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The mean operators and generalized products of fuzzy soft matrices and their applications in MCGDM

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Abstract

In this paper, we first generalize the products of two fuzzy soft matrices. Through these generalizations, three or more fuzzy soft matrices in the different types can be multiplied. Furthermore, we introduce the mean operators and normalized fuzzy weighted mean operators of the fuzzy soft matrices. We discuss the theoretical aspects of these operators. We describe the multicriteria group decision making (MCGDM) problem with different evaluation criterion sets, and then we create two algorithms using the mean operators and generalized products of fuzzy soft matrices to deal with such problems. To show the advantages of the proposed ones, we present the comparison results with some of the preexisting decision making algorithms of fuzzy soft sets. Finally, we create Scilab codes of our algorithms to expedite and facilitate the decision making process.

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References

  • Alcantud JCR (2016) A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter data set. Inf Fusion 29:142–148

    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 

  • Athira TM, John SJ, Garg H (2019) Entropy and distance measures of pythagorean fuzzy soft sets and their applications. J Intell Fuzzy Syst 37(3):4071–4084

    Google Scholar 

  • Basu TM, Mahapatra NK, Mondal SK (2012a) Different types of matrices in intuitionistic fuzzy soft set theory and their application in predicting terrorist attack. Int J Manag IT Eng 2(9):73–105

    Google Scholar 

  • Basu TM, Mahapatra NK, Mondal SK (2012b) Matrices in soft set theory and their applications in decision making problems. South Asian J Math 2(2):126–143

    MATH  Google Scholar 

  • Borah MJ, Neog TJ, Sut DK (2012) Fuzzy soft matrix theory and its decision making. Int J Mod Eng Res 2(2):121–127

    Google Scholar 

  • Büyüközkan G, Güleryüz S (2016) Multi criteria group decision making approach for smart phone selection using intuitionistic fuzzy topsis. Int J Comput Intell Syst 9(4):709–725

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Çağman N, Enginoğlu S (2010b) Soft set theory and uni-int decision making. Eur J Oper Res 207(2):848–855

    MathSciNet  MATH  Google Scholar 

  • Cagman N, Enginoglu S (2012) Fuzzy soft matrix theory and its application in decision making. Iran J Fuzzy Syst 9(1):109–119

    MathSciNet  MATH  Google Scholar 

  • Cagman N, Enginoglu S, Citak F (2011) Fuzzy soft set theory and its applications. Iran J Fuzzy Syst 8(3):137–147

    MathSciNet  MATH  Google Scholar 

  • Chang PT, Lee E (1995) The estimation of normalized fuzzy weights. Comput Math Appl 29(5):21–42

    MathSciNet  MATH  Google Scholar 

  • Das P, Borgohain R (2012) An application of fuzzy soft set in multicriteria decision making problem. Int J Comput Appl 38(12):33–37

    Google Scholar 

  • Elevli B (2014) Logistics freight center locations decision by using fuzzy-PROMETHEE. Transport 29(4):412–418

    Google Scholar 

  • Fan ZP, Li MY, Liu Y, You TH (2018) A method for multicriteria group decision making with different evaluation criterion sets. Math Probl Eng 2018:Article ID 7189451

  • Feng F, Juna YB, Liu X, Li L (2010) An adjustable approach to fuzzy soft set based decision making. J Comput Appl Math 234(1):10–20

    MathSciNet  MATH  Google Scholar 

  • Feng F, Li Y, Çağman N (2012) Generalized uni-int decision making schemes based on choice value soft sets. Eur J Oper Res 220(1):162–170

    MathSciNet  MATH  Google Scholar 

  • Feng F, Fujita H, Jun YB, Khan M (2014) Decomposition of fuzzy soft sets with finite value spaces. Sci World J 2014:Article ID 902687

  • Garg H, Arora R (2018) Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making. Appl Intell 48(2):343–356

    Google Scholar 

  • Garg H, Arora R (2019) Generalized intuitionistic fuzzy soft power aggregation operator based on t-norm and their application in multi criteria decision-making. Int J Intell Syst 34(2):215–246

    Google Scholar 

  • Gong K, Wang P, Xiao Z (2013) Bijective soft set decision system based parameters reduction under fuzzy environments. Appl Math Model 37(6):4474–4485

    MathSciNet  MATH  Google Scholar 

  • Guh YY, Po RW, Lee ES (2008) The fuzzy weighted average within a generalized means function. Comput Math Appl 55(12):2699–2706

    MathSciNet  MATH  Google Scholar 

  • Herawan T, Deris MM (2010) Soft decision making for patients suspected influenza. In: International conference on computational science and its applications. Springer, pp 405–418

  • Inthumathi V, Chitra V, Jayasree S (2017) Fuzzy soft min–max decision making and its applications. J Inf Math Sci 9(3):827–834

