Ranking L–R fuzzy number based on deviation degree

A New Sign Distance-Based Ranking Method for Fuzzy Numbers

“…Lim properties [5][6][7][8][9]. Besides that, fuzzy ranking is com s are presented as different shapes with different sprea [8].…”

“…Indeed, many fuzzy ranking methods have also been developed [1][5] [6]. These methods can be categorized into three categories [5][6]; i.e., (1) transforming a set of fuzzy numbers into crisp numbers and subsequently ranking the crisp numbers; (2) mapping a set of fuzzy numbers to crisp numbers based on a pre-defined reference set(s) for comparison; (3) ranking through pairwise comparison of fuzzy numbers. In this paper, our focus is on the first category, which is straightforward as compared with the other two categories.…”

“…In this paper, our focus is on the first category, which is straightforward as compared with the other two categories. Nevertheless, the challenge is to develop a method that satisfies a set of reasonable ordering properties [5][6][7][8][9], as detailed in Section 2.2. Recently, a number of methods, e.g., deviation degree-based [8][10], distancebased [9][11], centroid-based [12], and area-based [13], have been proposed.…”

“…Recently, a number of methods, e.g., deviation degree-based [8][10], distancebased [9][11], centroid-based [12], and area-based [13], have been proposed. However, many of these methods [8] [10][11][12][13] do not have analysis pertaining to fulfillment of the reasonable ordering cated when fuzzy numbers e.g., as illustrated in Fig. 1 …”

“…The dispersion coefficient is used to fine-tune the geometric centroid, and subsequently sign distance from the origin to the tuned geometric centroid is considered. As discussed in [5][6][7][8][9], an ideal fuzzy ranking method needs to satisfy seven reasonable fuzzy ordering properties. As a result, the capability of the proposed method in fulfilling these properties is analyzed and discussed.…”