ORIGINAL ARTICLE
Multiattribute decision making based on power operators for linguistic intuitionistic fuzzy set using set pair analysis
Harish Garg,
Kamal Kumar,
Corresponding Author
Harish Garg
School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala, Punjab, India
Correspondence
Harish Garg, School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala 147004, Punjab, India.
Email: [email protected]
Search for more papers by this authorKamal Kumar
School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala, Punjab, India
Search for more papers by this authorHarish Garg,
Kamal Kumar,
Corresponding Author
Harish Garg
School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala, Punjab, India
Correspondence
Harish Garg, School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala 147004, Punjab, India.
Email: [email protected]
Search for more papers by this authorKamal Kumar
School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala, Punjab, India
Search for more papers by this authorAbstract
The aim of the presented paper is to give a multiattribute decision making (MADM) method under the linguistic intuitionistic fuzzy (LIF) environment using the set pair analysis (SPA) theory. LIF set can express the qualitative information in terms of linguistic variables, whereas the connection number (CN) based on the “identity,” “discrepancy,” and “contrary” degrees of the SPA theory handles the uncertainties and certainties systems. On the basis of these features, we develop some series of linguistic CN (LCN) power weighted and ordered weighted geometric aggregation operator to aggregate the different LCNs. Several properties of the operators are also studied. Afterward, we present a novel MADM method to solve decision-making problems under LIF set environment and illustrate with several examples to validate it. A comparative analysis is also presented to show the results.
REFERENCES
- Arora, R., & Garg, H. (2018a). Robust aggregation operators for multi-criteria decision making with intuitionistic fuzzy soft set environment. Scientia Iranica E, 25(2), 931–942.
- Arora, R., & Garg, H. (2018b). A robust correlation coefficient measure of dual hesistant fuzzy soft sets and their application in decision making. Engineering Applications of Artificial Intelligence, 72, 80–92.
- Arora, R., & Garg, H. (2019). Group decision-making method based on prioritized linguistic intuitionistic fuzzy aggregation operators and its fundamental properties. Computational and Applied Mathematics, 38(2), 1–36. https://doi.org/10.1007/s40314-019-0764-1
- Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.
- Atanassov, K., & Gargov, G. (1989). Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31, 343–349.
- Cao, Y. X., Zhou, H., & Wang, J. Q. (2018). An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis. International Journal of Machine Learning and Cybernetics, 9(4), 629–640.
- ChangJian, W. (2007). Application of the set pair analysis theory in multiple attribute decision-making. Journal of Mechanical Strength, 6(029), 1009–1012.
- Chen, S. M., Cheng, S. H., & Chiou, C. H. (2016). Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology. Information Fusion, 27, 215–227.
- Chen, Z., Liu, P., & Pei, Z. (2015). An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers. Journal of Computational Intelligence Systems, 8(4), 747–760.
- Fu, S., & Zhou, H. (2016). Triangular fuzzy number multi-attribute decision-making method based on set-pair analysis. Journal of Software Engineering, 6(4), 52–58.
- Garg, H. (2016). Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making. Computers and Industrial Engineering, 101, 53–69.
- Garg, H. (2017). Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Engineering Applications of Artificial Intelligence, 60, 164–174.
- Garg, H. (2018). Some robust improved geometric aggregation operators under interval-valued intuitionistic fuzzy environment for multi-criteria decision -making process. Journal of Industrial & Management Optimization, 14(1), 283–308.
- Garg, H., & Arora, R. (2019). Generalized intuitionistic fuzzy soft power aggregation operator based on t-norm and their application in multi criteria decision-making. International Journal of Intelligent Systems, 34(2), 215–246.
- Garg, H., & Kaur, G. (2018). Algorithm for probabilistic dual hesitant fuzzy multi-criteria decision making based on aggregation operators with new distance measures. Mathematics, 6(12), 280. https://doi.org/10.3390/math6120280
- Garg, H., & Kumar, K. (2018a). An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making. Soft Computing, 22(15), 4959–4970.
- Garg, H., & Kumar, K. (2018b). Distance measures for connection number sets based on set pair analysis and its applications to decision making process. Applied Intelligence, 48(10), 3346–3359.
