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Current Chinese Computer Science

Editor-in-Chief

ISSN (Print): 2665-9972
ISSN (Online): 2665-9964

Research Article

Similarity Measures and Their Applications in Multiple Attribute Decision- Making Under Cubic Hesitant Environment

Author(s): Yohannes Belayneh, Rui Yong* and Yingying Zhang

Volume 2, Issue 1, 2022

Published on: 01 August, 2022

Article ID: e140522204785 Pages: 10

DOI: 10.2174/2665997202666220514132626

Abstract

Background: Cubic Hesitant Fuzzy Set (CHFS) is a hybrid set that can express uncertain and hesitancy fuzzy information simultaneously.

Objective: In this paper, we introduced three trigonometric similarity measures (e.g., cosine, tangent, and cotangent similarity measures) to measure the degree of similarity between the alternative and the ideal set under the CHFS environment. Various desirable characteristics of the cubic hesitant fuzzy set are studied. Then, we developed multiple attribute decision-making methods based on the weighted cosine, tangent, and cotangent similarity measures of CHFSs.

Methods: In this research, we presented the similarity measures of CHFSs based on the cosine, tangent, and cotangent functions. Then, illustrative examples of construction project management with CHFS information are presented to show the effectiveness and feasibility of the proposed Multiattribute Decision-making (MADM) method under CHFS environments.

Results: Based on the weighted similarity measures between each alternative and the ideal set, this method provides the ranking order according to the values of their similarity measure. The best alternatives can be easily identified from the ranking order obtained.

Conclusion: Based on the comparison of the decision results obtained, the tangent and cotangent similarity measures are better in similarity identification than the cosine similarity measure for solving MADM problems under a cubic hesitant environment.

Keywords: Cubic Hesitant Fuzzy Set (CHFS), trigonometric similarity measure, Multiple-Attribute Decision Making (MADM), hesitancy fuzzy information, construction management, environment.

[1]
E. Szafranko, "Decision problems in management of construction projects", IOP Conference Series: Materials Science and Engineering, vol. 251, 2017.
[http://dx.doi.org/10.1088/1757-899X/251/1/012048 ]
[2]
L.A. Zadeh, "Fuzzy sets", Inf. Control, vol. 8, no. 3, pp. 338-353, 1965.
[http://dx.doi.org/10.1016/S0019-9958(65)90241-X]
[3]
L.A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-I", Inf. Sci., vol. 8, no. 3, pp. 199-249, 1975.
[http://dx.doi.org/10.1016/0020-0255(75)90036-5]
[4]
Y.B. Jun, C.S. Kim, and K.O. Yang, "Cubic sets", Anna. Fuzzy Math. Info., vol. 4, pp. 83-98, 2012.
[5]
F. Smarandache, Neutrosophy: Neutrosophic probability, set, and Logic; American Res., Press: Rehoboth, USA, 1998.
[6]
M. Ali, I. Deli, and F. Smarandache, "The theory of neutrosophic cubic sets and their applications in pattern recognition", J. Intell. Fuzzy Syst., vol. 30, no. 4, pp. 1957-1963, 2016.
[http://dx.doi.org/10.3233/IFS-151906]
[7]
J. Zhan, M. Khan, M. Gulistan, and A. Ali, "Applications of neutrosophic cubic sets in multi-criteria decision making", Int. J. Uncertain. Quantif., vol. 7, no. 5, pp. 377-394, 2017.
[http://dx.doi.org/10.1615/Int.J.UncertaintyQuantification.2017020446]
[8]
D. Banerjee, B.C. Giri, S. Pramanik, and F. Smarandache, "GRA for multi attribute decision making in neutrosophic cubic set environment", Neutrosophic Sets Syst., vol. 15, pp. 64-73, 2017.
[http://dx.doi.org/10.5281/zenodo.570938]
[9]
S. Pramanik, S. Dalapati, S. Alam, T.K. Roy, and F. Smarandache, "Neutrosophic cubic MCGDM method based on similarity measure", Neutrosophic Sets Syst., vol. 16, pp. 44-56, 2017.
[http://dx.doi.org/10.5281/zenodo.831934]
[10]
V. Torra, "Hesitant fuzzy sets", Int. J. Intell. Syst., vol. 25, no. 6, pp. 529-539, 2010.
[http://dx.doi.org/10.1002/int.20418]
[11]
V. Torra, and Y. Narukawa, "On hesitant fuzzy sets and decision", IEEE International Conference on Fuzzy Systems, pp. 1378-1382, 2009.
[http://dx.doi.org/10.1109/FUZZY.2009.5276884]
[12]
Z. Xu, and S. Zhang, "An overview on the applications of the hesitant fuzzy sets in group decision-making: Theory, support and methods", Fron. Eng. Manag., vol. 6, no. 2, pp. 163-182, 2019.
[http://dx.doi.org/10.1007/s42524-019-0017-4]
[13]
S. Zolfaghari, and M.S. Meysam, "Construction-project risk assessment by a new decision model based on De-Novo multi-approaches analysis and hesitant fuzzy sets under uncertainty", J. Intell. Fuzzy Syst., vol. 35, no. 1, pp. 639-649, 2018.
[http://dx.doi.org/10.3233/JIFS-162013]
[14]
J. Fu, J. Ye, and W. Cui, "An evaluation method of risk grades for prostate cancer using similarity measure of cubic hesitant fuzzy sets", J. Biomed. Inform., vol. 87, pp. 131-137, 2018.
[http://dx.doi.org/10.1016/j.jbi.2018.10.003] [PMID: 30339927]
[15]
R. Yong, A. Zhu, and J. Ye, "Multiple attribute decision method using similarity measure of cubic hesitant fuzzy sets", J. Intell. Fuzzy Syst., vol. 37, no. 4, pp. 1-9, 2019.
[http://dx.doi.org/10.3233/JIFS-182555]
[16]
G. Salton, and M.J. McGill, Introduction to Modern Information Retrieval., McGraw-Hill, 1987.
[17]
K. Mondal, and S. Pramanik, "Neutrosophic refined similarity measure based on tangent function and its application to multi-attribute decision making", J. New Theory, no. 8, pp. 41-50, 2015.
[http://dx.doi.org/10.5281/zenodo.32286]
[18]
J. Ye, "Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of a steam turbine", Soft Comput., vol. 21, no. 3, pp. 817-825, 2017.
[http://dx.doi.org/10.1007/s00500-015-1818-y]
[19]
S.A. Erdogan, J. ҆aparauskas, and Z. Turskis, "Decision making in construction management: AHP and expert choice approach", Procedia Eng., vol. 172, pp. 270-276, 2017.
[http://dx.doi.org/10.1016/j.proeng.2017.02.111]
[20]
M.T. Wang, and H.Y. Chou, "Risk allocation and risk handling of highway projects in Taiwan", J. Manage. Eng., vol. 19, no. 2, pp. 60-68, 2003.
[http://dx.doi.org/10.1061/(ASCE)0742-597X(2003)19:2(60)]
[21]
D.B. Ashley, K.R. Molenaar, and J.E. Diekmann, Guide to Risk Assessment and Allocation for Highway Construction Management., Federal Highway Administration, Office of International Programs: United States, 2006.

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