Fermatean Hesitant Fuzzy Sets for Multiple Criteria Decision-Making with Applications

Murat Kirişci

doi:10.26599/FIE.2023.9270011

Fuzzy Information and Engineering 2023, 15(2): 100-127 https://doi.org/10.26599/FIE.2023.9270011

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Open Access | Issue | Published: 30 June 2023

Fermatean Hesitant Fuzzy Sets for Multiple Criteria Decision-Making with Applications

Show Author's Information Hide Author's Information Murat Kirişci^¹(

)

1Department of Biostatistics and Medical Informatics, Istanbul University-Cerrahpaşa, Istanbul 34442, Turkey

Keywords:

infectious disease, multiple criteria decision-making, Fermatean hesitant fuzzy set, Fermatean hesitant fuzzy aggregation operator

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Kirişci M. Fermatean Hesitant Fuzzy Sets for Multiple Criteria Decision-Making with Applications. Fuzzy Information and Engineering, 2023, 15(2): 100-127. https://doi.org/10.26599/FIE.2023.9270011

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Abstract

The Fermatean hesitant fuzzy set idea obtained by combining Fermatean fuzzy sets and hesitant fuzzy sets can be used in practice to simplify the solution of complicated multi-criteria decision-making problems. Initially, the notion of a Fermatean hesitant fuzzy set has been given, and the operations related to this concept have been presented. The basic properties of aggregation operators based on Fermatean hesitant fuzzy sets have been studied. To choose the best alternative in practice, a novel multi-criteria decision-making method that is obtained with operators has been created. Finally, numerical examples were examined to indicate the effectiveness of the suggested techniques. The main advantages of this work include three points: (1) extending hesitant fuzzy sets to the Fermatean fuzzy case and proposing two types of aggregation operators for the Fermatean hesitant fuzzy information; (2) considering the interaction among decision-makers and among attributes in decision problems, and dealing with this interrelationship by fuzzy measure; (3) introducing the new decision method for the Fermatean hesitant fuzzy environment and enriching the mathematical tools to solve multiple attributes decision-making problems.

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Fermatean Hesitant Fuzzy Sets for Multiple Criteria Decision-Making with Applications

Show Author's information Hide Author's Information Murat Kirişci^¹(

)

1Department of Biostatistics and Medical Informatics, Istanbul University-Cerrahpaşa, Istanbul 34442, Turkey

Abstract

Keywords: infectious disease, multiple criteria decision-making, Fermatean hesitant fuzzy set, Fermatean hesitant fuzzy aggregation operator

References(40)

[1]

L. A. Zadeh, Fuzzy sets, Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.

DOI Google Scholar

[2]

K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., vol. 20, no. 1, pp. 87–96, 1986.

DOI Google Scholar

[3]

R. R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE Trans. Fuzzy Syst., vol. 22, no. 4, pp. 958–965, 2014.

DOI Google Scholar

[4]

F. Feng, H. Fujita, M. I. Ali, R. R. Yager, and X. Liu, Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision making methods, IEEE Trans. Fuzzy Syst., vol. 27, no. 3, pp. 474–488, 2019.

DOI Google Scholar

[5]

H. Garg, Some series of intuitionistic fuzzy interactive averaging aggregation operators, SpringerPlus, vol. 5, no. 1, p. 999, 2016.

DOI Google Scholar

[6]

M. Kirişci, Comparison of medical decision-making with intuitionistic fuzzy parametrized fuzzy soft set and riesz summability, New Math. Nat. Comput., vol. 15, no. 2, pp. 351–359, 2019.

DOI Google Scholar

[7]

M. Kirişci, Ω-soft sets and medical decision-making application, Int. J. Comput. Math., vol. 98, no. 4, pp. 690–704, 2021.

DOI Google Scholar

[8]

J. J. Peng, J. Q. Wang, X. H. Wu, H. Y. Zhang, and X. H. Chen, The fuzzy cross-entropy for intuitionistic hesitant fuzzy sets and their application in multi-criteria decision-making, Int. J. Syst. Sci., vol. 46, no. 13, pp. 2335–2350, 2015.

DOI Google Scholar

[9]

X. Peng and G. Selvachandran, Pythagorean fuzzy set: State of the art and future directions, Artif. Intell. Rev., vol. 52, no. 3, pp. 1873–1927, 2019.

DOI Google Scholar

[10]

F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, in Proc. 2006 IEEE Int. Conf. Granular Computing, Atlanta, GA, USA, 2006, pp. 38–42.

[11]

R. R. Yager, Pythagorean fuzzy subsets, in Proc. 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), Edmonton, Canada, 2013, pp. 57–61.

DOI

[12]

R. R. Yager and A. M. Abbasov, Pythagorean membership grades, complex numbers, and decision making, Int. J. Intell. Syst., vol. 28, no. 5, pp. 436–452, 2013.

DOI Google Scholar

[13]

T. Senapati and R. R. Yager, Fermatean fuzzy sets, J. Ambient Intell. Humaniz. Comput., vol. 11, no. 2, pp. 663–674, 2020.

DOI Google Scholar

[14]

T. Senapati and R. R. Yager, Some new operations over fermatean fuzzy numbers and application of fermatean fuzzy WPM in multiple criteria decision making, Informatica, vol. 30, no. 2, pp. 391–412, 2019.

DOI Google Scholar

[15]

T. Senapati and R. R. Yager, Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods, Eng. Appl. Artif. Intell., vol. 85, pp. 112–121, 2019.

DOI Google Scholar

[16]

M. Kirişci, New entropy and distance measures for fermatean fuzzy soft sets with medical decision-making and pattern recognition applications, https://europepmc.org/article/PPR/PPR516614, 2022.

