Abstract
This paper presents a new compromising approach to multiple criteria group decision-making (MCGDM) for the treatment of uncertainty which is based on Pythagorean fuzzy (PF) sets. The present work intends to propose a novel linear programming technique for multidimensional analysis of preference (LINMAP) by way of some useful concepts related to PF dominance relations, individual consistency and inconsistency levels, and individual fit measurements. The concept of PF scalar function-based dominance measures is defined to conduct intracriterion comparisons concerning uncertain evaluation information based on Pythagorean fuzziness; moreover, several valuable properties are also investigated to demonstrate its effectiveness. For the assessment of overall dominance of alternatives, this paper provides a synthetic index, named a comprehensive dominance measure, which is the aggregation of the weighted dominance measures by combining unknown weight information and PF dominance measures of various criteria. For each decision-maker, this paper employs the proposed measures to evaluate the individual levels of rank consistency and rank inconsistency regarding the obtained overall dominance relations and the decision-maker’s preference comparisons over paired alternatives. In the framework of individual fit measurements, this paper constructs bi-objective mathematical programming models and then provides their corresponding parametric linear programming models for generating the best compromise alternative. Realistic applications with some comparative analyses concerning railway project investment are implemented to demonstrate the appropriateness and usefulness of the proposed methodology in addressing actual MCGDM problems.
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References
V. Srinivasan, A.D. Shocker, Linear programming techniques for multidimensional analysis of preference, Psychometrika. 38 (1973), 337–342.
M.-Y. Quan, Z.-L. Wang, H.-C. Liu, H. Shi, A hybrid MCDM approach for large group green supplier selection with uncertain linguistic information, IEEE Access. 6 (2018), 50372–50383.
M.H. Haghighi, S.M. Mousavi, V. Mohagheghi, A new soft computing model based on linear assignment and linear programming technique for multidimensional analysis of preference with interval type-2 fuzzy sets, Appl. Soft Comput. 77 (2019), 780–796.
W.-J. Zuo, D.-F. Li, G.-F. Yu, L.-P. Zhang, A large group decision-making method and its application to the evaluation of property perceived service quality, J. Intell. Fuzzy Syst. 37 (2019), 1513–1527.
X. Liu, X. Wang, Q. Qu, L. Zhang, Double hierarchy hesitant fuzzy linguistic mathematical programming method for MAGDM based on Shapley values and incomplete preference information, IEEE Access. 6 (2018), 74162–74179.
X. Gou, Z. Xu, H. Liao, Hesitant fuzzy linguistic possibility degree-based linear assignment method for multiple criteria decision-making, Int. J. Inf. Technol. Decis. Making. 18 (2019), 35–63.
W. Song, J. Zhu, S. Zhang, X. Liu, A multi-stage uncertain risk decision-making method with reference point based on extended LINMAP method, J. Intell. Fuzzy Syst. 35 (2018), 1133–1146.
S.-P. Wan, D.-F. Li, Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees, Inf. Sci. 325 (2015), 484–503.
S.-P. Wan, Z. Jin, J.-Y. Dong, Pythagorean fuzzy mathematical programming method for multi-attribute group decision making with Pythagorean fuzzy truth degrees, Knowl. Inf. Syst. 55 (2018), 437–466.
X. Zhang, Z. Xu, Interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives, Comput. Indus. Eng. 75 (2014), 217–229.
S.-P. Wan, D.-F. Li, Atanassov’s intuitionistic fuzzy programming method for heterogeneous multiattribute group decision making with Atanassov’s intuitionistic fuzzy truth degrees, IEEE Trans. Fuzzy Syst. 22 (2014), 300–312.
W. Zhang, Y. Ju, X. Liu, Interval-valued intuitionistic fuzzy programming technique for multicriteria group decision making based on Shapley values and incomplete preference information, Soft Comput. 21 (2016), 5787–5804.
W. Zhang, Y. Ju, X. Liu, M. Giannakis, A mathematical programming-based method for heterogeneous multicriteria group decision analysis with aspirations and incomplete preference information, Comput. Indus. Eng. 113 (2017), 541–557.
S.-P. Wan, Y.-L. Qin, J.-Y. Dong, A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees, Knowl. Based Syst. 138 (2017), 232–248.
Y.J. Xu, A. W. Xu, H.M. Wang, Hesitant fuzzy linguistic linear programming technique for multidimensional analysis of preference for multi-attribute group decision making, Int. J. Mach. Learn. Cybern. 7 (2016), 845–855.
H. Liao, L. Jiang, Z. Xu, J. Xu, F. Herrera, A linear programming method for multiple criteria decision making with probabilistic linguistic information, Inf. Sci. 415–416 (2017), 341–355.
J. Qin, X. Liu, W. Pedrycz, A multiple attribute interval type-2 fuzzy group decision making and its application to supplier selection with extended LINMAP method, Soft Comput. 21 (2017), 3207–3226.
