Title: A novel method for ranking fuzzy quantities using center of incircle and its application to a petroleum distribution center evaluation problem

Authors: Seyed Hadi Nasseri; Nemat Allah Taghi-Nezhad; Ali Ebrahimnejad

Addresses: Department of Mathematics, Mazandaran University, Babolsar, Iran ' Department of Mathematics, Mazandaran University, Babolsar, Iran ' Department of Mathematics, Qaemshahr Branch, Islamic Azad University, P.O. Box 163, Qaemshahr, Iran

Abstract: Ranking fuzzy numbers is an important issue in decision making analysis, optimisation, artificial intelligence and operations research. Therefore, many methods have been proposed for ranking fuzzy numbers in the literature. However, all of these methods have some limitations and shortcomings. Thus, in this paper, based on coordinates of the centre of incircle of triangles a novel ranking method is proposed to overcome the existing shortcomings. Since the incircle of each triangle is defined as unique, the coordinates of the incircle centre are used in the proposed ranking approach. The novel ranking method is proven to always guarantee consistency between the ranking of fuzzy quantities and that of their images. Unlike many existing methods, the proposed method not only can rank real numbers as well as normal and non-normal fuzzy numbers, but it also has some other noticeable mathematical properties that are proved in this paper. Moreover, several comparative examples are examined to show the superior validity, applicability, efficiency and simplicity of the proposed method in comparison with the existing methods. Finally, a petroleum distribution centre evaluation problem is given as a practical application to demonstrate the usage and applicability of the proposed ranking approach.

Keywords: fuzzy quantity; ranking; centroid points; incentre; petroleum distribution centre evaluation problem.

DOI: 10.1504/IJISE.2017.087832

International Journal of Industrial and Systems Engineering, 2017 Vol.27 No.4, pp.457 - 484

Received: 04 May 2015
Accepted: 28 Aug 2015
Published online: 06 Nov 2017 *

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