Multiple Objective Linear Programming Problem (MOLPP) deals with the problems where more than one objective are present. In decision making problems of real life, there exists many scenarios where the information regarding the problem is full of uncertainty and vagueness. In such cases, crisp MOLPP fails to solve these problems because of imprecise data. To overcome this difficulty, Fuzzy Multiple Objective Linear Programming Problem (FMOLPP) is used. On the other side, similarity measure (SMr) indicates how similar two objects are. The aim of the present study is to introduce a new method to solve Triangular Fuzzy Multi Objective Linear Programming Problem (TFMOLPP) with the help of a novel SMr. To carry out the present research, firstly, a novel SMr has been introduced. All the salient traits of an ideal SMr has been examined theoretically and also validated through numerical examples. Secondly, a closeness degree has been formulated to maximize the similarity of each of the objective value with the corresponding ideal value, regarded as the optimistic value (OV) of that objective. Here the aim of the present research is to find a solution which provides the objective values nearer to the ideal objective values. The proposed method has been illustrated by modelling and solving a numerical example. It could be observed that the proposed SMr based solution process elicits an efficient solution which provides the objective values nearer to their ideal values. To check the reliability of the proposed model, the results have been compared with the solutions obtained by an existing method.

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A Novel Approach to Solve Triangular Fuzzy Multi Objective Linear Programming Problem Using Novel Similarity Measure

  • Pallabi Pal,
  • Sayanta Chakraborty,
  • Apu Kumar Saha

摘要

Multiple Objective Linear Programming Problem (MOLPP) deals with the problems where more than one objective are present. In decision making problems of real life, there exists many scenarios where the information regarding the problem is full of uncertainty and vagueness. In such cases, crisp MOLPP fails to solve these problems because of imprecise data. To overcome this difficulty, Fuzzy Multiple Objective Linear Programming Problem (FMOLPP) is used. On the other side, similarity measure (SMr) indicates how similar two objects are. The aim of the present study is to introduce a new method to solve Triangular Fuzzy Multi Objective Linear Programming Problem (TFMOLPP) with the help of a novel SMr. To carry out the present research, firstly, a novel SMr has been introduced. All the salient traits of an ideal SMr has been examined theoretically and also validated through numerical examples. Secondly, a closeness degree has been formulated to maximize the similarity of each of the objective value with the corresponding ideal value, regarded as the optimistic value (OV) of that objective. Here the aim of the present research is to find a solution which provides the objective values nearer to the ideal objective values. The proposed method has been illustrated by modelling and solving a numerical example. It could be observed that the proposed SMr based solution process elicits an efficient solution which provides the objective values nearer to their ideal values. To check the reliability of the proposed model, the results have been compared with the solutions obtained by an existing method.