DOI

[17]

M. Kirişci, New cosine similarity and distance measures for Fermatean fuzzy sets and TOPSIS approach, Knowl. Inf. Syst., vol. 65, no. 2, pp. 855–868, 2023.

DOI Google Scholar

[18]

M. Kirişci, I. Demir, and N. Şimşek, Fermatean fuzzy ELECTRE multi-criteria group decision-making and most suitable biomedical material selection, Artif. Intell. Med., vol. 127, p. 102278, 2022.

DOI Google Scholar

[19]

R. R. Yager, Generalized orthopair fuzzy sets, IEEE Trans. Fuzzy Syst., vol. 25, no. 5, pp. 1222–1230, 2017.

DOI Google Scholar

[20]

D. Liu, Y. Liu, and X. Chen, Fermatean fuzzy linguistic set and its application in multicriteria decision making, Int. J. Intell. Syst., vol. 34, no. 5, pp. 878–894, 2019.

DOI Google Scholar

[21]

D. Liu, Y. Liu, and L. Wang, Distance measure for Fermatean fuzzy linguistic term sets based on linguistic scale function: An illustration of the TODIM and TOPSIS methods, Int. J. Intell. Syst., vol. 34, no. 11, pp. 2807–2834, 2019.

DOI Google Scholar

[22]

G. Shahzadi and M. Akram, Group decision-making for the selection of an antivirus mask under fermatean fuzzy soft information, J. Intell. Fuzzy Syst., vol. 40, no. 1, pp. 1401–1416, 2021.

DOI Google Scholar

[23]

G. Shahzadi, F. Zafar, and M. A. Alghamdi, Multiple-attribute decision-making using fermatean fuzzy hamacher interactive geometric operators, Math. Probl. Eng., vol. 2021, pp. 1–20, 2021.

DOI Google Scholar

[24]

G. Shahzadi, G. Muhiuddin, M. Arif Butt, and A. Ashraf, Hamacher interactive hybrid weighted averaging operators under fermatean fuzzy numbers, J. Math., vol. 2021, pp. 1–17, 2021.

DOI Google Scholar

[25]

N. Şimşek and M. Kirişci, Incomplete Fermatean fuzzy preference relations and group decision-making, Topol. Appl., vol. 11, no. 1, p. 20220125, 2023.

DOI

[26]

M. Akram, G. Ali, J. C. R. Alcantud, and A. Riaz, Group decision-making with Fermatean fuzzy soft expert knowledge, Artif. Intell. Rev., vol. 55, no. 7, pp. 5349–5389, 2022.

DOI Google Scholar

[27]

M. Akram, U. Amjad, J. C. R. Alcantud, and G. Santos-García, Complex fermatean fuzzy N-soft sets: a new hybrid model with applications, J. Ambient Intell. Humaniz. Comput., pp. 1–34, 2022.

DOI Google Scholar

[28]

M. Akram, G. Shahzadi, and A. Ali H Ahmadini, Decision-making framework for an effective sanitizer to reduce COVID-19 under fermatean fuzzy environment, J. Math., vol. 2020, pp. 1–19, 2020.

DOI Google Scholar

[29]

V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., vol. 8, pp. 529–539, 2010.

DOI Google Scholar

[30]

Z. Zhang, Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making, Inf. Sci., vol. 234, pp. 150–181, 2013.

DOI Google Scholar

[31]

G. Qian, H. Wang, and X. Feng, Generalized hesitant fuzzy sets and their application in decision support system, Knowl. Based Syst., vol. 37, pp. 357–365, 2013.

DOI Google Scholar

[32]

B. Zhu and Z. Xu, Some results for dual hesitant fuzzy sets, J. Intell. Fuzzy Syst., vol. 26, no. 4, pp. 1657–1668, 2014.

DOI Google Scholar

[33]

J. J. Peng, J. Q. Wang, J. Wang, and X. H. Chen, Multicriteria decision-making approach with hesitant interval-valued intuitionistic fuzzy sets, Sci. World J., vol. 2014, pp. 1–22, 2014.

DOI Google Scholar

[34]

M. S. Ali Khan, S. Abdullah, A. Ali, N. Siddiqui, and F. Amin, Pythagorean hesitant fuzzy sets and their application to group decision making with incomplete weight information, J. Intell. Fuzzy Syst., vol. 33, no. 6, pp. 3971–3985, 2017.

DOI Google Scholar

[35]

M. Xia and Z. Xu, Hesitant fuzzy information aggregation in decision making, Int. J. Approx. Reason., vol. 52, no. 3, pp. 395–407, 2011.

DOI Google Scholar

[36]

B. Bedregal, R. Reiser, H. Bustince, C. Lopez-Molina, V, Torra, Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms, Inform, Sciences, vol. 255, pp. 82–89, 2014.

DOI Google Scholar

[37]

B. Farhadinia, A series of score functions for hesitant fuzzy sets, Inf. Sci., vol. 277, pp. 102–110, 2014.

DOI Google Scholar

[38]

Z. Xu, On consistency of the weighted geometric mean complex judgement matrix in AHP¹, Eur. J. Oper. Res., vol. 126, no. 3, pp. 683–687, 2000.

DOI Google Scholar

[39]

S. H. Kim and B. S. Ahn, Interactive group decision making procedure under incomplete information, Eur. J. Oper. Res., vol. 116, no. 3, pp. 498–507, 1999.

DOI Google Scholar

[40]

Y. M. Wang, Using the method of maximizing deviation to make decision for multi-indices, vol. 8, no. 3, pp. 21–26, 1997.

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Received: 07 December 2022

Revised: 17 February 2023

Accepted: 12 March 2023

Published: 30 June 2023

Issue date: June 2023

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This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).