Abstract
Assessment cleaner production (CP) is an important and successful tool to resolve the contradiction between economic growth and environmental pollution. To avoid destroying the ecological environment in the utilization process of mineral resources, CP has been developed in many gold mines to achieve the goal of sustainable development. Further, the hamacher aggregation (HA) operator is a classical kind of aggregation operator used in fusion theory. The prominent characteristic of the HA operator is that it can capture the interrelationship among the multi‐input arguments. In this paper, the complex q-rung orthopair fuzzy sets (Cq-ROFSs) and their fundamental properties are developed. The HA operators based on Cq-ROFSs are pioneered and also study their existing methods. Moreover, we resolve the case of assessing CP in gold mines using multi-attribute group decision making (MAGDM) problem to examine the reliability and effectiveness of the proposed approach. Further, the comparative analysis, advantages and sensitive analysis of the proposed methods, using the cleaner production assessment in gold mines are also discussed.
Similar content being viewed by others
References
Al-Husban R, Salleh AR, Ahmad AG (2017) Complex intuitionistic fuzzy normal subgroup. Int J Pure Appl Math 115(3):199–210
Alkouri AM, Salleh AR (2012) Complex intuitionistic fuzzy sets. In: AIP Conference Proceedings (Vol. 1482, No. 1, pp. 464–470). AIP.
Alkouri AU, Salleh AR (2013) Complex atanassov's intuitionistic fuzzy relation. In: Abstract and Applied Analysis 2013 (Vol. 2013). Hindawi.
Atanassove KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96
Bai K, Zhu X, Wang J, Zhang R (2018) Some partitioned Maclaurin symmetric mean based on q-rung orthopair fuzzy information for dealing with multi-attribute group decision making. Symmetry 10(9):383
Boran FE, Genç S, Kurt M, Akay D (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36(8):11363–11368
Darko AP, Liang D (2020) Some q-rung orthopair fuzzy Hamacher aggregation operators and their application to multiple attribute group decision making with modified EDAS method. EngApplArtifIntell 1(87):103259
Dengfeng L, Chuntian C (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern RecognLett 23(1–3):221–225
Devi K, Yadav SP (2013) A multicriteria intuitionistic fuzzy group decision making for plant location selection with ELECTRE method. Int J AdvManufTechnol 66(9–12):1219–1229
Gao H (2018) Pythagorean fuzzy hamacher prioritized aggregation operators in multiple attribute decision making. J Intell Fuzzy Syst 35(2):2229–2245
Garg H (2016a) A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem J. Intell Fuzzy Syst 31(1):529–540
Garg H (2016b) A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes. Int J IntellSyst 31(12):1234–1252
Garg H (2017a) A novel improved accuracy function for interval valued Pythagorean fuzzy sets and its applications in the decision-making process. Int J IntellSyst 32(12):1247–1260
Garg H (2017b) Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process. Comput Math Organ Theory 23(4):546–571
Garg H (2017c) Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process. Int J IntellSyst 32(6):597–630
Garg H (2018a) New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making. Int J IntellSyst 33(3):653–683
Garg H (2018b) Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process. Int J IntellSyst 33(6):1234–1263
Garg H (2019a) Intuitionistic fuzzy hamacher aggregation operators with entropy weight and their applications to multi-criteria decision-making problems. Iran J SciTechnol Trans Elect Eng 43(3):597–613
Garg H (2019b) New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications. Int J IntellSyst 34(1):82–106
Garg H, Rani D (2019a) Some results on information measures for complex intuitionistic fuzzy sets. Int J Intell Syst
Garg H, Rani D (2019b) A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making. ApplIntell 49(2):496–512
Garg H, Rani D (2019c) Complex interval-valued intuitionistic fuzzy sets and their aggregation operators. Fund Inform 164(1):61–101
Garg H, Rani D (2019d) Some generalized complex intuitionistic fuzzy aggregation operators and their application to multicriteria decision-making process. Arab J SciEng 44(3):2679–2698
Huang JY (2014) Intuitionistic fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 27(1):505–513
Kumar T, Bajaj RK (2014) On complex intuitionistic fuzzy soft sets with distance measures and entropies. J Math 2014
Li L, Zhang R, Wang J, Shang X (2018) Some q-rung orthopair linguistic Heronian mean operators with their application to multi-attribute group decision making. Arch Control Sci
Liang Z, Shi P (2003) Similarity measures on intuitionistic fuzzy sets. Pattern RecognLett 24(15):2687–2693
Liu P (2013) Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making. IEEE Trans Fuzzy Syst 22(1):83–97
Liu P, Li Y (2019) Multi-attribute decision making method based on generalized maclaurin symmetric mean aggregation operators for probabilistic linguistic information. ComputIndEng 131:282–294
Liu P, Liu J (2018) Some q-rung orthopai fuzzy Bonferroni mean operators and their application to multi-attribute group decision making. Int J IntellSyst 33(2):315–347
Liu P, Wang P (2018a) Multiple-attribute decision making based on Archimedean Bonferroni operators of q-rung orthopair fuzzy numbers, IEEE Transactions on Fuzzy Systems
Liu P, Wang P (2018b) Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J IntellSyst 33(2):259–280
Liu P, You X (2019) Linguistic neutrosophic partitioned Maclaurin symmetric mean operators based on clustering algorithm and their application to multi-criteria group decision-making. Artif Intell Rev 1–40.
