Appl. Soft Comput..

[21]  Yian-Kui Liu,et al.  Methods of critical value reduction for type-2 fuzzy variables and their applications , 2011, J. Comput. Appl. Math..

[22]  Jerry M. Mendel,et al.  Interval Type-2 Fuzzy Logic Systems Made Simple , 2006, IEEE Transactions on Fuzzy Systems.

[23]  Manoranjan Maiti,et al.  Multi-objective solid transportation problems with budget constraint in uncertain environment , 2014, Int. J. Syst. Sci..