Improved fuzzy ranking procedure for decision making in product design

Abstract

In this paper, we present a method for ranking any number of normal fuzzy numbers using trapezoidal fuzzy numbers as a general form, where rectangular and triangular fuzzy numbers are particular cases of such a form. This general form is supported by 29 cases, which is enough to consider all the possible situations between two normal fuzzy numbers, such as trapezoidal, triangular, or rectangular. The ranking procedure is performed using four ordering criteria into a pseudo-order preference model considering the type of the fuzzy preference relation. Two examples are given to illustrate and validate the applicability and practicality of this fuzzy ranking method. A comparison and an analysis of the proposed method is presented to demonstrate its usefulness and its contribution to the improvement of the decision making processes as a result of its management of vague or imprecise information, and whether or not that information should be allowed to be entered into such processes.

Keywords:

• fuzzy ranking
• fuzzy decision making
• fuzzy numbers
• fuzzy preference relations

Acknowledgments

The research conducted by the second author was partially supported by funding from the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT).