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Aggregation operators of Pythagorean fuzzy bi-polar soft sets with application in multiple attribute decision making

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Abstract

It is always useful to have information assembled or fused into a single value that represents the whole class of information. Aggregation operators (AOs) play a vital role in combining information. Therefore in this paper, we will investigate the multiple attribute decision-making problems using AOs that are developed in the environment of Pythagorean fuzzy bi-polar soft set (PFBSS). First, the concept of PFBSS is presented which is based on the novel fuzzy bi-polar soft sets (FBSS). We have developed Pythagorean fuzzy bi-polar soft aggregation operators like, Pythagorean fuzzy bi-polar soft- weighted averaging (PFBSWA) operator, Pythagorean fuzzy bi-polar soft-ordered weighted averaging operator (PFBSOW), Pythagorean fuzzy bi-polar soft- weighted geometric (PFBSWG) operator, and Pythagorean fuzzy bi-polar soft-ordered weighted geometric (PFBSOWG) operator. Basic properties of these aggregation operators are studied. Next, we have used these operators to develop some approaches for solving Pythagorean fuzzy bi-polar soft multiple attribute decision-making problems. At the end, a practical example is provided and the stability of the proposed method has been shown by providing the comparative analysis with some existing work.

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References

  • Abdullah S, Aslam M, Ullah K (2014) Bipolar fuzzy soft sets and its applications in decision making problem. J Intell Fuzzy Syst 27(2):729–742

    Article  MathSciNet  Google Scholar 

  • Alcantud JCR, Santos-García G (2017) A new criterion for soft set based decision making problems under incomplete information. Int J Comput Intell Syst 10(1):394–404

    Article  Google Scholar 

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    MATH  Google Scholar 

  • Babitha K, Sunil J (2010) Soft set relations and functions. Comput Math Appl 60(7):1840–1849

    Article  MathSciNet  Google Scholar 

  • Çağman N, Enginoğlu S (2010) Soft matrix theory and its decision making. Comput Math Appl 59(10):3308–3314

    Article  MathSciNet  Google Scholar 

  • Çağman N, Karataş S (2013) Intuitionistic fuzzy soft set theory and its decision making. J Intell Fuzzy Syst 24(4):829–836

    Article  MathSciNet  Google Scholar 

  • Chen SM (1997) Interval-valued fuzzy hypergraph and fuzzy partition. IEEE Trans Syst Man and Cybern Part B (Cybern) 27(4):725–733

    Article  Google Scholar 

  • Chen SM, Hsiao WH (2000) Bidirectional approximate reasoning for rule-based systems using interval-valued fuzzy sets. Fuzzy Sets Syst 113(2):185–203

    Article  MathSciNet  Google Scholar 

  • Chen SM, Randyanto Y (2013) A novel similarity measure between intuitionistic fuzzy sets and its applications. Int J Pattern Recognit Artif Intell 27(07):1350021

    Article  Google Scholar 

  • Chen SM, Hsiao WH, Jong WT (1997) Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 91(3):339–353

    Article  MathSciNet  Google Scholar 

  • Chen SM, Chang YC, Pan JS (2012) Fuzzy rules interpolation for sparse fuzzy rule-based systems based on interval type-2 gaussian fuzzy sets and genetic algorithms. IEEE Trans Fuzzy Syst 21(3):412–425

    Article  Google Scholar 

  • Chen SM, Randyanto Y, Cheng SH (2016) Fuzzy queries processing based on intuitionistic fuzzy social relational networks. Inf Sci 327:110–124

    Article  MathSciNet  Google Scholar 

  • Kirişci M (2019) New type pythagorean fuzzy soft set and decision-making application. arXiv preprint. arXiv:190404064

  • Kirişci M (2019) A case study for medical decision making with the fuzzy soft sets. Afrika Matematika 31:1–8

    MathSciNet  Google Scholar 

  • Lee K (2000) Bipolar-valued fuzzy sets and their operations. In: Proceedings of international conference on intelligent technologies, Bangkok, Thailand, 2000, pp 307–312

  • Liu P, Chen SM, Wang Y (2020) Multiattribute group decision making based on intuitionistic fuzzy partitioned maclaurin symmetric mean operators. Inf Sci 512:830–854

