Methods in ranking fuzzy numbers: a unified index and comparative reviews
type: Item
instance of: scholarly article
title: Methods in ranking fuzzy numbers: a unified index and comparative reviews
zbMATH Open document ID: 1373.03118
DOI: 10.1155/2017/3083745
author: Thanh-Lam Nguyen
published in: Complexity
publication date: 2017-10-26T00:00:00Z
review text: Summary: 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 progress 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.
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 6798505
zbMATH Keywords: fuzzy sets
zbMATH Keywords: ranking fuzzy numbers
Wikidata QID: Q57947197
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/3083745
OpenAlex ID: W2735975727
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DBLP publication ID: journals/complexity/Nguyen17
description: scientific article; zbMATH DE number 6798505