Ranking function-based solutions of fully fuzzified minimal cost flow problem

Ghatee, Mehdi; Hashemi, S. Mehdi

doi:10.1016/j.ins.2007.05.007

Cited by 37 publications

(37 citation statements)

References 49 publications

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“…(1) In all the existing methods [9][10][11][12][13][14] the fuzzy linear programming formulation of balanced fully fuzzy minimal cost flow problem is presented but in none of the paper it is provided that how it will be checked that chosen fully fuzzy minimal cost flow problem is balanced or unbalanced, due to which the following shortcomings are occurring in the existing work.…”

Section: Shortcomings Of the Existing Methodsmentioning

confidence: 99%

“…Since total fuzzy supply is not equal to the total fuzzy demand. So it is an unbalanced fully fuzzy minimal cost flow problem while Ghatee and Hashemi [9] have obtained the optimal solution of the problem by using the fuzzy linear programming formulation of balanced fully fuzzy minimal cost flow problems. Similarly it is clear from the data presented in [14, Table 2, pp.…”

Section: Shortcomings Of the Existing Methodsmentioning

confidence: 99%

“…On the basis of the shortcomings of the existing methods [9][10][11][12][13][14], pointed out in Section 4, it may be concluded that the existing methods may be used only to find the exact fuzzy optimal solution of balanced fuzzy transportation problems, e.g., the balanced fuzzy transportation problem, chosen in Example 1, may be solved by using the existing methods [9][10][11][12][13][14].…”

Section: Limitations Of Existing Methodsmentioning

confidence: 99%

“…Ghatee and Hashemi [9,10,11,12] proposed the fuzzy linear programming formulation of balanced fully fuzzy minimal cost flow problems. In case of balanced fully fuzzy transportation problem, the same fuzzy linear programming formulation will be converted into the following fuzzy linear programming formulation:…”

Section: Linear Programming Formulation Of Fuzzy Transportation Problemsmentioning

confidence: 99%

“…To deal with uncertainties of supply and demand parameters, Gupta and Mehlawat [15] transformed the past data pertaining to the amount of supply of the i th supply point and the amount of demand of the j th demand point using level (λ, ρ) interval-valued fuzzy numbers. Ghatee and Hashemi [9] investigated fully fuzzified minimal cost flow problems considering a large variety of ranking functions. Ghatee and Hashemi [10] presented some different cases of fuzzy minimal cost flow problems utilizing a total order and nominal flows.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Application of Classical Transportation Methods to Find the Fuzzy Optimal Solution of Fuzzy Transportation Problems

Kumar

Kaur

2011

Fuzzy Information and Engineering

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To the best of our knowledge till now there is no method in the literature to find the exact fuzzy optimal solution of unbalanced fully fuzzy transportation problems. In this paper, the shortcomings and limitations of some of the existing methods for solving the problems are pointed out and to overcome these shortcomings and limitations, two new methods are proposed to find the exact fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as LR flat fuzzy numbers. To show the advantages of the proposed methods over existing methods, a fully fuzzy transportation problem which may not be solved by using any of the existing methods, is solved by using the proposed methods and by comparing the results, obtained by using the existing methods and proposed methods. It is shown that it is better to use proposed methods as compared to existing methods.

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