Ranking Z-numbers with an improved ranking method for generalized fuzzy numbers

A new improved method for ranking generalized fuzzy numbers where the weight of centroid points, degrees of fuzziness and the spreads of fuzzy numbers are taken into consideration is proposed, which can overcome some drawbacks of exiting methods and is very efficient for evaluating symmetric fuzzy numbers and crisp numbers.

Abstract

Z-number, a new concept describes both the restriction and the reliability of evaluation, is more applicable than fuzzy numbers in the fields of decision making, risk assessment etc. However, how to deal with the restriction and the reliability properly is still a problem which is discussed few and inadequately in the existing literatures. In this paper, firstly, a new improved method for ranking generalized fuzzy numbers where the weight of centroid points, degrees of fuzziness and the spreads of fuzzy numbers are taken into consideration is proposed, which can overcome some drawbacks of exiting methods and is very efficient for evaluating symmetric fuzzy numbers and crisp numbers. Then, a procedure for evaluating Z-numbers with the method for ranking generalized fuzzy numbers is presented, which considers the status of two parts (( A ˜ , B ˜ )) of Z-numbers and gives the principles of ranking Z-numbers. The main advantage of the proposed method is utilization of Z-numbers which can express more vague information compared with the fuzzy number. In addition, instead of converting B ˜ to a crisp number as the existing methods of ranking Z-numbers did, the proposed method retains the fuzzy information of B ˜ which can reduce the loss of information. Finally, several numerical examples are provided to illustrate the superiority and the rationality of the proposed procedure.