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Current Chinese Computer Science

Editor-in-Chief

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

Research Article

Weighted Aggregation Operators of Fuzzy Credibility Cubic Numbers and their Decision Making Strategy for Slope Design Schemes

Author(s): Jun Ye*, Shigui Du, Rui Yong and Fangwei Zhang

Volume 1, Issue 1, 2021

Published on: 17 July, 2020

Page: [28 - 34] Pages: 7

DOI: 10.2174/2665997201999200717165743

Abstract

Background: A Fuzzy Cubic Set (FCS) is composed of a Fuzzy Set (FS) (certain fuzzy numbers) and an Interval-Valued Fuzzy Set (IVFS) (uncertain fuzzy numbers) to describe the hybrid information of both. To enhance the credibility of both, they should be closely related to the measures/degrees of credibility owing to the vagueness and uncertainty of humans’ cognitions regarding the real world.

Objective: This paper presents the notions of a Fuzzy Cubic Credibility Set (FCCS) and a Fuzzy Cubic Credibility Number (FCCN) as the new generalization of the FCS notion to enhance the credibility level of FCS by means of the credibility degrees of both FS and IVFS. Next, we define operations of FCCNs, an expected value of FCCN, and the FCCN Weighted Arithmetic Averaging (FCCNWAA) and FCCN Weighted Geometric Averaging (FCCNWGA) operators for Decision Making (DM) strategy.

Methods: A DM strategy using the FCCNWAA or FCCNWGA operator is proposed to solve multicriteria DM problems in the environment of FCCNs. Then, the proposed DM strategy is applied to a DM example of slope design schemes for an open-pit mine in the environment of FCCNs to reflect the feasibility of the proposed DM strategy.

Result: By comparison with the fuzzy cubic DM strategy, the DM results with and without the degrees of credibility, can impact on the ranking of alternatives in the DM example to reflect the effectiveness of the proposed DM strategy.

Conclusion: However, the highlighting advantage of this study is that the proposed DM strategy not only indicates the degrees of credibility regarding the assessed values of FCNs in the DM process but also enhances the DM reliability in the environment of FCCNs. Hence, the proposed DM strategy is superior to the fuzzy cubic DM strategy in the environment of FCCNs.

Keywords: Fuzzy credibility cubic set, Fuzzy credibility cubic number, Expected value, Fuzzy credibility cubic number weighted arithmetic averaging (FCCNWAA) operator, Fuzzy credibility cubic number weighted geometric averaging (FCCNWGA) operator, Decision-making strategy, Slope design scheme.

Graphical Abstract
[1]
L.A. Zadeh, "Fuzzy sets", Inf. Control, vol. 8, pp. 338-353, 1965.
[http://dx.doi.org/10.1016/S0019-9958(65)90241-X]
[2]
C. Kahraman, S.C. Onar, and B. Oztaysi, "Fuzzy multicriteria decision-making: A literature review", Int. J. Comp. Intelligence Syst., vol. 8, no. 4, pp. 637-666, 2015.
[http://dx.doi.org/10.1080/18756891.2015.1046325]
[3]
M.M. Pandey, D. Shukla, and A. Graham, "Evaluating the human performance factors of air traffic control in Thailand using fuzzy multi criteria decision making method", J. Air Transp. Manage., vol. 81, no. 101708, 2019.
[http://dx.doi.org/10.1016/j.jairtraman.2019.101708]
[4]
B. Bostancı, and N. Erdem, "Investigating the satisfaction of citizens in municipality services using fuzzy modeling", Socioecon. Plann. Sci., vol. 69, no. 100754, 2020.
[5]
M. Kacewicz, "Fuzzy slope stability method", In: Mathematics in Geology, vol. 19. 1987, no. no. 8, pp. 757-767.
[http://dx.doi.org/10.1007/BF00893013]
[6]
A.I.H. Malkawi, W.F. Hassan, and F.A. Abdulla, "Uncertainty and reliability analysis applied to slope stability", Struct. Saf., vol. 22, no. 2, pp. 161-187, 2000.
[http://dx.doi.org/10.1016/S0167-4730(00)00006-0]
[7]
M.B. Gorzałczany, "A method of inference in approximate reasoning based on interval valued fuzzy sets", Fuzzy Sets Syst., vol. 21, no. 1, pp. 1-17, 1987.
[http://dx.doi.org/10.1016/0165-0114(87)90148-5]
[8]
Y.B. Jun, C.S. Kim, and K.O. Yang, "Cubic sets", Annals of Fuzzy Mathematics and Informatics, vol. 4, no. 1, pp. 83-98, 2012.
[9]
Y.B. Jun, S.T. Jung, and M.S. Kim, "Cubic subgroups", Annals of Fuzzy Mathematics and Informatics, vol. 2, no. 1, pp. 9-15, 2011.
[10]
Y.B. Jun, and A. Khan, "Cubic ideals in semigroups", Honam Mathematical Journal, vol. 35, no. 4, pp. 607-623, 2013.
[http://dx.doi.org/10.5831/HMJ.2013.35.4.607]
[11]
S. Vijayabalaji, and S. Sivaramakrishnan, "“A cubic set theoretical approach to linear space”, Abstract and Applied Analysis, vol", Article ID, vol. 523129, pp. 1-8, 2015.
[http://dx.doi.org/10.1155/2015/523129]
[12]
J.M. Wang, W.H. Cui, and J. Ye, "Slope stability evaluation using tangent similarity measure of fuzzy cube sets", Soft Computing in Civil Engineering, vol. 3, no. 1, pp. 27-35, 2019.
[13]
V. Torra, "Hesitant fuzzy sets", Int. J. Intell. Syst., vol. 25, no. 6, pp. 529-539, 2010.
[14]
Q. Khan, T. Mahmood, and F. Mehmood, "Cubic hesitant fuzzy sets and their applications to multi criteria decision making", International Journal of Algebra and Statistics, vol. 5, pp. 19-51, 2016.
[http://dx.doi.org/10.20454/ijas.2016.1055]
[15]
A. Fahmi, and F. Amin, "Precursor selection for Sol–Gel synthesis of titanium carbide nanopowders by a new hesitant cubic fuzzy multi-attribute group decision-making model", New Maths. Natural Comput., vol. 15, no. 01, pp. 145-167, 2019.
[http://dx.doi.org/10.1142/S1793005719500091]
[16]
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]
[17]
J. Fu, J. Ye, and W. Cui, "The Dice measure of cubic hesitant fuzzy sets and its initial evaluation method of benign prostatic hyperplasia symptoms", Sci. Rep., vol. 9, no. 1, p. 60, 2019.
[http://dx.doi.org/10.1038/s41598-018-37228-9] [PMID: 30635593]
[18]
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. 1, pp. 1075-1083, 2019.
[http://dx.doi.org/10.3233/JIFS-182555]
[19]
J. Fu, and J. Ye, "Similarity measure with indeterminate parameters regarding cubic hesitant neutrosophic numbers and its risk grade assessment approach for prostate cancer patients", Appl. Intell., vol. 50, pp. 2120-2131, 2020.
[http://dx.doi.org/10.1007/s10489-020-01653-z]
[20]
J. Read, and P. Stacey, Guidelines for open pit slope design., CSIRO Publishing: Collingwood, 2009.
[http://dx.doi.org/10.1071/9780643101104]

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