Korean J. Math. Vol. 28 No. 2 (2020) pp.343-359
DOI: https://doi.org/10.11568/kjm.2020.28.2.343

Aggregation operators of cubic picture fuzzy quantities and their application in decision support systems

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Published: Jun 30, 2020
Keywords:
Cubic Picture Fuzzy Set, Algebraic Aggregation Operators, Algebraic* Aggregation Operators, Multi-attribute decision making problem.
Mathematics Subject Classification:
03E72, 62C86

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Shahzaib Ashraf
Department of Mathematics, Abdul Wali Khan University Mardan 23200, Pakistan
Saleem Abdullah
Department of Mathematics, Abdul Wali Khan University Mardan 23200, Pakistan
Tahir Mahmood
Department of Mathematics and Statistics International Islamic University, Islamabad 44000, Pakistan

Abstract

The paper aim is to resolve the issue of ranking to the fuzzy numbers in decision analysis, artificial intelligence and optimization. In the literature lot of ideologies have been established for ranking to the fuzzy numbers, that ideologies have some restrictions and limitations. In this paper, we proposed a method based on cubic picture fuzzy information's, for ranking to defeat the existing restrictions. Further introduced some cubic picture fuzzy algebraic and cubic picture fuzzy algebraic* aggregated operators for aggregated the information. Finally, a multi-attribute decision making problem is assumed as a practical application to establish the appropriateness and suitability of the proposed ranking approach.


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References

[1] S. Abdullah and S. Ashraf, Cubic picture fuzzy sets and their application to a petroleum circulation center evaluation problem, Sigma 10 (2 (2019)), 99–133. Google Scholar

[2] S. Ashraf, T. Mahmood, S. Abdullah, and Q. Khan, Different approaches to multi-criteria group decision making problems for picture fuzzy environment, Bulletin of the Brazilian Mathematical Society. New Series, 50 (2) (2019), 373- 397. Google Scholar

[3] S. Ashraf, S. Abdullah, T. Mahmood, and M. Aslam, Cleaner Production Evaluation in Gold Mines Using Novel Distance Measure Method with Cubic Picture Fuzzy Numbers, International Journal of Fuzzy Systems 21 (8) (2019), 2448– 2461. Google Scholar

[4] S. Ashraf and S. Abdullah, Some novel aggregation operators for cubic picture fuzzy information: application in multi-attribute decision support problem, Granular Computing (2020), 1–16. https://doi.org/10.1007/s41066-020-00219-1 Google Scholar

[5] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, and T. Mahmood, Spherical fuzzy sets and their applications in multi-attribute decision making problems, Journal of Intelligent & Fuzzy Systems, 36 (3) (2019), 2829–2844. Google Scholar

[6] S. Ashraf, and S. Abdullah, Spherical aggregation operators and their application in multiattribute group decision-making, International Journal of Intelligent Systems, 34 (3) (2019), 493–523. Google Scholar

[7] S. Ashraf, S. Abdullah and T. Mahmood, Spherical fuzzy Dombi aggre- gation operators and their application in group decision making problems, Journal of Ambient Intelligence and Humanized Computing, 2019. 1–19. https://doi.org/10.1007/s12652-019-01333-y Google Scholar

[8] S. Ashraf, S. Abdullah, M. Aslam, M. Qiyas, and M.A. Kutbi, Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms, Journal of Intelligent & Fuzzy Systems, 36 (6) (2019), 6089–6102. Google Scholar

[9] S. Ashraf, S. Abdullah, and L. Abdullah, Child Development Influence Environmental Factors Determined Using Spherical Fuzzy Distance Measures, Mathe- matics 7 (8) (2019), p.661. Google Scholar

[10] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87–96. Google Scholar

[11] K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 31 (1989), 343–349. Google Scholar

[12] K. Atanassov, Remark on intuitionistic fuzzy numbers, Notes on intuitionistic fuzzy sets 13 (2007), 29–32. Google Scholar

