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Not-ordered quasi-distance measures of generalised trapezoidal hesitant fuzzy numbers and their application to decision making problems

Year 2022, Volume: 11 Issue: 2, 162 - 181, 31.08.2022
https://doi.org/10.54187/jnrs.1160127

Abstract

As an extension of the trapezoidal fuzzy number, the generalised trapezoidal hesitant fuzzy number is an effective mathematical tool for handling uncertainty and vagueness in decision-making problems. Considering that the quasi-distance measure has a strong ability to process and analyse data, we initiated some novel quasi-distance measures to measure the strength of the relationship between generalised trapezoidal hesitant fuzzy numbers in this paper. Moreover, based on the proposed measures, a new multi-criteria decision-making approach is proposed to address uncertain real-life situations. Finally, a practical application of the proposed approach is also illustrated to demonstrate the effectiveness and applicability.

References

  • L. A. Zadeh, Fuzzy sets, Information and Control, 8(3), (1965) 338-353.
  • V. Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems, 25(6), (2009) 529-539.
  • V. Torra, Y. Narukawa, On hesitant fuzzy sets and decision, IEEE International Conference on Fuzzy Systems 2009, Jeju Island, Korea, 2009, pp. 1378-1382.
  • S. K. Tyagi, Multiple attribute decision making using hesitant triangular fuzzy sets, International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT) 2016, Chennai, India, 2016, pp. 1502-1510.
  • J. J. Chen, X. J. Huang, Hesitant triangular intuitionistic fuzzy information and its application to multi-attribute decision making problem, Journal of Nonlinear Science and Application 10, (2017) 1012-1029.
  • M. Erdoğan, I. Kaya, Selection of the best outsourcing firm for WEEE under hesitant fuzzy environment, Journal of Intelligent and Fuzzy Systems, 35(3), (2018) 3295-3306.
  • Z. S. Xu, M. M. Xia, On distance and correlation measures of hesitant fuzzy information, International Journal of Intelligent Systems, 26(5), (2013) 410-425.
  • A. Fahmi, S. Abdullah, A. Ali, R. Ahmad, F. Ghani, Triangular cubic linguistic hesitant fuzzy aggregation operators and their application in group decision making, Journal of Intelligent and Fuzzy Systems, 34(4), (2018) 2401-2416.
  • F. J. Estrella, S. C. Onar, R. M. Rodríguez, B. Oztaysi, L. Martinez, C. Kahraman, Selecting firms in university technoparks: A hesitant linguistic fuzzy TOPSIS model for heterogeneous contexts, Journal of Intelligent and Fuzzy Systems, 33(2), (2017) 1155-1172.
  • C. Kahraman, S. C. Onar, B. Öztayşi, Present worth analysis using hesitant fuzzy sets, in: J. M. Alonso, H. Bustince, M. Reformat (Eds.) Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology 2015, Gijon, Asturias (Spain), 2015, pp. 255-259.
  • G. Qian, H. Wang, X. Feng, Generalized of hesitant fuzzy sets and their application in decision support system, Knowledge-Based Systems, 37, (2013) 357-365.
  • T. Rashid, S. M. Husnine, Multicriteria group decision making by using trapezoidal valued hesitant fuzzy sets, The Scientific World Journal, 2014, (2014) Article ID: 304834, 1-8.
  • S. Memii, S. Enginoğlu, U. Erkan, Numerical data classification via distance-based similarity measures of fuzzy parameterized fuzzy soft matrices, IEEE Access, 9, (2021) 88583-88601.