    Google Scholar 

  • Kamacı H (2019) Similarity measure for soft matrices and its applications. J Intell Fuzzy Syst 36(4):3061–3072

    Google Scholar 

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

    Google Scholar 

  • Kamacı H, Atagün AO, Toktaş E (2018b) Bijective soft matrix theory and multi-bijective linguistic soft decision system. Filomat 32(11):3799–3814

    MathSciNet  Google Scholar 

  • Kamacı H, Atagün AO, Aygün E (2019) Difference operations of soft matrices with applications in decision making. Punjab Univ J Math 51(3):1–21

    MathSciNet  Google Scholar 

  • Khan MJ, 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 

  • Kharal A (2014) Soft approximations and uni-int decision making. Sci World J2014:Article ID 327408

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

    MathSciNet  MATH  Google Scholar 

  • Maji P, Roy A, 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 

  • Majumdar P, Samanta SK (2010) Generalized fuzzy soft sets. Comput Math Appl 59(4):1425–1432

    MathSciNet  MATH  Google Scholar 

  • Molodtsov D (1999) Soft set theory—first results. Comput Math Appl 27(4–5):19–31

    MathSciNet  MATH  Google Scholar 

  • Perveen FFA, John SJ, Bibitha KV, Garg H (2019) Spherical fuzzy soft sets and its application in decision making process. J Intell Fuzzy Syst 37(6):8237–8250

    Google Scholar 

  • Renukadevi V, Sangeetha G (2016) A novel approach to decision making via fuzzy soft sets. Turk J Fuzzy Syst (TJFS) 7(1):41–54

    Google Scholar 

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

    MATH  Google Scholar 

  • Selvachandran G, Garg H, Alaroud MHS, Salleh AR (2018a) Similarity measure of complex vague soft sets and its application to pattern recognition. Int J Fuzzy Syst 20(6):1901–1914

    MathSciNet  Google Scholar 

  • Selvachandran G, Garg H, Quek SG (2018b) Vague entropy measure for complex vague soft sets. Entropy 20(6):403. https://doi.org/10.3390/e20060403

    Article  MathSciNet  Google Scholar 

  • Vijayabalaji S, Ramesh A (2013) A new decision making theory in soft matrices. Int J Pure Applied Math 86(6):927–939

    Google Scholar 

  • Wang YM, Elhag TM (2006) On the normalization of interval and fuzzy weights. Fuzzy Sets Syst 157(18):2456–2471

    MathSciNet  MATH  Google Scholar 

  • Xiao Z, Gong K, Zou Y (2009) A combined forecasting approach based on fuzzy soft sets. J Comput Appl Math 228(1):326–333

    MathSciNet  MATH  Google Scholar 

  • Yang Y, Ji C (2011) Fuzzy soft matrices and their applications. In: International conference on artificial intelligence and computational intelligence. Springer, pp 618–627

  • Yang X, Yu D, Yang J, Wu C (2007) Generalization of soft set theory: from crisp to fuzzy case. In: Fuzzy information and engineering. Springer, pp 345–354

  • Yang Y, Tan X, Meng CC (2013) The multi-fuzzy set and its application in decision making. Appl Math Model 37:4915–4923

    MathSciNet  MATH  Google Scholar 

  • Yang YW, He PF, Xin XL (2014) A decision making method for the quality identification of wines based on fuzzy soft sets. Fuzzy Inf Eng 6(1):19–27

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  • Zhan J, Zhu K (2015) Reviews on decision making methods based on (fuzzy) soft sets and rough soft sets. J Intell Fuzzy Syst 29(3):1169–1176

    MathSciNet  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, University College of Engineering, Nagercoil, Tamilnadu, 629004, India

    Subramanian Petchimuthu

  2. School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, Punjab, 147004, India

    Harish Garg

  3. Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, 66100, Yozgat, Turkey

    Hüseyin Kamacı

  4. Department of Mathematics, Faculty of Science and Arts, Ahi Evran University, 40100, Kırşehir, Turkey

    Akın Osman Atagün

Authors
  1. Subramanian Petchimuthu
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  2. Harish Garg
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  3. Hüseyin Kamacı
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  4. Akın Osman Atagün
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Corresponding author

Correspondence to Harish Garg.

Additional information

Communicated by Rosana Sueli da Motta Jafelice.

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Appendix

Appendix

Scilab codes

We supply the following Scilab codes, which provide great convenience for the steps in the above fuzzy soft multicriteria group decision making algorithms (Algorithms 1 and 2).

figure b
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Petchimuthu, S., Garg, H., Kamacı, H. et al. The mean operators and generalized products of fuzzy soft matrices and their applications in MCGDM. Comp. Appl. Math. 39, 68 (2020). https://doi.org/10.1007/s40314-020-1083-2

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  • DOI: https://doi.org/10.1007/s40314-020-1083-2

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