A new fuzzy transportation algorithm for finding fuzzy optimal solution

There are several methods, in literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, two new methods (based on fuzzy linear programming formulation and classical transportation methods) are proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as trapezoidal fuzzy numbers. The advantages of the proposed methods over existing methods are also discussed. To illustrate the proposed methods a fuzzy transportation problem (FTP) is solved by using the proposed methods and the obtained results are discussed. The proposed methods are easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

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PSK Method for Solving Intuitionistic Fuzzy Solid Transportation Problems

International Journal of Fuzzy System Applications ◽

10.4018/ijfsa.2018100104 ◽

2018 ◽

Vol 7 (4) ◽

pp. 62-99 ◽

Cited By ~ 6

Author(s):

P.Senthil Kumar

Keyword(s):

Real Life ◽

Optimal Solution ◽

Transportation Problems ◽

Intuitionistic Fuzzy Numbers ◽

Intuitionistic Fuzzy ◽

Fuzzy Optimal Solution ◽

Fuzzy Representation ◽

Objective Value

This article proposes a method for solving intuitionistic fuzzy solid transportation problems (IFSTPs) in which only the transportation costs are represented in terms of intuitionistic fuzzy numbers (IFNs). The remaining parameters, namely: supply, demand and conveyance capacity, are all considered into crisp numbers. This type of STP is called a type-2 IFSTP. When solving the real life solid transportation problems (STPs) those tend to face the uncertainty state as well as hesitation due to many uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this article, the author tried to categorise the STPs under the uncertain environment. He formulates the intuitionistic fuzzy STPs and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P.Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the type-2 IFSTP and the optimal objective value of type-2 IFSTP is obtained in terms of TIFN. The main advantage of this method is that the optimal solution of type-2 IFSTP is obtained without using the basic feasible solution and the method of testing optimality. Moreover, the proposed method is computationally very simple and easy to understand. A case study is presented to illustrate the procedure of the proposed method.

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Exact fuzzy optimal solution of fully fuzzy linear programming problems with unrestricted fuzzy variables

Applied Intelligence ◽

10.1007/s10489-011-0318-8 ◽

2011 ◽

Vol 37 (1) ◽

pp. 145-154 ◽

Cited By ~ 15

Author(s):

Jagdeep Kaur ◽

Amit Kumar

Keyword(s):

Linear Programming ◽

Optimal Solution ◽

Fuzzy Linear Programming ◽

Fuzzy Variables ◽

Fuzzy Optimal Solution ◽

Linear Programming Problems

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Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

Mathematical Problems in Engineering ◽

10.1155/2016/7069804 ◽

2016 ◽

Vol 2016 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Aihong Ren

Keyword(s):

Linear Programming ◽

Programming Problem ◽

Linear Programming Problem ◽

Function Method ◽

Optimal Solution ◽

Ranking Function ◽

Objective Functions ◽

Bilevel Linear Programming ◽

Fuzzy Optimal Solution ◽

Deviation Degree

This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.

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