[13] B. Batool, M. Ahmad, S. Abdullah, S. Ashraf, and R. Chinram, Entropy Based Pythagorean Probabilistic Hesitant Fuzzy Decision Making Technique and Its Application for Fog-Haze Factor Assessment Problem, Entropy 22 (3) (2020), p.318. Google Scholar

[14] B. C. Cuong, V. H. Phan, Some fuzzy logic operations for picture fuzzy sets, in preceding of seventh international conference on knowledge and system engi- neering (IEEE) (2015). Google Scholar

[15] B. C. Cuong, K. Vladik, T. N. Roan , A classification of representable t-norm operators for picture fuzzy sets, in preceding of eight international conference on knowledge and system engineering (IEEE) (2016). Google Scholar

[16] B. C. Cuong, Picture Fuzzy Sets- a new concept for computational intelligence problems, In Proceedings of the Third World Congress on Information and Communication Technologies (2013), 1–6. Google Scholar

[17] H. Garg, Some Picture Fuzzy Aggregation Operators and Their Applications to Multicriteria Decision-Making, Arabian Journal For Science And Engineering (2017). Google Scholar

[18] Y. B. Jun, C. S. Kim and K. O. Yang, Cubic sets, Ann. Fuzzy Math. Inform. 4 (1) (2012) , 83–98. Google Scholar

[19] Y. B. Jun, C. S. Kim and M. S. Kang, Cubic subalgebras and ideals of BCK/BCI- algebras, Far East. J. Math. Sci. 44 (2010), 239–250. Google Scholar

[20] Y. B. Jun, C. S. Kim and J. G. Kang, Cubic q-ideals of BCI-algebras, Ann. Fuzzy Math. Inf. 1 (2011), 25–34. Google Scholar

[21] H. Jin, S. Ashraf, S. Abdullah, M. Qiyas, M. Bano, and S. Zeng, Linguistic Spherical Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems, Mathematics 7 (5) (2019), p.413. Google Scholar

[22] Y. Jin, S. Ashraf, and S. Abdullah, Spherical Fuzzy Logarithmic Aggregation Operators Based on Entropy and Their Application in Decision Support Systems, Entropy 21 (7) (2019), p.628. Google Scholar

[23] T. Mahmood, F. Mehmood, Q. Khan, Cubic Hesitant Fuzzy Sets and Their Applications to Multi Criteria Decision Making, International Journal of Algebra and Statistics 5 (1) (2016), 19–51. Google Scholar

[24] T. Mahmood, S. Abdullah, S. Rashid, M. Bilal, Multicriteria Decision Making Based On Cubic Sets, Journal of New Theory 16 (2017), 01–09. Google Scholar

[25] M. Qiyas, S. Abdullah, S. Ashraf, and M. Aslam, Utilizing linguistic picture fuzzy aggregation operators for multiple-attribute decision-making problems, International Journal of Fuzzy Systems 22 (1) (2020), 310–320. Google Scholar

[26] M. Qiyas, S. Abdullah, S. Ashraf, and L. Abdullah, Linguistic Picture Fuzzy Dombi Aggregation Operators and Their Application in Multiple Attribute Group Decision Making Problem, Mathematics 7 (8) (2019), p.764. Google Scholar

[27] P. Singh, Correlation coefficients for picture fuzzy sets, J. Intell. Fuzzy Syst. 28, 591–604 (2015). Google Scholar

[28] L. H. Son, Generalized picture distance measure and applications to picture fuzzy clustering, Appl. Soft Comput. 46 (2016), 284–295. Google Scholar

[29] G. W. Wei, Picture fuzzy cross-entropy for multiple attribute decision making problems, J. Bus. Econ. Manag. 17 (4) (2016), 491–502. Google Scholar

[30] R. R. Yager, Pythagorean fuzzy subsets. In: Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, June 24-28th (2013), 57–61. Google Scholar

[31] L. A. Zadeh, Fuzzy sets, Information and Control 8 (3) (1965), 338–356. Google Scholar

[32] S. Zeng, S. Asharf, M. Arif, and S. Abdullah, Application of exponential jensen picture fuzzy divergence measure in multi-criteria group decision making, Mathematics 7 (2) (2019), p.191. Google Scholar