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Complexity
Volume 2017 (2017), Article ID 3083745, 13 pages
https://doi.org/10.1155/2017/3083745
Research Article

Methods in Ranking Fuzzy Numbers: A Unified Index and Comparative Reviews

Office of Scientific Research, Lac Hong University, Dong Nai, Vietnam

Correspondence should be addressed to Thanh-Lam Nguyen; moc.liamg@nv.tser4neerg

Received 6 April 2017; Revised 30 May 2017; Accepted 7 June 2017; Published 13 July 2017

Academic Editor: Omar Abu Arqub

Copyright © 2017 Thanh-Lam Nguyen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Fuzzy set theory, extensively applied in abundant disciplines, has been recognized as a plausible tool in dealing with uncertain and vague information due to its prowess in mathematically manipulating the knowledge of imprecision. In fuzzy-data comparisons, exploring the general ranking measure that is capable of consistently differentiating the magnitude of fuzzy numbers has widely captivated academics’ attention. To date, numerous indices have been established; however, counterintuition, less discrimination, and/or inconsistency on their fuzzy-number rating outcomes have prohibited their comprehensive implementation. To ameliorate their manifested ranking weaknesses, this paper proposes a unified index that multiplies weighted-mean and weighted-area discriminatory components of a fuzzy number, respectively, called centroid value and attitude-incorporated left-and-right area. From theoretical proof of consistency property and comparative studies for triangular, triangular-and-trapezoidal mixed, and nonlinear fuzzy numbers, the unified index demonstrates conspicuous ranking gains in terms of intuition support, consistency, reliability, and computational simplicity capability. More importantly, the unified index possesses the consistency property for ranking fuzzy numbers and their images as well as for symmetric fuzzy numbers with an identical altitude which is a rather critical property for accurate matching and/or retrieval of information in the field of computer vision and image pattern recognition.