Novel Interval Valued T-Spherical Fuzzy Mclaurin Symmetric Mean Operators and Their Applications in Multi-Attribute Group Decision Making Problems

Authors

  • Kifayat Ullah Department of Mathematics, Riphah Institute of Computing & Applied Sciences (RICAS), Riphah International University (Lahore Campus), Lahore, Pakistan
  • Abrar Hussain Department of Mathematics, Riphah Institute of Computing & Applied Sciences (RICAS), Riphah International University (Lahore Campus), Lahore, Pakistan
  • Adeel Ahmad Department of Mathematics, Riphah Institute of Computing & Applied Sciences (RICAS), Riphah International University (Lahore Campus), Lahore, Pakistan
  • Zeeshan Ali Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan

Keywords:

Aggregation operators, Interval-valued T-spherical fuzzy numbers, McLaurin symmetric mean operator, Multi-attribute group decision-making techniques

Abstract

Educational institutes play a significant role to build up a nation and developing society. Education is an important factor that can help a man to judge his destiny, and shape the coming future. This article aims to extend the concepts of interval-valued T-spherical fuzzy (IVTSF) set (IVTSFS) based on Maclaurin symmetric mean (MSM) operators. The main concentration of this manuscript is to study the interrelationship among any number of IVTSF numbers (IVTSFNs) by the use of Maclaurin symmetric mean (MSM) operators. We explore and develop IVTSF Maclaurin symmetric mean (IVTSFMSM) operator, IVTSF weighted MSM (IVTSFWMSM) operator, IVTSF dual MSM (IVTSFDMSM) operator, IVTSF weighted dual MSM (IVTSFWDMSM) operator. By using these examined operators, some special cases of the discovered operators are also established and their properties are examined. In addition, a procedure for handling multi-attribute group decision-making (MAGDM) techniques based on MSM operators in the IVTSF setting.  A demonstrative example to check the applicability of the MSM operators of IVTSFSs is presented which established the selection of applicants. To show the supremacy of the newly established MSM operators, a comprehensive comparative study is designed numerically.

References

Ali, Z., & Mahmood, T. (2020). Maclaurin symmetric mean operators and their applications in the environment of complex q-rung orthopair fuzzy sets. Computational and Applied Mathematics, 39(3), 1-27.

Ashtiani, B., Haghighirad, F., Makui, A., & ali Montazer, G. (2009). Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets. Applied Soft Computing, 9(2), 457-461.

Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96.

Atanassov, K. T. (1999). Interval valued intuitionistic fuzzy sets. Intuitionistic fuzzy sets. Physica, Heidelberg.

Burillo, P., & Bustince, H. (1996). Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy sets and systems, 78(3), 305-316.

Bustince, H., Barrenechea, E., Pagola, M., & Fernández, J. (2009). Interval-valued fuzzy sets constructed from matrices: Application to edge detection. Fuzzy Sets and systems, 160(13), 1819-1840.

Cuong, B. C., & Kreinovich, V. (2013). Picture Fuzzy Sets-a new concept for computational intelligence problems. In 2013 third world congress on information and communication technologies WICT 2013, 1-6.

DeTemple, D. W., & Robertson, J. M. (1979). On generalized symmetric means of two variables. Publikacije Elektrotehničkog fakulteta. Serija Matematika i fizika, 634 (677), 236-238.

Garg, H. (2016). A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem. Journal of Intelligent & Fuzzy Systems, 31(1), 529-540.

Garg, H. (2018). A linear programming method based on an improved score function for interval-valued Pythagorean fuzzy numbers and its application to decision-making. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 26(01), 67-80.

Garg, H. (2021). A new possibility degree measure for interval‐valued q‐rung orthopair fuzzy sets in decision‐making. International Journal of Intelligent Systems, 36(1), 526-557.

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, 27(12), 2302-2311.

Garg, H., & Rani, D. (2019). Complex interval-valued intuitionistic fuzzy sets and their aggregation operators. Fundamenta Informaticae, 164(1), 61-101.

Garg, H., & Rani, D. (2019). Novel aggregation operators and ranking method for complex intuitionistic fuzzy sets and their applications to decision-making process. Artificial Intelligence Review. 1-26.

Garg, H., Agarwal, N., & Tripathi, A. (2017). Some improved interactive aggregation operators under interval-valued intuitionistic fuzzy environment and its application to decision making process. Scientia Iranica, 24(5), 2581-2604.

Garg, H., Ali, Z., & Mahmood, T. (2021). Algorithms for complex interval‐valued q‐rung orthopair fuzzy sets in decision making based on aggregation operators, AHP, and TOPSIS. Expert Systems, 38(1), e12609.

Garg, H., Munir, M., Ullah, K., Mahmood, T., & Jan, N. (2018). Algorithm for T-spherical fuzzy multi-attribute decision making based on improved interactive aggregation operators. Symmetry, 10(12), 670.

Garg, H., Ullah, K., Mahmood, T., Hassan, N., & Jan, N. (2021). T-spherical fuzzy power aggregation operators and their applications in multi-attribute decision making. journal of Ambient Intelligence and Humanized Computing. 1-14.

Gorzałczany, M. B. (1987). A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy sets and systems, 21(1), 1-17.

