A New Sign Distance-Based Ranking Method for Fuzzy Numbers

Abstract

Abstract. In this paper, a new sign distance-based ranking method for fuzzy numbers is proposed. It is a synthesis of geometric centroid and sign distance. The use of centroid and sign distance in fuzzy ranking is not new. Most existing methods (e.g., distance-based method [9]) adopt the Euclidean distance from the origin to the centroid of a fuzzy number. In this paper, a fuzzy number is treated as a polygon, in which a new geometric centroid for the fuzzy number is proposed. Since a fuzzy number can be represented in different shapes with different spreads, a new dispersion coefficient pertaining to a fuzzy number is formulated. 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. Positive experimental results are obtained.

An interval-valued fuzzy distance measure between two interval-valued fuzzy numbers

“…For such situations, many distances have been developed in space of fuzzy sets Hajighasemi 2006, 2010;Blanco-Fernandez et al 2014;Bloch 1999;Chakraborty and Communicated by Rosana Sueli da Motta Jafelice. Chakraborty 2006;Chai et al 2015;Chen and Hsieh 2000;Chatzis and Pitas 1999;Du 2018;Guha and Chakraborty 2010;Hajjari and Abbasbandy 2011;Hesamian and Akbari 2018;Heilpern 1997;Hajjari 2011;Hsieh and Chen 1998;Kaufmann and Gupta 1991;Liu 1992;Pedrycz 2007;Saha et al 2002;Tran and Duckstein 2002;Voxman 1998). Note that the membership degree of expert opinions in a fuzzy set takes a single value between zero and one.…”