  • A. Fahmi, M. Aslam, S. Abdullah, Analysis of migraine in mutlicellular organism based on trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method, International Journal of Biomathematics, 12(8), (2019). https://doi.org/10.1142/S1793524519500840
  • A. Fahmi, M. Aslam, F. A. A. Almahdi, F. Amin, New type of cancer patients based on triangular cubic hesitant fuzzy TOPSIS method, International Journal of Biomathematics, 13(1), (2019) 1-24. doi:10.1142/s1793524520500023.
  • A. Fahmi, M. Aslam, S. Abdullah, F. Amin, A. Asada, W. A. Khan, Some geometric operators with triangular cubic linguistic hesitant fuzzy number and their application in group decision making, Journal of Intelligent and Fuzzy Systems, 35(2), (2018) 2485-2499.
  • S., Hussain, M. Aslam, F. Amin, S. Abdullah, A. Fahmi, Trapezoidal linguistic cubic fuzzy TOPSIS method and application in a group decision making problem, Journal of Intelligent Systems, 29(1), (2019) 1283-1300.
  • X. Peng Hesitant trapezoidal fuzzy aggregation operators based on Archimedean $t$-norm and $t$-conorm and their application in MADM with completely unknown weight information, International Journal for Uncertainty Quantification, 7(6), (2017) 475-510.
  • X. Zhang, Z. Xu, M. Liu, Hesitant trapezoidal fuzzy QUALIFLEX method and its application in the evaluation of green supply chain initiatives, Sustainability, 8(9), (2016) 1-17.
  • X. Zhang, T. Yang, W. Liang, M. Xiong, Closeness degree-based hesitant trapezoidal fuzzy multicriteria decision making method for evaluating green suppliers with qualitative information, Discrete Dynamics in Nature and Society, 2018, (2018) Article ID: 3178039, 1-13.
  • F. Amin, A . Fahmi, S. Abdullah, Dealer using a new trapezoidal cubic hesitant fuzzy TOPSIS method and application to group decision-making program, Soft Computing, 23(14), (2019) :5353-5366.
  • A. Fahmi, S. Abdullah, F. Amin, A. Ali, R. Ahmed, M. Shakeel, Trapezoidal cubic hesitant fuzzy aggregation operators and their application in group decision-making, Journal of Intelligent and Fuzzy Systems, 36(4), (2019) 3619-3635.
  • A. Fahmi, S. Abdullah, F. Amin, M. Aslam, S. Hussain, Trapezoidal linguistic cubic fuzzy TOPSIS method and application in a group decision making program, Journal of Intelligent Systems 29(1), (2020) 1283-1300.
  • A. Fahmi., F. Amin, S. Abdullah, M. Shakeel, Power average operators of trapezoidal cubic fuzzy numbers and application to multi-attribute group Decision making, Journal of Intelligent Systems, 29(1), (2020) 1643-1661.
  • İ. Deli, F. Karaaslan, Generalized trapezoidal hesitant fuzzy numbers and their applications to multiple criteria decision making problems, Soft Computing, 25(2), (2021) 1017-1032.
  • İ. Deli, A TOPSIS method by using generalized trapezoidal hesitant fuzzy numbers and application to a robot selection problem, Journal of Intelligent and Fuzzy Systems, 38(1), (2020) 779-793.
  • E. Ö. Çelik, Some distance and correlation coefficient measures of generalized trapezoidal hesitant fuzzy numbers and their application to decision making problems, Master's Thesis, Kilis 7 Aralık University (2022), Kilis, Turkiye (in Turkish).
  • İ. Deli, Bonferroni mean operators of generalized trapezoidal hesitant fuzzy numbers and their application to decision-making problems, Soft Computing, 25(6), (2021) 4925-4949.
Year 2022, Volume: 11 Issue: 2, 162 - 181, 31.08.2022
https://doi.org/10.54187/jnrs.1160127

