Generalized MULTIMOORA method and Dombi prioritized weighted aggregation operators based on T-spherical fuzzy sets and their applications
Tahir Mahmood
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
Search for more papers by this authorMuhammad S. Warraich
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
Search for more papers by this authorZeeshan Ali
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
Search for more papers by this authorCorresponding Author
Dragan Pamucar
Department of Logistics, Military Academy, University of Defence in Belgrade, Belgrade, Serbia
Correspondence Dragan Pamucar, Department of Logistics, Military academy, University of Defence in Belgrade, Pavla Jurisica Sturma 33, 11000 Belgrade, Serbia.
Email: [email protected]
Search for more papers by this authorTahir Mahmood
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
Search for more papers by this authorMuhammad S. Warraich
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
Search for more papers by this authorZeeshan Ali
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
Search for more papers by this authorCorresponding Author
Dragan Pamucar
Department of Logistics, Military Academy, University of Defence in Belgrade, Belgrade, Serbia
Correspondence Dragan Pamucar, Department of Logistics, Military academy, University of Defence in Belgrade, Pavla Jurisica Sturma 33, 11000 Belgrade, Serbia.
Email: [email protected]
Search for more papers by this authorAbstract
In this manuscript, the technique of the generalized MULTIMOORA method is investigated by using the concept of a T-spherical fuzzy set (T-SFS), which is the modified idea of a picture fuzzy set to handle awkward and vague information in daily life problems. T-SFS covers the degree of truth, abstinence, and falsity with a rule that the sum of the qth-powers of all degrees is restricted to the unit interval. Moreover, for examining the interrelationships among any number of T-SFSs, we construct the idea of T-spherical fuzzy Dombi prioritized weighted arithmetic (T-SFDPWA) aggregation operators, T-spherical fuzzy Dombi prioritized arithmetic, T-spherical fuzzy Dombi prioritized geometric, and T-spherical fuzzy Dombi prioritized weighted geometric (T-SFDPWG) aggregation operators are given. Then, the basic properties of T-SFDPWA and T-SFDPWG aggregation operators are investigated and discussed in some of their cases. The investigated operators based on T-SFS are utilized in the environment of multiattribute decision-making problems to find the consistency and proficiency of the developed operators. In last, we illustrated some numerical examples based on explored operators is to examine the reliability and validity of the investigated operators with the help of comparative analysis and graphical representations with some existing ideas to show the presented approaches are extensive powerful.
REFERENCES
- 1
Zadeh LA. Fuzzy sets. Inf Control. 1965; 8(3): 338-353.
10.1016/S0019-9958(65)90241-X Google Scholar
- 2 Atanassov KT. Intuitionistic fuzzy sets. Intuitionistic Ffuzzy Sets. Heidelberg: Physica; 1999: 1-137.
- 3
Atanassov KT. Interval valued intuitionistic fuzzy sets. Intuitionistic Fuzzy Sets. Heidelberg: Physica; 1999: 139-177.
10.1007/978-3-7908-1870-3_2 Google Scholar
- 4
Kushwaha DK, Panchal D, Sachdeva A. Risk analysis of cutting system under intuitionistic fuzzy environment. Reports Mech Eng. 2020; 1(1): 162-173.
10.31181/rme200101162k Google Scholar
- 5 Ramakrishnan KR, Chakraborty S. A cloud TOPSIS model for green supplier selection. Facta Universitatis, series: Mechanical Engineering. 2020; 18(3): 375-397.
- 6 Yager RR. Pythagorean fuzzy subsets. In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS); 2013:57-61. IEEE.
- 7 Peng X, Yang Y. Some results for Pythagorean fuzzy sets. Int J Intell Syst. 2015; 30(11): 1133-1160.
- 8 Wei G, Wei Y. Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications. Int J Intell Syst. 2018; 33(3): 634-652.
- 9 Ullah K, Mahmood T, Ali Z, Jan N. On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex Intell Syst. 2020; 6(1): 15-27.
- 10 Pamucar DS, Savin LM. Multiple-criteria model for optimal off-road vehicle selection for passenger transportation: BWM-COPRAS model. Military Tech Courier. 2020; 68(1): 28-64.
- 11 Yager RR. Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst. 2016; 25(5): 1222-1230.
- 12 Liu P, Wang P. Multiple-attribute decision-making based on Archimedean Bonferroni Operators of q-rung orthopair fuzzy numbers. IEEE Trans Fuzzy Syst. 2018; 27(5): 834-848.
- 13 Gao H, Ran L, Wei G, Wei C, Wu J. VIKOR method for MAGDM based on q-rung interval-valued orthopair fuzzy information and its application to supplier selection of medical consumption products. Int J Environ Res Public Health. 2020; 17(2): 525.
- 14
Riaz M, Çagman N, Wali N, Mushtaq A. Certain properties of soft multi-set topology with applications in multi-criteria decision making. Decision Making: Appl Manage Eng. 2020; 3(2): 70-96.
10.31181/dmame2003070r Google Scholar
- 15 Liu Z, Wang X, Li L, Zhao X, Liu P. Q-rung orthopair fuzzy multiple attribute group decision-making method based on normalized bidirectional projection model and generalized knowledge-based entropy measure. J Ambient Intell Humanized Comput. 2020; 12: 1-16.
