Pushpinder Singh

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.

A new similarity measure between interval-valued intuitionistic fuzzy sets

Interval-valued intuitionistic fuzzy sets gained attention from researcher for their applications in various field. The main of this paper is to propose a new similarity measure for interval-valued intuitionistic fuzzy sets. Some properties of proposed similarity measure has been presented this paper. Also the proposed and existing similarity measure are compared to show that the proposed similarity measure is more reasonable than some of the existing similarity measures. For practical use, proposed similarity measure is applied to pattern recognition and in a bidirectional approximate reasoning systems.

Risk analysis of combustion system using vague ranking method

A new approach for vague risk analysis based on the ranking of trapezoidal vague sets is proposed. Firstly, a new method for ranking of vague sets is presented. Then, the proposed method is applied to developed a new method for dealing with vague risk analysis problems. This analysis helps us to find out the probability of failure of each components of combustion system, which could be used for managerial decision making and future system maintenance strategy. The proposed method provides a useful way for handling vague risk analysis problems.

Two Phase Method for Solving Fuzzy Linear Programming Problems using Ranking of Generalized Fuzzy Numbers

Ranking of fuzzy numbers play an important role in decision making problems. Fuzzy numbers must be ranked before an action is taken by a decision maker. Chen (Operations on fuzzy numbers with function principal, Tamkang Journal of Management Science 6 (1985) 13-25) pointed out that in many cases it is not to possible to restrict the membership function to the normal form and proposed the concept of generalized fuzzy numbers. In this paper two phase method is proposed for solving a special type of fuzzy linear programming (FLP) problems using generalized fuzzy numbers. To illustrate the proposed method a numerical example is solved and the advantages of the proposed method are discussed. Since the proposed method is a direct ex- tension of classical method so it is very easy to understand and apply the proposed method to find the fuzzy optimal solution of FLP problems occurring in the real life situations.