Interval-valued q-rung orthopair fuzzy integrals and their application in multi-criteria group decision making

Document Type : Original Manuscript

Authors

1 Sichuan University

2 School of Business Administration, Southwestern University of Finance and Economics, Chengdu 610207, China

Abstract

The generalized interval-valued orthopair fuzzy sets provide an extension of Yager’s generalized orthopair fuzzy sets, where membership and non-membership degrees are subsets of closed interval [0, 1]. Due to the uncertainty and ambiguity of real life, it is more superior for decision makers to provide their judgments by intervals rather than crisp numbers. Moreover, in the era of huge scale and rapid updating of information, individual weights have been quietly diluted, and the integration of information one by one is time-consuming and complicated. In recent years, some  cholars have conducted research on the calculus of generalized orthopair fuzzy sets, but no research has further revealed the intrinsic connection between the integrals of generalized interval-valued orthopair fuzzy sets and traditional aggregation operators, which is very important in applications such as large group decision making. In order to fill this theoretical gap, this paper aims to study the integrals of generalized interval-valued orthopair fuzzy functions. In detail, we define the indefinite integral starting from the inverse operations of the interval-valued q-rung orthopair fuzzy functions  (IVq-ROFFs)’ derivatives, and some fundamental properties with rigorous mathematical proofs are also discussed. To be more  practical, we continue to develop definite integrals for both simplified and generalized IVq-ROFFs. Besides, we give the corresponding Newton-Leibniz formula through limit procedure, which shows the calculation relationship between the  indefinite and definite integrals of the IVq-ROFFs. After obtaining the basic calculus results under generalized interval-valued orthopair fuzzy circumstance, we further reveal the inherent link between the integrals of generalized IVq-ROFFs and the traditional discrete aggregation operators. Finally, the practicability and feasibility of the proposed definite  integral models are illustrated by an example of public health emergency group decision-making, and sensitivity analysis and comparison are also carried out. 