- 16
Pamucar D, Jankovic A. The application of the hybrid interval rough weighted Power-Heronian operator in multi-criteria decision making. Operation Res Eng Sci: Theory Appl. 2020; 3(2): 54-73.
10.31181/oresta2003049p Google Scholar
- 17 Wang J, Wei G, Wei C, Wei Y. MABAC method for multiple attribute group decision making under q-rung orthopair fuzzy environment. Defence Technol. 2020; 16(1): 208-216.
- 18 Liu D, Huang A. Consensus reaching process for fuzzy behavioral TOPSIS method with probabilistic linguistic q-rung orthopair fuzzy set based on correlation measure. Int J Intell Syst. 2020; 35(3): 494-528.
- 19 Cuong BC, Kreinovich V. Picture fuzzy sets. J Comput Sci Cybernet. 2014; 30(4): 409-420.
- 20 Cuong BC, Van Hai P. Some fuzzy logic operators for picture fuzzy sets. In: 2015 seventh international conference on knowledge and systems engineering (KSE); 2015:132-137. IEEE.
- 21 Tian C, Peng JJ, Zhang S, Zhang WY, Wang JQ. Weighted picture fuzzy aggregation operators and their applications to multi-criteria decision-making problems. Comput Ind Eng. 2019; 137:106037.
- 22 Jana C, Senapati T, Pal M, Yager RR. Picture fuzzy Dombi aggregation operators: application to MADM process. Appl soft Comput. 2019; 74: 99-109.
- 23 Wei G. Picture fuzzy cross-entropy for multiple attribute decision making problems. J Business Econ Manage. 2016; 17(4): 491-502.
- 24 Mahmood T, Ullah K, Khan Q, Jan N. An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput Appl. 2019; 31(11): 7041-7053.
- 25 Wu MQ, Chen TY, Fan JP. Divergence measure of T-spherical fuzzy sets and its applications in Pattern Recognition. IEEE Access. 2019; 8: 10208-10221.
- 26 Liu P, Zhu B, Wang P, Shen M. An approach based on linguistic spherical fuzzy sets for public evaluation of shared bicycles in China. Eng Appl Artif Intelligence. 2020; 87:103295.
- 27 Shishavan SAS, Gündoğdu FK, Farrokhizadeh E, Donyatalab Y, Kahraman C. Novel similarity measures in spherical fuzzy environment and their applications. Eng Appl Artif Intell. 2020; 94:103837.
- 28 Karande P, Chakraborty S. Application of multi-objective optimization on the basis of ratio analysis (MOORA) method for materials selection. Mater Des. 2012; 37: 317-324.
- 29 Baležentis T, Zeng S. Group multi-criteria decision making based upon interval-valued fuzzy numbers: an extension of the MULTIMOORA method. Expert Syst Appl. 2013; 40(2): 543-550.
- 30 Aydemir SB, Gündüz SY. Extension of multi-Moora method with some q-rung orthopair fuzzy Dombi prioritized weighted aggregation operators for multi-attribute decision making. Soft Comput. 2020; 24: 1-19.
- 31 Garg H, Munir M, Ullah K, Mahmood T, Jan N. Algorithm for T-spherical fuzzy multi-attribute decision making based on improved interactive aggregation operators. Symmetry. 2018; 10(12): 670.
- 32 Liu P, Khan Q, Mahmood T, Hassan N. T-spherical fuzzy power Muirhead mean operator based on novel operational laws and their application in multi-attribute group decision making. IEEE Access. 2019; 7: 22613-22632.
- 33 Ullah K, Hassan N, Mahmood T, Jan N, Hassan M. Evaluation of investment policy based on multi-attribute decision-making using interval valued T-spherical fuzzy aggregation operators. Symmetry. 2019; 11(3): 357-14.
- 34 Munir M, Kalsoom H, Ullah K, Mahmood T, Chu YM. T-spherical fuzzy Einstein hybrid aggregation operators and their applications in multi-attribute decision making problems. Symmetry. 2020; 12(3): 365.
- 35 Liu P, Zhu B, Wang P. A multi-attribute decision-making approach based on spherical fuzzy sets for Yunnan Baiyao's R&D project selection problem. Int J Fuzzy Syst. 2019; 21(7): 2168-2191.
- 36 Khan MJ, Kumam P, Deebani W, Kumam W, Shah Z. Distance and similarity measures for spherical fuzzy sets and their applications in selecting mega projects. Mathematics. 2020; 8(4): 519.
- 37 Guleria A, Bajaj RK. T-spherical fuzzy graphs: operations and applications in various selection processes. Arabian J Sci Eng. 2020; 45(3): 2177-2193.
- 38 Wu MQ, Chen TY, Fan JP. Similarity measures of T-spherical fuzzy sets based on the cosine function and their applications in pattern recognition. IEEE Access. 2020; 8: 98181-98192.
- 39 Guleria A, Bajaj RK. T-spherical fuzzy soft sets and its aggregation operators with application in decision making. Scientia Iranica. 2019; 28: 1014-1029. https://doi.org/10.24200/sci.2019.53027.3018
- 40 Ashraf S, Abdullah S, Abdullah L. Child development influence environmental factors determined using spherical fuzzy distance measures. Mathematics. 2019; 7(8): 661.
- 41 Mahmood T. A novel approach towards bipolar soft sets and their applications. J Math. 2020; 2020: 1-11.