A New Approach to Group Decision-Making Method Based on TOPSIS Under Fuzzy Soft Environment

Year 2019, Volume: 8 Issue: 2, 42 - 52, 31.12.2019

Serdar Enginoğlu , Samet Memiş , Faruk Karaaslan

Abstract

TOPSIS, developed in 1981 by Hwang and Yoon, is one of the known multi-criteria decision-making (MCDM) methods. In 2015, the group decision-making method based on TOPSIS under fuzzy soft environment was defined and applied to a decision-making problem by Eraslan and Karaaslan. Recently, this method has been configured by Enginoğlu and Memiş via fuzzy parameterized fuzzy soft matrices (fpfs-matrices), faithfully to the original, because a more general form is needed for the method in the event that the parameters have uncertainties. However, the configured method has two drawbacks which affect its running time and the ranking order negatively. We, in this study, improve this method by removing the disadvantages. We then compare the running time of these algorithms. The results show that the new method outperforms it, in particular, a large number of data come into question. For example, the proposed method offers up to 97.7672% of time advantage for ten objects and 9000 parameters. Afterwards, we apply the new method to a performance-based value assignment to seven state-of-art filters used in image denoising, so that we can order them in terms of performance. Finally, we discuss the need for further research.

Keywords

Fuzzy sets, Soft sets, Soft decision-making, Soft matrices, fpfs-matrices

Supporting Institution

Çanakkale Onsekiz Mart University

Project Number

FBA-2018-1367

Thanks

This work was supported by the Office of Scientific Research Projects Coordination at Çanakkale Onsekiz Mart University, Grant number: FBA-2018-1367.

