Title: A new method for fuzzy numbers ranking on the basis of hypotenuse set

Authors: Nasser Shahsavari-Pour; Reza Tavakkoli-Moghaddam; Hamed Mohammadi Andargoli; Mohammad Hossein Abolhasani-Ashkezari; Mojtaba Kazemi

Addresses: Department of Industrial Management, Vali-e-Asr University, First of Yazd road, 22 Bahman Square, Rafsanjan 7718897111, Iran ' Department of Industrial Engineering, University of Tehran, Tehran, Iran ' Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Alley 59, Goldasht Street, Kerman, Iran ' Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Alley 59, Goldasht Street, Kerman, Iran ' Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Alley 59, Goldasht Street, Kerman, Iran

Abstract: The fuzzy numbers ranking plays a significant role in many fuzzy application systems. This paper presents a new approach for fuzzy numbers ranking and six definitions are introduced for comparing fuzzy numbers. The purpose of paper is to rank the trapezoidal/triangular fuzzy numbers based on the hypotenuse set for each fuzzy number. Each member (hypotenuse) of the set (L-R) is resulted from a certain level (λ-cut) of membership degree. The hypotenuse length is calculated for each level based on the distance of each fuzzy number with fuzzy number indicator. The fuzzy number indicator is affected by all the fuzzy numbers for ranking. Therefore, the relative preference is measured in each level (λ-cut) and the absolute preference is totally represented in terms of all levels. Additionally, the proposed method is compared with the available methods. Several examples are studies for expressing the advantages of the reasonable performance of proposed method.

Keywords: fuzzy number ranking; trapezoidal fuzzy numbers; triangular fuzzy numbers; fuzzy environment; hypotenuse set.

DOI: 10.1504/IJMOR.2017.083190

International Journal of Mathematics in Operational Research, 2017 Vol.10 No.3, pp.370 - 398

Received: 01 Mar 2015
Accepted: 28 Jun 2015
Published online: 22 Mar 2017 *

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