Abstract
There are several methods for solving fuzzy critical path problems in which ranking approaches are used to compare fuzzy numbers. In this paper, some fuzzy critical path problems are chosen to show that the results obtained with fuzzy critical path methods that use existing ranking approaches are not appropriate according to real life situations. To obtain appropriate results, a new ranking approach the Mehar ranking approach, is proposed for comparing LR flat fuzzy numbers. To show the advantages of the Mehar ranking approach over existing approaches, selected fuzzy critical path problems are solved by using the existing methods together with the Mehar ranking approach. It is shown that the obtained results are appropriate.
Highlights
The theory of fuzzy sets was first introduced by Zadeh [24]
Certain fuzzy critical path problems are chosen to show that the results obtained by using the existing fuzzy critical path methods with existing ranking approaches are not appropriate according to real life situations
It is shown that the results of the fuzzy critical path problem chosen in Example 3.1, and obtained by using the different existing fuzzy critical path methods [18, 22, 4, 13, 14, 16, 12, 10, 5, 6, 19] with different existing ranking approaches [21, 17, 15, 7, 23, 8, 3, 25, 2], are not appropriate according to real life situations
Summary
The theory of fuzzy sets was first introduced by Zadeh [24]. Since the theory of fuzzy sets has been applied in many fields such as pattern recognition, control theory, management sciences, and picture processing. Several authors [18, 22, 4, 13, 14, 16, 12, 10, 5, 6, 19] have proposed fuzzy critical path methods that are based on different ranking approaches for solving fuzzy critical path problems. Certain fuzzy critical path problems are chosen to show that the results obtained by using the existing fuzzy critical path methods with existing ranking approaches are not appropriate according to real life situations. To obtain appropriate results for fuzzy critical path problems, a new ranking approach named ‘Mehar's’ is proposed for comparing LR flat fuzzy numbers.
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