Parmpreet Kaur

RM Approach for Ranking of Generalized Trapezoidal Fuzzy Numbers

Ranking of fuzzy numbers play an important role in decision making, optimization and forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples, it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (3): 6833) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as an RM approach. The main advantage of the proposed approach is that the proposed approach provides the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets and Systems 118 (3): 375).

RM approach for ranking of L – R type generalized fuzzy numbers

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Syst Appl 36:6833–6842, 2009) is incorrect. The main aim of this paper is to propose a new approach for the ranking of L–R type generalized fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as RM approach. The main advantage of the proposed approach is that it provides the correct ordering of generalized and normal fuzzy numbers and it is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets Syst 118:375–385, 2001).

A new approach for ranking nonnormal p-norm trapezoidal fuzzy numbers

Ranking of fuzzy numbers play an important role in decision-making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that the results proposed by Chen and Tang [C.C. Chen, H.C. Tang, Ranking of nonnormal p-norm trapezoidal fuzzy numbers with integral value, Computers and Mathematics with Applications 56 (2008) 2340-2346] are applicable only for the nonnormal p-norm trapezoidal fuzzy numbers with equal heights and a new approach is proposed for the ranking of nonnormal p-norm trapezoidal fuzzy numbers with different heights. The results proposed by Chen and Tang are modified and to illustrate the proposed approach the counter examples are solved using the proposed approach. It is also shown that the proposed approach and the results, obtained by using the proposed approach, are valid.

Linear programming approach for solving fuzzy critical path problems with fuzzy parameters

Abstract To the best of our knowledge, there is no method in the literature to find the fuzzy optimal solution of fully fuzzy critical path (FFCP) problems i.e., critical path problems in which all the parameters are represented by LR flat fuzzy numbers. In this paper, a new method is proposed for the same. Also, it is shown that it is better to use JMD representation of LR flat fuzzy numbers in the proposed method as compared to the other representation of LR flat fuzzy numbers.

A new approach for fuzzy critical path analysis

A new method, named as Mehars method is proposed to solve fuzzy critical path problems. To show the advantages of the Mehars method over an existing method the results of a fuzzy critical path problem, obtained by using the existing and Mehars method, are compared. Also, it is shown that although the results, obtained by using the existing and Mehars method, are mathematically correct but the obtained and the existing results have no physical meaning. To overcome this shortcoming a new subtraction operation, named as Mehars subtraction, is introduced and the Mehars method is further modified with Mehars subtraction.

Fuzzy optimal solution of fully fuzzy project crashing problems with new representation of LR flat fuzzy numbers

In this paper, a new method, named as Mehars method, is proposed for solving fully fuzzy project crashing problems and a new representation of LR flat fuzzy numbers, named as JMD representation of LR flat fuzzy numbers, are introduced. Also, it is shown that it is better to use JMD representation of LR flat fuzzy numbers as compared to the existing representation of LR flat fuzzy numbers.