E. Haktanır, C. Kahraman, A novel interval-valued Pythagorean fuzzy QFD method and its application to solar photovoltaic technology development, Comput. Indus. Eng. 132 (2019), 361–372.
R.R. Yager, Pythagorean fuzzy subsets, in Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, 2013, pp. 57–61.
R.R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE Trans. Fuzzy Syst. 22 (2014), 958–965.
R.R. Yager, Properties and applications of Pythagorean fuzzy sets, in: P. Angelov, S. Sotirov (Eds.), Imprecision and Uncertainty in Information Representation and Processing, Studies in Fuzziness and Soft Computing, vol. 332, Springer, Cham, Switzerland, 2016, pp. 119–136.
R.R. Yager, A.M. Abbasov, Pythagorean membership grades, complex numbers, and decision making, Int. J. Intell. Syst. 28 (2013), 436–452.
M.S.A. Khan, The Pythagorean fuzzy Einstein Choquet integral operators and their application in group decision making, Comput. Appl. Math. 38 (2019), 128.
Y.-L. Lin, L.-H. Ho, S.-L. Yeh, T.-Y. Chen, A Pythagorean fuzzy TOPSIS method based on novel correlation measures and its application to multiple criteria decision analysis of inpatient stroke rehabilitation, Int. J. Comput. Intell. Syst. 12 (2019), 410–425.
J.-C. Wang, T.-Y. Chen, Multiple criteria decision analysis using correlation-based precedence indices within Pythagorean fuzzy uncertain environments, Int. J. Comput. Intell. Syst. 11 (2018), 911–924.
W. Xue, Z. Xu, X. Zhang, X. Tian, Pythagorean fuzzy LINMAP method based on the entropy theory for railway project investment decision making, Int. J. Intell. Syst. 33 (2018), 93–125.
L. Liu, X. Zhang, Comment on Pythagorean and complex fuzzy set operations, IEEE Trans. Fuzzy Syst. 26 (2018), 3902–3904.
W. Zeng, D. Li, Q. Yin, Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making, Int. J. Intell. Syst. 33 (2018), 2236–2254.
X. Zhang, Z. Xu, Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets, Int. J. Intell. Syst. 29 (2014), 1061–1078.
X. Peng, Y. Yang, Some results for Pythagorean fuzzy sets, Int. J. Intell. Syst. 30 (2015), 1133–1160.
X. Zhang, Multicriteria Pythagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index-based ranking methods, Inf. Sci. 330 (2016), 104–124.
D. Li, W. Zeng, Distance measure of Pythagorean fuzzy sets, Int. J. Intell. Syst. 33 (2018), 348–361.
T.-Y. Chen, A novel PROMETHEE-based outranking approach for multiple criteria decision analysis with Pythagorean fuzzy information, IEEE Access. 6 (2018), 54495–54506.
T.-Y. Chen, Novel generalized distance measure of Pythagorean fuzzy sets and a compromise approach for multiple criteria decision analysis under uncertainty, IEEE Access. 7 (2019), 58168–58185.
T.-Y. Chen, A novel PROMETHEE-based method using a Pythagorean fuzzy combinative distance-based precedence approach to multiple criteria decision making, Appl. Soft Comput. 82 (2019), 1–27.
F.K. Gündoǧdu, A spherical fuzzy extension of MULTIMOORA method, J. Intell. Fuzzy Syst. 38 (2020), 963–978.
S. Mete, Assessing occupational risks in pipeline construction using FMEA-based AHP-MOORA integrated approach under Pythagorean fuzzy environment, Hum. Ecol. Risk Assess. 25 (2019), 1645–1660.
N.E. Oz, S. Mete, F. Serin, M. Gul, Risk assessment for clearing and grading process of a natural gas pipeline project: an extended TOPSIS model with Pythagorean fuzzy sets for prioritizing hazards, Hum. Ecol. Risk Assess. 25 (2019), 1615–1632.
L. Pérez-Domínguez, L.A. Rodríguez-Picón, A. Alvarado-Iniesta, D. Luviano Cruz, Z. Xu, MOORA under Pythagorean fuzzy set for multiple criteria decision making, Complexity. 2018 (2018), 1–10.
P. Rani, A.R. Mishra, K.R. Pardasani, A. Mardani, H. Liao, D. Streimikiene, A novel VIKOR approach based on entropy and divergence measures of Pythagorean fuzzy sets to evaluate renewable energy technologies in India, J. Clean. Prod. 238 (2019), 1–17.
S. Seker, N. Aydin, Hydrogen production facility location selection for Black Sea using entropy based TOPSIS under IVPF environment, Int. J. Hydrogen Energy. (2020), (in press).
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Wang, JC., Chen, TY. A Novel Pythagorean Fuzzy LINMAP-Based Compromising Approach for Multiple Criteria Group Decision-Making with Preference Over Alternatives. Int J Comput Intell Syst 13, 444–463 (2020). https://doi.org/10.2991/ijcis.d.200408.001
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DOI: https://doi.org/10.2991/ijcis.d.200408.001