Abstract

References

  • L. A. Zadeh, Fuzzy sets, Information and Control, 8(3), (1965) 338-353.
  • V. Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems, 25(6), (2009) 529-539.
  • V. Torra, Y. Narukawa, On hesitant fuzzy sets and decision, IEEE International Conference on Fuzzy Systems 2009, Jeju Island, Korea, 2009, pp. 1378-1382.
  • S. K. Tyagi, Multiple attribute decision making using hesitant triangular fuzzy sets, International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT) 2016, Chennai, India, 2016, pp. 1502-1510.
  • J. J. Chen, X. J. Huang, Hesitant triangular intuitionistic fuzzy information and its application to multi-attribute decision making problem, Journal of Nonlinear Science and Application 10, (2017) 1012-1029.
  • M. Erdoğan, I. Kaya, Selection of the best outsourcing firm for WEEE under hesitant fuzzy environment, Journal of Intelligent and Fuzzy Systems, 35(3), (2018) 3295-3306.
  • Z. S. Xu, M. M. Xia, On distance and correlation measures of hesitant fuzzy information, International Journal of Intelligent Systems, 26(5), (2013) 410-425.
  • A. Fahmi, S. Abdullah, A. Ali, R. Ahmad, F. Ghani, Triangular cubic linguistic hesitant fuzzy aggregation operators and their application in group decision making, Journal of Intelligent and Fuzzy Systems, 34(4), (2018) 2401-2416.
  • F. J. Estrella, S. C. Onar, R. M. Rodríguez, B. Oztaysi, L. Martinez, C. Kahraman, Selecting firms in university technoparks: A hesitant linguistic fuzzy TOPSIS model for heterogeneous contexts, Journal of Intelligent and Fuzzy Systems, 33(2), (2017) 1155-1172.
  • C. Kahraman, S. C. Onar, B. Öztayşi, Present worth analysis using hesitant fuzzy sets, in: J. M. Alonso, H. Bustince, M. Reformat (Eds.) Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology 2015, Gijon, Asturias (Spain), 2015, pp. 255-259.
  • G. Qian, H. Wang, X. Feng, Generalized of hesitant fuzzy sets and their application in decision support system, Knowledge-Based Systems, 37, (2013) 357-365.
  • T. Rashid, S. M. Husnine, Multicriteria group decision making by using trapezoidal valued hesitant fuzzy sets, The Scientific World Journal, 2014, (2014) Article ID: 304834, 1-8.
  • S. Memii, S. Enginoğlu, U. Erkan, Numerical data classification via distance-based similarity measures of fuzzy parameterized fuzzy soft matrices, IEEE Access, 9, (2021) 88583-88601.
  • A. Fahmi, M. Aslam, S. Abdullah, Analysis of migraine in mutlicellular organism based on trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method, International Journal of Biomathematics, 12(8), (2019). https://doi.org/10.1142/S1793524519500840
  • A. Fahmi, M. Aslam, F. A. A. Almahdi, F. Amin, New type of cancer patients based on triangular cubic hesitant fuzzy TOPSIS method, International Journal of Biomathematics, 13(1), (2019) 1-24. doi:10.1142/s1793524520500023.
  • A. Fahmi, M. Aslam, S. Abdullah, F. Amin, A. Asada, W. A. Khan, Some geometric operators with triangular cubic linguistic hesitant fuzzy number and their application in group decision making, Journal of Intelligent and Fuzzy Systems, 35(2), (2018) 2485-2499.
  • S., Hussain, M. Aslam, F. Amin, S. Abdullah, A. Fahmi, Trapezoidal linguistic cubic fuzzy TOPSIS method and application in a group decision making problem, Journal of Intelligent Systems, 29(1), (2019) 1283-1300.
  • X. Peng Hesitant trapezoidal fuzzy aggregation operators based on Archimedean $t$-norm and $t$-conorm and their application in MADM with completely unknown weight information, International Journal for Uncertainty Quantification, 7(6), (2017) 475-510.
  • X. Zhang, Z. Xu, M. Liu, Hesitant trapezoidal fuzzy QUALIFLEX method and its application in the evaluation of green supply chain initiatives, Sustainability, 8(9), (2016) 1-17.
  • X. Zhang, T. Yang, W. Liang, M. Xiong, Closeness degree-based hesitant trapezoidal fuzzy multicriteria decision making method for evaluating green suppliers with qualitative information, Discrete Dynamics in Nature and Society, 2018, (2018) Article ID: 3178039, 1-13.
  • F. Amin, A . Fahmi, S. Abdullah, Dealer using a new trapezoidal cubic hesitant fuzzy TOPSIS method and application to group decision-making program, Soft Computing, 23(14), (2019) :5353-5366.
  • A. Fahmi, S. Abdullah, F. Amin, A. Ali, R. Ahmed, M. Shakeel, Trapezoidal cubic hesitant fuzzy aggregation operators and their application in group decision-making, Journal of Intelligent and Fuzzy Systems, 36(4), (2019) 3619-3635.
  • A. Fahmi, S. Abdullah, F. Amin, M. Aslam, S. Hussain, Trapezoidal linguistic cubic fuzzy TOPSIS method and application in a group decision making program, Journal of Intelligent Systems 29(1), (2020) 1283-1300.
  • A. Fahmi., F. Amin, S. Abdullah, M. Shakeel, Power average operators of trapezoidal cubic fuzzy numbers and application to multi-attribute group Decision making, Journal of Intelligent Systems, 29(1), (2020) 1643-1661.
  • İ. Deli, F. Karaaslan, Generalized trapezoidal hesitant fuzzy numbers and their applications to multiple criteria decision making problems, Soft Computing, 25(2), (2021) 1017-1032.
  • İ. Deli, A TOPSIS method by using generalized trapezoidal hesitant fuzzy numbers and application to a robot selection problem, Journal of Intelligent and Fuzzy Systems, 38(1), (2020) 779-793.
  • E. Ö. Çelik, Some distance and correlation coefficient measures of generalized trapezoidal hesitant fuzzy numbers and their application to decision making problems, Master's Thesis, Kilis 7 Aralık University (2022), Kilis, Turkiye (in Turkish).
  • İ. Deli, Bonferroni mean operators of generalized trapezoidal hesitant fuzzy numbers and their application to decision-making problems, Soft Computing, 25(6), (2021) 4925-4949.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