References

• Çağman, N., Enginoğlu, S., 2010a. Soft Set Theory and Uni-Int Decision Making. European Journal of Operational Research. 207(2): 848-855.
• Çağman, N., Enginoǧlu, S., 2010b. Soft Matrix Theory and Its Decision Making. Computer and Mathematics with Applications. 59(10): 3308-3314.
• Çağman, N., Enginoǧlu, S., 2012. Fuzzy Soft Matrix Theory and Its Application in Decision Making. Iranian Journal of Fuzzy Systems. 9(1): 109-119.
• Çağman, N., Çıtak, F., Enginoğlu, S., 2010. Fuzzy Parameterized Fuzzy Soft Set Theory and Its Applications. Turkish Journal of Fuzzy Systems. 1(1): 21-35.
• Çağman, N., Çıtak, F., Enginoğlu, S., 2011a. FP-soft Set Theory and Its Applications. Annals of Fuzzy Mathematics and Informatics. 2(2): 219-226.
• Çağman, N., Enginoğlu, S., Çıtak, F., 2011b. Fuzzy Soft Set Theory and Its Applications. Iranian Journal of Fuzzy Systems. 8(3): 137-147.
• Deli, İ., Çağman, N., 2015. Relations on FP-soft Sets Applied to Decision Making Problems. Journal of New Theory. 3: 98-107.
• Enginoǧlu, S., 2012. Soft Matrices. PhD dissertation. Gaziosmanpaşa University. Graduate School of Natural and Applied Sciences, Department of Mathematics, p.85, Tokat –Turkey (in Turkish).
• Enginoğlu, S., Çağman, N., n.d. Fuzzy Parameterized Fuzzy Soft Matrices and Their Application in Decision-Making. TWMS Journal of Applied and Engineering Mathematics. In Press.
• Enginoğlu, S., Erkan, U., Memiş, S., 2019. Pixel Similarity-Based Adaptive Riesz Mean Filter for Salt-and-Pepper Noise Removal. Multimedia Tools and Applications. 78(24): 35401-35418.
• Enginoğlu, S., Memiş, S., 2018a. A Configuration of Some Soft Decision-Making Algorithms via fpfs-matrices. Cumhuriyet Science Journal. 39(4): 871-881.
• Enginoğlu, S., Memiş, S., 2018b. Comment on “Fuzzy soft sets” [The Journal of Fuzzy Mathematics, 9(3), 2001, 589–602]. International Journal of Latest Engineering Research and Applications. 3(9): 1-9.
• Enginoğlu, S., Memiş, S., 2018c. A Review on An Application of Fuzzy Soft Set in Multicriteria Decision Making Problem [P.K. Das, R. Borgohain, International Journal of Computer Applications 38 (12) (2012) 33-37]. Eds: Akgül, M., Yılmaz, İ., İpek, A. International Conference on Mathematical Studies and Applications, October 4-6, Karaman, Turkey.
• Enginoğlu, S., Memiş, S., Arslan, B., 2018a. Comment (2) on Soft Set Theory and uni-int Decision Making [European Journal of Operational Research, (2010) 207, 848-855]. Journal of New Theory. 25: 85-102.
• Enginoğlu, S., Memiş, S., Çağman, N., 2019. A Generalisation of Fuzzy Soft Max-Min Decision-Making Method and Its Application to A Performance-Based Value Assignment in Image Denoising. El-Cezerî Journal of Science and Engineering. 6(3): 466-481.
• Enginoğlu, S., Memiş, S., Öngel, T., 2018b. Comment on Soft Set Theory and Uni-Int Decision Making [European Journal of Operational Research, (2010) 207, 848-855]. Journal of New Results in Science. 7(3): 28-43.
• Enginoğlu, S., Çağman, N., Karataş, S., Aydın, T., 2015. On Soft Topology. El-Cezerî Journal of Science and Engineering. 2(3): 23-38.
• Eraslan, S., Karaaslan, F., 2015. A Group Decision Making Method Based on TOPSIS Under Fuzzy Soft Environment. Journal of New Theory. 3: 30-40.
• Hwang, C.L., Yoon, K., 1981. Multiple attribute decision making: Methods and applications, Springer-Verlag, New York.
• Karaaslan, F., 2016. Soft classes and soft rough classes with applications in decision making. Mathematical Problems in Engineering. Article ID1584528, 11 pages.
• Karaaslan, F., Çağman, N., Enginoğlu, S., 2012. Soft lattices. Journal of New Results in Sciences. 1(1): 5-17.
• Maji, P K., Biswas, R., Roy, A.R., 2001. Fuzzy Soft Sets. The Journal of Fuzzy Mathematics. 9(3): 589-602.
• Maji, P.K., Biswas, R., Roy, A.R., 2003. Soft Set Theory. Computer and Mathematics with Applications. 45(4-5): 555-562.
• Molodtsov, D., 1999. Soft Set Theory-First Results. Computers and Mathematics with Applications. 37(4-5): 19-31.
• Razak, S.A., Mohamad, D., 2011. A Soft Set Based Group Decision Making Method with Criteria Weight. International Scholarly and Scientific Research & Innovation. 5(10): 1641-1646.
• Razak, S.A., Mohamad, D., 2013. Decision Making Method using Fuzzy Soft Sets. Malaysian Journal of Fundamental and Applied Sciences. 9(2): 99-104.
• Riaz, M., Hashmi, R., 2017. Fuzzy Parameterized Fuzzy Soft Topology with Applications. Annals of Fuzzy Mathematics and Informatics. 13(5): 593-613.
• Riaz, M., Hashmi, R., 2018. Fuzzy Parameterized Fuzzy Soft Compact Spaces with Decision-Making, Punjab University Journal of Mathematics. 50(2): 131-145.
• Riaz, M., Hashmi, R., Farooq, A., 2018. Fuzzy Parameterized Fuzzy Soft Metric Spaces. Journal of Mathematical Analysis. 9(2): 25-36.
• Sezgin, A., Çağman, N., Çıtak, F., 2019. α-Inclusions Applied to Group Theory via Soft Set and Logic. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics. 68(1): 334-352.
• Şenel, G., 2018. Analyzing The Locus of Soft Spheres: Illustrative Cases and Drawings. European Journal of Pure and Applied Mathematics. 11(4): 946-957.
• Ullah, A., Karaaslan, F., Ahmad, I., 2018. Soft Uni-Abel-Grassmann’s Groups. European Journal of Pure and Applied Mathematics. 11(2): 517-536.
• Zorlutuna, İ., Atmaca, S., 2016. Fuzzy Parametrized Fuzzy Soft Topology. New Trends in Mathematical Sciences. 4(1): 142-152.