Keywords

References

[1] M. I. Ali, Another view on q-rung orthopair fuzzy sets, International Journal of Intelligent Systems, 33(11) (2018), 2139-2153.
[2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96.
[3] K. T. Atanassov, P. Vassilev, On the intuitionistic fuzzy sets of n-th type, Advances in Data Analysis with Computational Intelligence Methods, (2018), 265-274.
[4] W. S. Du, Minkowski-type distance measures for generalized orthopair fuzzy sets, International Journal of Intelligent Systems, 33(4) (2018), 802-817.
[5] S. Fan, H. M. Liang, Y. C. Dong, W. Pedrycz, A personalized individual semantics-based multi-attribute group decision making approach with flexible linguistic expression, Expert Systems with Applications, 192 (2022), 116392.
[6] H. M. A. Farid, M. Riaz, Some generalized q-rung orthopair fuzzy Einstein interactive geometric aggregation operators with improved operational laws, International Journal of Intelligent Systems, 36(12) (2021), 7239-7273.
[7] J. Gao, Z. L. Liang, J. Shang, Z. S. Xu, Continuities, derivatives, and differentials of q-rung orthopair fuzzy functions, IEEE Transactions on Fuzzy Systems, 27(8) (2018), 1687-1699.
[8] J. Gao, Z. L. Liang, Z. S. Xu, Additive integrals of q-rung orthopair fuzzy functions, IEEE Transactions on Cybernetics, 50(10) (2019), 4406-4419.
[9] J. Gao, Z. S. Xu, Differential calculus of interval-valued q-rung orthopair fuzzy functions and their applications, International Journal of Intelligent Systems, 34(12) (2019), 3190-3219.
[10] X. J. Gou, Z. S. Xu, H. C. Liao, Hesitant fuzzy linguistic entropy and cross-entropy measures and alternative queuing method for multiple criteria decision making, Information Sciences, 388-389 (2017), 225-246.
[11] B. P. Joshi, A. Singh, P. K. Bhatt, K. S. Vaisla, Interval valued q-rung orthopair fuzzy sets and their properties, Journal of Intelligent and Fuzzy Systems, (2018), 1-6.
[12] Y. H. Li, G. Kou, G. X. Li, H. M. Wang, Multi-attribute group decision making with opinion dynamics based on social trust network, Information Fusion, 75 (2021), 102-115.
[13] D. C. Liang, Y. Y. Fu, Z. S. Xu, W. T. Tang, Loss function information fusion and decision rule deduction of three way decision by constructing interval-valued q-rung orthopair fuzzy integral, IEEE Transactions on Fuzzy Systems, 30(9) (2021), 3645-3660.
[14] P. D. Liu, S. M. Chen, P. Wang, Multiple-attribute group decision-making based on q-rung orthopair fuzzy power Maclaurin symmetric mean operators, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 99 (2018), 1-16.
[15] P. D. Liu, P. Wang, Multiple-attribute decision-making based on Archimedean Bonferroni operators of q-rung orthopair fuzzy numbers, IEEE Transactions on Fuzzy Systems, 27(5) (2018), 834-848.
[16] P. D. Liu, P. Wang, Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making, International Journal of Intelligent Systems, 33(2) (2018), 259-280.
[17] P. D. Liu, Y. M. Wang, Multiple attribute decision making based on q-rung orthopair fuzzy generalized Maclaurin symmetic mean operators, Information Sciences, 518 (2020), 181-210.
[18] X. D. Peng, J. G. Dai, H. Garg, Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decision-making method with a new score function, International Journal of Intelligent Systems, 33(11) (2018), 2255-2282.
[19] P. Vassilev, R. Parvathi, K. T. Atanassov, Note on intuitionistic fuzzy sets of p-th type, Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 6 (2008), 43-50.
[20] B. Wan, J. Huang, X. Chen, Y. Cheng, J. Wang, Interval-valued q-rung orthopair fuzzy choquet integral operators and their application in group decision-making, Mathematical Problems in Engineering, 2022 (2022). DOI: 10.1155/2022/7416723.
[21] G. W. Wei, H. Gao, Y. Wei, Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making, International Journal of Intelligent Systems, 33(7) (2018), 1426-1458.
[22] G. W. Wei, M. Lu, Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making, International Journal of Intelligent Systems, 33(5) (2018), 1043-1070.
[23] Z. S. Xu, Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control and Decision, 22(2) (2007), 215-219.
[24] R. R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE Transactions on Fuzzy Systems, 22(4) (2014), 958-965.
[25] R. R. Yager, Generalized orthopair fuzzy sets, IEEE Transactions on Fuzzy Systems, 25(5) (2017), 1222-1230.
[26] R. R. Yager, N. Alajlan, Approximate reasoning with generalized orthopair fuzzy sets, Information Fusion, 38 (2017), 65-73.
[27] X. L. Zhang, Multicriteria Pythagorean fuzzy decision analysis: A hierarchical QUALIFLEX approach with the closeness index-based ranking methods, Information Sciences, 330 (2016), 104-124.
[28] H. D. Zhang, T. B. Nan, Y. P. He, q-rung orthopair fuzzy N-soft aggregation operators and corresponding applica[1]tions to multiple-attribute group decision making, Soft Computing, (2022), 1-13.
[29] X. L. Zhang, Z. S. Xu, Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets, International Journal of Intelligent Systems, 29(12) (2014), 1061-1078.
[30] R. C. Zhang, Z. S. Xu, X. J. Gou, ELECTRE II method based on the cosine similarity to evaluate the performance of financial logistics enterprises under double hierarchy hesitant fuzzy linguistic environment, Fuzzy Optimization and Decision Making, 22 (2023), 23-49.
[31] R. R. Zhao, M. X. Luo, S. G. Li, L. N. Ma, A parametric similarity measure between picture fuzzy sets and its applications in multi-attribute decision-making, Iranian Journal of Fuzzy Systems, 20(1) (2023), 87-102.
Iranian Journal of Fuzzy Systems
Volume 20, Issue 7
Invited Paper
November and December 2023
Pages 1-26

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