    Article  MathSciNet  Google Scholar 

  • Maji P, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44(8–9):1077–1083

    Article  MathSciNet  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45(4–5):555–562

    Article  MathSciNet  Google Scholar 

  • Mohana K, Jansi R (2018) Bipolar pythagorean fuzzy sets and their application based on multi-criteria decision-making problems. Int J Res Advent Technol 6:3754–764

    Google Scholar 

  • Molodtsov D (1999) Soft set theory -first results. Comput Math Appl 37(4–5):19–31

    Article  MathSciNet  Google Scholar 

  • Naz M, Shabir M (2014) On fuzzy bipolar soft sets, their algebraic structures and applications. J Intell Fuzzy Syst 26(4):1645–1656

    Article  MathSciNet  Google Scholar 

  • Rahman K, Ali A, Shakeel M, Khan MA, Ullah M (2017) Pythagorean fuzzy weighted averaging aggregation operator and its application to decision making theory. Nucleus 54(3):190–196

    Google Scholar 

  • Roy AR, Maji P (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203(2):412–418

    Article  Google Scholar 

  • Saeed M, Ali U, Ali J, Dayan F (2020) Fuzzy soft relative method and its application in decision making problem: fuzzy soft relative method and its application in decision making problem. Proc Pak Acad Sci Phys Comput Sci 57(1):21–30

    Google Scholar 

  • Senapati T, Yager RR (2020) Fermatean fuzzy sets. J Ambient Intell Humaniz Comput 11(2):663–674

    Article  Google Scholar 

  • Turksen IB (1986) Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 20(2):191–210

    Article  MathSciNet  Google Scholar 

  • Wang L, Qin K (2019) Incomplete fuzzy soft sets and their application to decision-making. Symmetry 11(4):535

    Article  Google Scholar 

  • Wei G, Alsaadi FE, Hayat T, Alsaedi A (2018) Bipolar fuzzy Hamacher aggregation operators in multiple attribute decision making. Int J Fuzzy Syst 20(1):1–12

    Article  MathSciNet  Google Scholar 

  • Xu Z, Hu H (2010) Projection models for intuitionistic fuzzy multiple attribute decision making. Int J Inf Technol Decis Mak 9(02):267–280

    Article  Google Scholar 

  • Yager RR (2013) Pythagorean fuzzy subsets. In: 2013 Joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), IEEE, pp 57–61

  • Zadeh L (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  Google Scholar 

  • Zeb A, Khan A, Izhar M, Hila K (2021) Aggregation operators of fuzzy bi-polar soft sets and its application in decision making. J Multi Valued Logic Soft Comput 36(6):569–599

    Google Scholar 

  • Zeng S, Chen SM, Kuo LW (2019) Multiattribute decision making based on novel score function of intuitionistic fuzzy values and modified vikor method. Inf Sci 488:76–92

    Article  Google Scholar 

  • Zhang Z, Chen SM, Wang C (2020) Group decision making with incomplete intuitionistic multiplicative preference relations. Inf Sci 516:560–571

    Article  MathSciNet  Google Scholar 

  • Zou XY, Chen SM, Fan KY (2020) Multiple attribute decision making using improved intuitionistic fuzzy weighted geometric operators of intuitionistic fuzzy values. Inf Sci 535:242–253

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, China

    Aurang Zeb

  2. Department of Mathematics, Abdul Wali Khan University, Mardan, KP, 23200, Pakistan

    Aurang Zeb, Asghar Khan & Muhammad Fayaz

  3. Govt. College Garhi Kapura, Mardan, KP, 23200, Pakistan

    Muhammad Izhar

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  1. Aurang Zeb
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  2. Asghar Khan
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  3. Muhammad Fayaz
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  4. Muhammad Izhar
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Correspondence to Aurang Zeb.

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Zeb, A., Khan, A., Fayaz, M. et al. Aggregation operators of Pythagorean fuzzy bi-polar soft sets with application in multiple attribute decision making. Granul. Comput. 7, 931–950 (2022). https://doi.org/10.1007/s41066-021-00307-w

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