- Garg, H., & Kumar, K. (2018c). Group decision making approach based on possibility degree measures and the linguistic intuitionistic fuzzy aggregation operators using Einstein norm operations. Journal of Multiple-Valued Logic & Soft Computing, 31(1/2), 175–209.
- Garg, H., & Kumar, K. (2018d). A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application. Scientia Iranica E, 25(4), 2373–2388.
- Garg, H., & Kumar, K. (2018e). A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory. Artificial Intelligence Review, 1–30. https://doi.org/10.1007/s10462-018-9668-5
- Garg, H., & Kumar, K. (2018f). Some aggregation operators for linguistic intuitionistic fuzzy set and its application to group decision-making process using the set pair analysis. Arabian Journal for Science and Engineering, 43(6), 3213–3227.
- Garg, H., & Kumar, K. (2019). Linguistic interval-valued atanassov intuitionistic fuzzy sets and their applications to group decision-making problems. IEEE Transactions on Fuzzy Systems, 1–10. https://doi.org/10.1109/TFUZZ.2019.2897961
- Garg, H., & Rani, D. (2019). Complex interval- valued intuitionistic fuzzy sets and their aggregation operators. Fundamenta Informaticae, 164(1), 61–101.
- Herrera, F., & Martínez, L. (2001). A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making. IEEE Transactions on Systems, Man, and Cybernetics Part B (Cybernetics), 31(2), 227–234.
- Hu, J., & Yang, L. (2011). Dynamic stochastic multi-criteria decision making method based on cumulative prospect theory and set pair analysis. Systems Engineering Procedia, 1, 432–439.
- Jiang, Y. L., Xu, C. F., Yao, Y., & Zhao, K. Q. (2004). Systems information in set pair analysis and its applications. In Proceedings of 2004 International Conference on Machine Learning and Cybernetics, 3, Shanghai, China, China, pp. 1717–1722.
- Kaur, G., & Garg, H. (2018a). Cubic intuitionistic fuzzy aggregation operators. International Journal for Uncertainty Quantification, 8(5), 405–427.
- Kaur, G., & Garg, H. (2018b). Multi-attribute decision-making based on Bonferroni mean operators under cubic intuitionistic fuzzy set environment. Entropy, 20(1), 65. https://doi.org/10.3390/e20010065
- Kaur, G., & Garg, H. (2019). Generalized cubic intuitionistic fuzzy aggregation operators using t-norm operations and their applications to group decision-making process. Arabian Journal for Science and Engineering, 44(3), 2775–2794.
- Khalil, A. M., Li, S. G., Garg, H., Li, H. X., & Ma, S. Q. (2019). New operations on interval-valued picture fuzzy set, interval-valued picture fuzzy soft set and their applications. IEEE Access, 7, 51236–51253.
- Kumar, K., & Garg, H. (2018a). Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making. Applied Intelligence, 48(8), 2112–2119.
- Kumar, K., & Garg, H. (2018b). Prioritized linguistic interval-valued aggregation operators and their applications in group decision-making problems. Mathematics, 6(10), 209. https://doi.org/10.3390/math6100209
- Kumar, K., & Garg, H. (2018c). TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Computational and Applied Mathematics, 37(2), 1319–1329.
- Liu, P., & Liu, X. (2017). Multiattribute group decision making methods based on linguistic intuitionistic fuzzy power bonferroni mean operators. Complexity, 2017, Article ID 3571459. 15 pages.
- Liu, P., Liu, Z., & Zhang, X. (2014). Some intuitionistic uncertain linguistic heronian mean operators and their application to group decision making. Applied Mathematics and Computation, 230, 570–586.
- Liu, P., & Qin, X. (2017a). Maclaurin symmetric mean operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision-making. Journal of Experimental & Theoretical Artificial Intelligence, 29(6), 1173–122.
- Liu, P., & Qin, X. (2017b). Power average operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision making. Journal of Intelligent & Fuzzy Systems, 32(1), 1029–1043.
- Liu, P., & Wang, P. (2017). Some improved linguistic intuitionistic fuzzy aggregation operators and their applications to multiple-attribute decision making. International Journal of Information Technology & Decision Making, 16(3), 817–850.
