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New algorithms for parameter reduction of intuitionistic fuzzy soft sets

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Abstract

The intuitionistic fuzzy soft set (IFSS) is one of the useful mathematical tools for uncertainty description and has many applications in real-world decision-making problems. However, the computations become more complex when these decision-making problems involve less important or redundant parameters. To solve this problem, in this paper, we study the problem of parameter reduction of IFSS based on evaluation score criteria. Initially, we developed a new approach to IFSS-based decision-making. Then using the new decision criteria, we propose three different algorithms for parameter reduction of IFSSs satisfying the different needs of decision-makers. We compare the proposed algorithms with Ghosh et al.’s algorithms in terms of different aspects. It is evident from the comparison results that the proposed algorithms are much better than Ghosh et al.’s algorithms in terms of efficiency and applicability. We also provide a comparative study among the new algorithms to decide their feasibilities in different situations. Finally, we take a university recruitment problem to verify the effectiveness of the proposed algorithms in real-life decision-making problems.

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References

  • Aktaş H, Çağman N (2007) Soft sets and soft groups. Inf Sci 177(13):2726–2735

    MathSciNet  MATH  Google Scholar 

  • Alcantud JCR, Santos-García G, Hernández-Galilea E (2015) Glaucoma diagnosis: a soft set based decision making procedure. In: Conference of the Spanish Association for Artificial Intelligence. Springer, pp 49–60

  • Ali MI, Feng F, Liu X, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547–1553

    MathSciNet  MATH  Google Scholar 

  • Ali G, Akram M, Koam AN, Alcantud JCR (2019) Parameter reductions of bipolar fuzzy soft sets with their decision-making algorithms. Symmetry 11(8):949

    Google Scholar 

  • Atagün AO, Kamacı H, Oktay O (2018) Reduced soft matrices and generalized products with applications in decision making. Neural Comput Appl 29(9):445–456

    Google Scholar 

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

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Chen S-M, Tan J-M (1994) Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 67(2):163–172

    MathSciNet  MATH  Google Scholar 

  • Chen D, Tsang E, Yeung DS, Wang X (2005) The parameterization reduction of soft sets and its applications. Comput Math Appl 49(5–6):757–763

    MathSciNet  MATH  Google Scholar 

  • Danjuma S, Herawan T, Ismail MA, Chiroma H, Abubakar AI, Zeki AM (2017) A review on soft set-based parameter reduction and decision making. IEEE Access 5:4671–4689

    Google Scholar 

  • Danjuma S, Ismail MA, Herawan T (2017) An alternative approach to normal parameter reduction algorithm for soft set theory. IEEE Access 5:4732–4746

    Google Scholar 

  • Das S, Kar S (2014) Group decision making in medical system: an intuitionistic fuzzy soft set approach. Appl Soft Comput 24:196–211

    Google Scholar 

  • Deli I, Çağman N (2015) Intuitionistic fuzzy parameterized soft set theory and its decision making. Appl Soft Comput 28:109–113

    Google Scholar 

  • Fatimah F, Rosadi D, Hakim RF, Alcantud JCR (2019) Probabilistic soft sets and dual probabilistic soft sets in decision-making. Neural Comput Appl 31(1):397–407

    Google Scholar 

  • Ghosh S, Das S (2016) Parameter reduction of intuitionistic fuzzy soft sets and its related algorithms. In: Proceedings of the 4th international conference on frontiers in intelligent computing: theory and applications (FICTA) 2015. Springer, pp 405–412

  • Hong DH, Choi C-H (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 114(1):103–113

    MATH  Google Scholar 

  • Jiang Y, Tang Y, Chen Q, Liu H, Tang J (2010) Interval-valued intuitionistic fuzzy soft sets and their properties. Comput Math Appl 60(3):906–918

    MathSciNet  MATH  Google Scholar 

  • Jiang Y, Tang Y, Chen Q (2011) An adjustable approach to intuitionistic fuzzy soft sets based decision making. Appl Math Model 35(2):824–836

    MathSciNet  MATH  Google Scholar 

  • Kamacı H, Atagün AO, Sönmezoğlu A (2018) Row-products of soft matrices with applications in multiple-disjoint decision making. Appl Soft Comput 62:892–914

    Google Scholar 

  • Kamacı H, Saltık K, Fulya Akız H, Osman Atagün A (2018) Cardinality inverse soft matrix theory and its applications in multicriteria group decision making. J Intell Fuzzy Syst 34(3):2031–2049

    Google Scholar 

  • Karaaslan F, Karataş S (2016) Or and and-products of ifp-intuitionistic fuzzy soft sets and their applications in decision making. J Intell Fuzzy Syst 31(3):1427–1434