Grzegorzewski, P. (2004). Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy sets and systems, 148(2), 319-328.

Hussain, A., Alsanad, A., Ullah, K., Ali, Z., Jamil, M. K., & Mosleh, M. A. (2021). Investigating the short-circuit problem using the planarity index of complex q-rung orthopair fuzzy planar graphs. Complexity.

Hussain, A., Ullah, K., Alshahrani, M. N., Yang, M. S., & Pamucar, D. (2022). Novel Aczel–Alsina Operators for Pythagorean Fuzzy Sets with Application in Multi-Attribute Decision Making. Symmetry, 14(5), 940.

Hwang, C., & Rhee, F. C. H. (2004). An interval type-2 fuzzy C spherical shells algorithm. In 2004 IEEE International Conference on Fuzzy Systems, 2, 1117-1122.

Joshi, B. P., Singh, A., Bhatt, P. K., & Vaisla, K. S. (2018). Interval valued q-rung orthopair fuzzy sets and their properties. Journal of Intelligent & Fuzzy Systems, 35(5), 5225-5230.

Kalathian, S., Ramalingam, S., Srinivasan, N., Raman, S., & Broumi, S. (2020). Embedding of fuzzy graphs on topological surfaces. Neural computing and applications, 32(9), 5059-5069.

Khalil, A. M., Li, S. G., Garg, H., Li, H., & Ma, S. (2019). New operations on interval-valued picture fuzzy set, interval-valued picture fuzzy soft set and their applications. Ieee Access, 7, 51236-51253.

Liu, J., Zhou, N., Zhuang, L. H., Li, N., & Jin, F. F. (2017). Interval-valued hesitant fuzzy multiattribute group decision making based on improved hamacher aggregation operators and continuous entropy. Mathematical Problems in Engineering.

Liu, P., Munir, M., Mahmood, T., & Ullah, K. (2019). Some similarity measures for interval-valued picture fuzzy sets and their applications in decision making. Information, 10(12), 369.

Maclaurin C. A. (1729). second letter to Martin Folkes, Esq.; concerning the roots of equations, with demonstration of other rules of algebra, Philos Trans Roy Soc London Ser A, 36, 59–96.

Mahmood, T., Ullah, K., Khan, Q., & Jan, N. (2019). An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Computing and Applications, 31(11), 7041-7053.

Peng, X., & Li, W. (2019). Algorithms for interval-valued pythagorean fuzzy sets in emergency decision making based on multiparametric similarity measures and WDBA. Ieee Access, 7, 7419-7441.

Qin, J., & Liu, X. (2014). An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. Journal of Intelligent & Fuzzy Systems, 27(5), 2177-2190.

Ullah, K., Hassan, N., Mahmood, T., Jan, N., & Hassan, M. (2019). Evaluation of investment policy based on multi-attribute decision-making using interval valued T-spherical fuzzy aggregation operators. Symmetry, 11(3), 357.

Ullah, K., Hussain, A., Mahmood, T., Ali, Z., Alabrah, A., & Rahman, S. M. M. (2022). Complex q-rung orthopair fuzzy competition graphs and their applications. Electronic Research Archive, 30(4), 1558-1605.

Ullah, K., Mahmood, T., Jan, N., & Ahmad, Z. (2020). Policy decision making based on some averaging aggregation operators of t-spherical fuzzy sets; a multi-attribute decision making approach. Annals of Optimization Theory and Practice, 3(3), 69-92.

Wang, J., Wei, G., Wang, R., Alsaadi, F. E., Hayat, T., Wei, C., ... & Wu, J. (2019). Some q‐rung interval‐valued orthopair fuzzy Maclaurin symmetric mean operators and their applications to multiple attribute group decision making. International Journal of Intelligent Systems, 34(11), 2769-2806.

Wei, G., Garg, H., Gao, H., & Wei, C. (2018). Interval-valued Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making. Ieee Access, 6, 67866-67884.

Wei, G., Zhang, S., Lu, J., Wu, J., & Wei, C. (2019). An extended bidirectional projection method for picture fuzzy MAGDM and its application to safety assessment of construction project. Ieee Access, 7, 166138-166147.

Yager, R. R. (2013). Pythagorean fuzzy subsets. In 2013 joint IFSA world congress and NAFIPS annual meeting. 57-61.

Yager, R. R. (2016). Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems, 25(5), 1222-1230.

Zadeh, L.A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.

Zhang, W., Li, X., & Ju, Y. (2014). Some aggregation operators based on Einstein operations under interval-valued dual hesitant fuzzy setting and their application. Mathematical Problems in Engineering.

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Published

2022-08-29

How to Cite

Ullah, K., Hussain, A., Ahmad, A., & Ali, Z. . (2022). Novel Interval Valued T-Spherical Fuzzy Mclaurin Symmetric Mean Operators and Their Applications in Multi-Attribute Group Decision Making Problems. Operations Research and Engineering Letters, 1(1), 44–75. Retrieved from http://orel.unionnikolatesla.edu.rs/index.php/orel/article/view/15

Issue

Vol. 1 No. 1 (2022): Operations Research and Engineering Letters

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Articles

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Copyright (c) 2022 Kifayat Ullah, Abrar Hussain, Adeel Ahmad, Zeeshan Ali

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