İrfan Deli 0000-0003-1875-1067

Elif Özge Çelik 0000-0001-9109-154X

Publication Date August 31, 2022
Published in Issue Year 2022 Volume: 11 Issue: 2

Cite

APA Deli, İ., & Çelik, E. Ö. (2022). Not-ordered quasi-distance measures of generalised trapezoidal hesitant fuzzy numbers and their application to decision making problems. Journal of New Results in Science, 11(2), 162-181. https://doi.org/10.54187/jnrs.1160127
AMA Deli İ, Çelik EÖ. Not-ordered quasi-distance measures of generalised trapezoidal hesitant fuzzy numbers and their application to decision making problems. JNRS. August 2022;11(2):162-181. doi:10.54187/jnrs.1160127
Chicago Deli, İrfan, and Elif Özge Çelik. “Not-Ordered Quasi-Distance Measures of Generalised Trapezoidal Hesitant Fuzzy Numbers and Their Application to Decision Making Problems”. Journal of New Results in Science 11, no. 2 (August 2022): 162-81. https://doi.org/10.54187/jnrs.1160127.
EndNote Deli İ, Çelik EÖ (August 1, 2022) Not-ordered quasi-distance measures of generalised trapezoidal hesitant fuzzy numbers and their application to decision making problems. Journal of New Results in Science 11 2 162–181.
IEEE İ. Deli and E. Ö. Çelik, “Not-ordered quasi-distance measures of generalised trapezoidal hesitant fuzzy numbers and their application to decision making problems”, JNRS, vol. 11, no. 2, pp. 162–181, 2022, doi: 10.54187/jnrs.1160127.
ISNAD Deli, İrfan - Çelik, Elif Özge. “Not-Ordered Quasi-Distance Measures of Generalised Trapezoidal Hesitant Fuzzy Numbers and Their Application to Decision Making Problems”. Journal of New Results in Science 11/2 (August 2022), 162-181. https://doi.org/10.54187/jnrs.1160127.
JAMA Deli İ, Çelik EÖ. Not-ordered quasi-distance measures of generalised trapezoidal hesitant fuzzy numbers and their application to decision making problems. JNRS. 2022;11:162–181.
MLA Deli, İrfan and Elif Özge Çelik. “Not-Ordered Quasi-Distance Measures of Generalised Trapezoidal Hesitant Fuzzy Numbers and Their Application to Decision Making Problems”. Journal of New Results in Science, vol. 11, no. 2, 2022, pp. 162-81, doi:10.54187/jnrs.1160127.
Vancouver Deli İ, Çelik EÖ. Not-ordered quasi-distance measures of generalised trapezoidal hesitant fuzzy numbers and their application to decision making problems. JNRS. 2022;11(2):162-81.


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