    MATH  Google Scholar 

  • Khameneh AZ, Kılıçman A (2018) Parameter reduction of fuzzy soft sets: an adjustable approach based on the three-way decision. Int J Fuzzy Syst 20(3):928–942

    Google Scholar 

  • Khan A, Zhu Y (2019) An improved algorithm for normal parameter reduction of soft set. J Intell Fuzzy Syst 37(2):2953–2968

    Google Scholar 

  • Khan A, Zhu Y (2019) A novel approach to parameter reduction of fuzzy soft set. IEEE Access 7:128956–128967

    Google Scholar 

  • Khan M, Kumam P, Liu P, Kumam W, Ashraf S (2019) A novel approach to generalized intuitionistic fuzzy soft sets and its application in decision support system. Mathematics 7(8):742

    Google Scholar 

  • Kolmogorov (2018) A Foundations of the theory of probability: Second English Edition

  • Kong Z, Gao L, Wang L, Li S (2008) The normal parameter reduction of soft sets and its algorithm. Comput Math Appl 56(12):3029–3037

    MathSciNet  MATH  Google Scholar 

  • Kong Z, Ai J, Wang L, Li P, Ma L, Lu F (2019) New normal parameter reduction method in fuzzy soft set theory. IEEE Access 7:2986–2998

    Google Scholar 

  • Kong Z, Wang L, Jia W (2015) Approximate normal parameter reduction of fuzzy soft set based on harmony search algorithm. In: 2015 IEEE fifth international conference on big data and cloud computing. IEEE, pp 321–324

  • Li Z, Wen G, Han Y (2014) Decision making based on intuitionistic fuzzy soft sets and its algorithm. J Comput Anal Appl 17(4):620–631

    MathSciNet  MATH  Google Scholar 

  • Ma X, Qin H (2018) A distance-based parameter reduction algorithm of fuzzy soft sets. IEEE Access 6:10530–10539

    Google Scholar 

  • Ma X, Sulaiman N, Qin H, Herawan T, Zain JM (2011) A new efficient normal parameter reduction algorithm of soft sets. Comput Math Appl 62(2):588–598

    MathSciNet  MATH  Google Scholar 

  • Ma X, Qin H, Sulaiman N, Herawan T, Abawajy JH (2013) The parameter reduction of the interval-valued fuzzy soft sets and its related algorithms. IEEE Trans Fuzzy Syst 22(1):57–71

    Google Scholar 

  • Ma X, Zhan J, Ali MI, Mehmood N (2018) A survey of decision making methods based on two classes of hybrid soft set models. Artif Intell Rev 49(4):511–529

    Google Scholar 

  • Maji PK, Biswas R, Roy AR (2001) fuzzy soft sets. J Fuzzy Math 9(3):589–602

    MathSciNet  MATH  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2001) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692

    MathSciNet  MATH  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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Mao J, Yao D, Wang C (2013) Group decision making methods based on intuitionistic fuzzy soft matrices. Appl Math Model 37(9):6425–6436

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356

    MATH  Google Scholar 

  • Wu H, Su X (2017) Group generalized interval-valued intuitionistic fuzzy soft sets and their applications in decision making. Iran J Fuzzy Syst 14(1):1–21

    MathSciNet  MATH  Google Scholar 

  • Xu Z (2007) Intuitionistic preference relations and their application in group decision making. Inf Sci 177(11):2363–2379

    MathSciNet  MATH  Google Scholar 

  • Xu W, Ma J, Wang S, Hao G (2010) Vague soft sets and their properties. Comput Math Appl 59(2):787–794

    MathSciNet  MATH  Google Scholar 

  • Yang X, Lin TY, Yang J, Li Y, Yu D (2009) Combination of interval-valued fuzzy set and soft set. Comput Math Appl 58(3):521–527

    MathSciNet  MATH  Google Scholar 

  • Yuksel S, Dizman T, Yildizdan G, Sert U (2013) Application of soft sets to diagnose the prostate cancer risk. J Inequal Appl 2013(1):229

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Zhan J, Alcantud JCR (2019) A survey of parameter reduction of soft sets and corresponding algorithms. Artif Intell Rev 52(3):1839–1872

    Google Scholar 

  • Zhao H, Ma W, Sun B (2017) A novel decision making approach based on intuitionistic fuzzy soft sets. Int J Mach Learn Cybern 8(4):1107–1117

    Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant no. 61673011).

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Correspondence to Abid Khan.

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Communicated by Anibal Tavares de Azevedo.

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Khan, A., Zhu, Y. New algorithms for parameter reduction of intuitionistic fuzzy soft sets. Comp. Appl. Math. 39, 232 (2020). https://doi.org/10.1007/s40314-020-01279-4

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