Ranking approach based on incenter in triangle of centroids to solve type-1 and type-2 fuzzy transportation problem

Several methods have been introduced in literature to rank a fuzzy number for solving fuzzy transportation problem. But complexity and problem specific nature encourages the readers to work more on ranking techniques. In the present paper, incentre of centroids has been employed to convert trapezoidal fuzzy transportation problem of type 1 and type-2 both into crisp one, which is easy to approach and is applicable on existent problems of transportation. Once the crisp form is obtained from fuzzy, it is resolved by north-west corner technique to obtain the primary solution. Optimality is checked through modified distribution method. The merits of the proposed ranking technique over existing schemes are conferred by some examples. The acquired consequences show the efficiency of the suggested method.Several methods have been introduced in literature to rank a fuzzy number for solving fuzzy transportation problem. But complexity and problem specific nature encourages the readers to work more on ranking techniques. In the present paper, incentre of centroids has been employed to convert trapezoidal fuzzy transportation problem of type 1 and type-2 both into crisp one, which is easy to approach and is applicable on existent problems of transportation. Once the crisp form is obtained from fuzzy, it is resolved by north-west corner technique to obtain the primary solution. Optimality is checked through modified distribution method. The merits of the proposed ranking technique over existing schemes are conferred by some examples. The acquired consequences show the efficiency of the suggested method.

[1]  Shyi-Ming Chen,et al.  A NEW METHOD FOR HANDLING MULTICRITERIA FUZZY DECISION-MAKING PROBLEMS USING FN-IOWA OPERATORS , 2003, Cybern. Syst..

[2]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads , 2009, Expert Syst. Appl..

[3]  Suresh Kumar Goyal,et al.  Improving VAM for Unbalanced Transportation Problems , 1984 .

[4]  Amarpreet Kaur,et al.  A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers , 2012, Appl. Soft Comput..

[5]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers , 2007, Applied Intelligence.

[6]  Nirbhay Mathur,et al.  Trapezoidal fuzzy model to optimize transportation problem , 2016, Int. J. Model. Simul. Sci. Comput..

[7]  Mangey Ram,et al.  Role of Fuzzy Logic in Flexible Manufacturing System , 2018 .

[8]  Amit Kumar,et al.  A new method for solving fuzzy transportation problems using ranking function , 2011 .

[9]  C. Ramakrishnan.  An Improvement to Goyal's Modified VAM for the Unbalanced Transportation Problem , 1988 .

[10]  Ali Ebrahimnejad,et al.  A simplified new approach for solving fuzzy transportation problems with generalized trapezoidal fuzzy numbers , 2014, Appl. Soft Comput..

[11]  H. Zimmermann.  Fuzzy programming and linear programming with several objective functions , 1978 .

[12]  Suresh Kumar Goyal,et al.  Resolution of Degeneracy in Transportation Problems , 1988 .

[13]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights , 2012, Expert Syst. Appl..

[14]  T. Koopmans.  Optimum Utilization of the Transportation System , 1949 .