- Lü, W. S., & Zhang, B. (2012). Set pair analysis method of containing target constraint mixed interval multi-attribute decision-making, Applied Mechanics and Materials, Vol. 226. Trans Tech Publ, 2222–2226.
- Nancy, & Garg, H. (2019). A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment. Journal of Intelligent & Fuzzy Systems, 36(1), 101–115.
- Peng, X., Dai, J., & Garg, H. (2018). 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), 2255–2282.
- Peng, X. D., & Garg, H. (2018). Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure. Computers & Industrial Engineering, 119, 439–452.
- Peng, H. G., Wang, J. Q., & Cheng, P. F. (2018). A linguistic intuitionistic multi-criteria decision-making method based on the frank heronian mean operator and its application in evaluating coal mine safety. International Journal of Machine Learning and Cybernetics, 9, 1053–1068.
- Rani, D., & Garg, H. (2018). Complex intuitionistic fuzzy power aggregation operators and their applications in multi-criteria decision-making. Expert Systems, 35(6), e12325. https://doi.org/10.1111/exsy.12325
- Rani, D., & Garg, H. (2019). Some modified results of the subtraction and division operations on interval neutrosophic sets. Journal of Experimental & Theoretical Artificial Intelligence, 1–22. https://doi.org/10.1080/0952813X.2019.1592236
- Singh, S., & Garg, H. (2017). Distance measures between type-2 intuitionistic fuzzy sets and their application to multicriteria decision-making process. Applied Intelligence, 46(4), 788–799.
- Singh, S., & Garg, H. (2018). Symmetric triangular interval type-2 intuitionistic fuzzy sets with their applications in multi criteria decision making. Symmetry, 10(9), 401. https://doi.org/10.3390/sym10090401
- Wang, X., & Triantaphyllou, E. (2008). Ranking irregularities when evaluating alternatives by using some ELECTRE methods. Omega - International Journal of Management Science, 36, 45–63.
- Wei, G., Zhao, X., Lin, R., & Wang, H. (2013). Uncertain linguistic Bonferroni mean operators and their application to multi attribute decision making. Applied Mathematical Modelling, 37(7), 5277–5285.
- Xie, Z., Zhang, F., Cheng, J., & Li, L. (2013). Fuzzy multi-attribute decision making methods based on improved set pair analysis. In Sixth International Symposium on Computational Intelligence and Design, 2, Hangzhou, China, pp. 386–389.
- Xu, Z. (2004). Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Information Science, 168(1), 171–184.
- Xu, Z. (2005). An approach based on similarity measure to multiple attribute decision making with trapezoid fuzzy linguistic variables. In International Conference on Fuzzy Systems and Knowledge Discovery, Berlin, Heidelberg, pp. 110–117.
- Xu, Z. (2006). An approach based on the uncertain lowg and induced uncertain lowg operators to group decision making with uncertain multiplicative linguistic preference relations. Decision Support Systems, 41(2), 488–499.
- Xu, Z. S. (2007). Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15, 1179–1187.
- Xu, Z. (2011). Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowledge-Based Systems, 24(6), 749–760.
- Xu, Z., & Chen, J. (2007). On geometric aggregation over interval-valued intuitionistic fuzzy information. In Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007), 2, Haikou, China, pp. 466–471.
- Xu, Z., He, Y., & Wang, X. (2019). An overview of probabilistic-based expressions for qualitative decision-making: Techniques, comparisons and developments. International Journal of Machine Learning and Cybernetics, 10(6), 1513–1528.
- Xu, Z. S., & Yager, R. R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems, 35, 417–433.
- Xu, Z., & Yager, R. R. (2010). Power-geometric operators and their use in group decision making. IEEE Transactions on Fuzzy Systems, 18(1), 94–105.
- Yager, R. R. (2001). The power average operator. IEEE Systems, Man, and Cybernetics Society, 31(6), 724–731.
- Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.
- Zhang, H. (2014). Linguistic intuitionistic fuzzy sets and application in MAGDM. Journal of Applied Mathematics, 2014, Article ID 432092 11 pages. https://doi.org/10.1155/2014/432092
- Zhao, K. (1989). Set pair and set pair analysis—A new concept and systematic analysis method. In Proceedings of the National Conference on System Theory and Regional Planning, pp. 87–91.