Liu P, Zhang X (2019) A multicriteria decision-making approach with linguistic D numbers based on the choquet integral. Cogn Comput 1–16.
Liu C, Tang G, Liu P (2017) An approach to multicriteria group decision-making with unknown weight information based on Pythagorean fuzzy uncertain linguistic aggregation operators. Math Prob Eng 2017.
Liu Z, Liu P, Liu W, Pang J (2017) Pythagorean uncertain linguistic partitioned Bonferroni mean operators and their application in multi-attribute decision making. J Intell Fuzzy Syst 32(3):2779–2790
Liu P, Chen SM, Wang P (2018) Multiple-attribute group decision-making based on q-rung orthopair fuzzy power maclaurin symmetric mean operators. IEEE Trans Syst Man CybernSyst 99:1–16.
Liu P, Gao H, Ma J (2019) Novel green supplier selection method by combining quality function deployment with partitioned Bonferroni mean operator in interval type-2 fuzzy environment. InfSci 490:292–316
Mahmood T, Ullah K, Khan Q, Jan N (2018) An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput Appl 1–13.
Ramot D, Milo R, Friedman M, Kandel A (2002) Complex fuzzy sets. IEEE Trans Fuzzy Syst 10(2):171–186
Rani D, Garg H (2017) Distance measures between the complex intuitionistic fuzzy sets and their applications to the decision-making process. Int J Uncert Quant 7(5).
Rani D, Garg H (2018) Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision-making. Expert Syst 35(6):e12325
Tan C, Chen X (2010) Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert SystAppl 37(1):149–157
Teng F, Liu Z, Liu P (2018) Some power Maclaurin symmetric mean aggregation operators based on Pythagorean fuzzy linguistic numbers and their application to group decision making. Int J IntellSyst 33(9):1949–1985
Ullah K, Mahmood T, Jan N (2018) Similarity measures for T-spherical fuzzy sets with applications in pattern recognition. Symmetry 10(6):193
Ullah K, Mahmood T, Ali Z, Jan N (2019) On some distance measures of complex pythagorean fuzzy sets and their applications in pattern recognition. Complex Intell Syst 2019:1–3.
Wei G, Gao H, Wei Y (2018) Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making. Int J IntellSyst 33(7):1426–1458
Wu SJ, Wei GW (2017) Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Int J KnowlIntellEngSyst 21(3):189–201
Xu Z (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187
Xu Y, Wang H, Merigó JM (2014) Intuitionistic fuzzy Einstein Choquet integral operators for multiple attribute decision making. Technol Econ Dev Econ 20(2):227–253
Yager RR (2013) Pythagorean fuzzy subsets. In: 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS) 2013 Jun 24 (pp. 57–61). IEEE.
Yager RR (2013) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965
Yager RR (2016) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230
Ye J (2011) Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math Comput Model 53(1–2):91–97
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
Zhang SF, Liu SY (2011) A GRA-based intuitionistic fuzzy multi-criteria group decision making method for personnel selection. Expert SystAppl 38(9):11401–11405
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mahmood, T., Ali, Z. A novel approach of complex q-rung orthopair fuzzy hamacher aggregation operators and their application for cleaner production assessment in gold mines. J Ambient Intell Human Comput 12, 8933–8959 (2021). https://doi.org/10.1007/s12652-020-02697-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12652-020-02697-2