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ISSN (Print): 2666-2558
ISSN (Online): 2666-2566

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Research Article

Dimensionality Reduction Technique in Decision Making Using Pythagorean Fuzzy Soft Matrices

Author(s): Rakesh Kumar Bajaj* and Abhishek Guleria

Volume 13, Issue 3, 2020

Page: [406 - 413] Pages: 8

DOI: 10.2174/2213275912666190119160621

Price: $65

Abstract

Background: Dimensionality reduction plays an effective role in downsizing the data having irregular factors and acquires an arrangement of important factors in the information. Sometimes, most of the attributes in the information are found to be correlated and hence redundant. The process of dimensionality reduction has a wider applicability in dealing with the decision making problems where a large number of factors are involved.

Objective: To take care of the impreciseness in the decision making factors in terms of the Pythagorean fuzzy information which is in the form of soft matrix. The perception of the information has the parameters - degree of membership, degree of indeterminacy (neutral) and degree of nonmembership, for a broader coverage of the information.

Methods: We first provided a technique for finding a threshold element and value for the information provided in the form of Pythagorean fuzzy soft matrix. Further, the proposed definitions of the object-oriented Pythagorean fuzzy soft matrix and the parameter-oriented Pythagorean fuzzy soft matrix have been utilized to outline an algorithm for the dimensionality reduction in the process of decision making.

Results: The proposed algorithm has been applied in a decision making problem with the help of a numerical example. A comparative analysis in contrast with the existing methodologies has also been presented with comparative remarks and additional advantages.

Conclusion: The example clearly validates the contribution and demonstrates that the proposed algorithm efficiently encounters the dimension reduction. The proposed dimensionality reduction technique may further be applied in enhancing the performance of large scale image retrieval.

Keywords: Pythagorean fuzzy soft matrix, dimensionality reduction, multiple criteria decision making, object-oriented matrix, parameter-oriented matrix, linear sequence discriminant analysis.

Graphical Abstract

[1]
D. Chen, E.C.C. Tsang, D.S. Yeungand, and X. Wang, "The parameterization reduction of soft sets and its application", Comput. Math. Appl., vol. 49, pp. 757-763, 2005.
[2]
X. Xu, T. Liang, J. Zhu, D. Zheng, and T. Sun, "Review of classical dimensionality reduction and sample selection methods for large-scale data processing", Neurocomputing, vol. 7, no. 328, pp. 5-15, February 2019.
[3]
B. Su, X. Ding, H. Wang, and Y. Wu, "Discriminative dimensionality reduction for multi-dimensional sequences", IEEE Trans. Pattern Anal. Mach. Intell., vol. 40, no. 1, pp. 77-91, 2018.
[4]
I. Perfilieva, "Dimensionality reduction by fuzzy transforms with applications to mathematical finance", In: Anh L., Dong L., Kreinovich V., Thach N. (eds) Econometrics for Financial Applications. ECONVN 2018. Stud. Comput. Intell., vol. 760. Springer: Cham, 2018.
[5]
A.A. Konaté, H. Pan, H. Ma, X. Cao, Y.Y. Ziggah, M. Oloo, and N. Khan, "Application of dimensionality reduction technique to improve geo- physical log data classification performance in crystalline rocks", J. Petrol. Sci. Eng., vol. 133, pp. 633-645, 2015.
[6]
M. Sabitha, and M. Mayilvahanan, "Application of dimensionality reduction techniques in real time dataset", Int. J. Adv. Research Comput. Eng. Technol., vol. 5, no. 7, 2016.
[7]
P. Chatterjee, S. Mondal, S. Boral, A. Banerjee, and S. Chakraborty, "A novel hybrid method for non-traditional machining process selection using factor relationship and Multi-Attributive Border Approximation Method", Facta Univ. Ser. Mech. Eng., vol. 15, pp. 439-456, 2017.
[8]
I. Mukhametzyanov, and D. Pamucar, "A sensitivity analysis in MCDM problems: A statistical approach", DMAME, vol. 1, no. 2, pp. 51-80, 2018.
[9]
D.A. Molodstov, "Soft set theory-first result", Comput. Math. Appl., vol. 27, pp. 19-31, 1999.
[10]
P.K. Maji, R. Biswas, and A.R. Roy, "Intuitionistic fuzzy soft sets", J. Fuzzy Math., vol. 9, pp. 677-692, 2001.
[11]
P.K. Maji, R. Biswas, and A.R. Roy, "An application of soft sets in a decision making problem", Comput. Math. Appl., vol. 44, pp. 1077-1083, 2002.
[12]
P.K. Maji, R. Biswas, and A.R. Roy, "Soft Set Theory", Comput. and Math. with Appl., vol. 45, pp. 555-562, 2003.
[13]
C. Kahraman, S.C. Onar, and B. Oztaysi, "Fuzzy multicriteria decision-making: A literature review", Int. J. Comput. Intel. Sys., vol. 8, no. 4, pp. 637-666, 2015.
[14]
F. Liu, G. Aiwu, V. Lukovac, and M. Vukic, "A multicriteria model for the selection of the transport service provider: A single valued neutrosophic DEMATEL multicriteria model", DMAME, vol. 1, no. 2, pp. 121-130, October 2018.
[15]
T. Kumar, and R.K. Bajaj, “On complex intuitionistic fuzzy soft sets with distance measures and entropies,” J. Math..Article ID–972198, pp. 12, 2014.
[16]
D.S. Hooda, and B.K. Hooda, "Dimension reduction in multivariate analysis using maximum entropy criterion", J. Stats. Manag., vol. 9, no. 1, pp. 175-183, 2006.
[17]
X. Peng, Y. Yang, J. Song, and Y. Jiang, "Pythagorean fuzzy soft set and its application", Comput. Eng., vol. 41, pp. 224-229, 2015.
[18]
C. Naim, and E. Serdar, "Soft matrix theory and its decision making", Comput. Math. Appl., vol. 59, pp. 3308-3314, 2010.
[19]
Y. Yong, and J. Chenli, "Fuzzy Soft Matrices and their Applications", Lect. Notes Comput. Sci., vol. 7002, pp. 618-627, 2011.
[20]
B. Chetia, and P.K. Das, "Some results of intuitionistic fuzzy soft matrix theory", Adv. Appl. Sci. Res., vol. 3, pp. 412-423, 2012.
[21]
D.S. Hooda, and R. Kumari, "On applications of fuzzy soft sets in dimension reduction and medical diagnosis", Adv. Res., vol. 12, no. 2, pp. 1-9, 2017.
[22]
A. Guleria, and R.K. Bajaj, "On pythagorean fuzzy soft matrices, operations and their applications in decision making and medical diagnosis", Soft Comput., 2018.
[http://dx.doi.org/10.1007/s00500-018-3419-z]
[23]
K.T. Atanassov, (1983, 2016). “Intuitionistic Fuzzy Sets,” VII ITKR Session, Sofia, pp. 20-23, June 1983. (Deposed in Centr. Sci.- Techn. Library of the Bulg. Acad. of Sci., 1697/84). Reprinted:Int. J. Bioautomat., vol. 20, no. S1, pp. S1-S6, 2016.
[24]
K.T. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets Syst., vol. 20, pp. 87-96, 1986.
[25]
K.T. Atanassov, "Geometrical interpretation of the elements of the intuitionistic fuzzy objects, Preprint IM-MFAIS-1-89,” Sofia, 1989. Reprinted:", Int. J. Bioautomat., vol. 20, no. S1, pp. S27-S42, 2016.
[26]
R.R. Yager, "Pythagorean fuzzy subsets"Proceedings of Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp. 57-61. 2013.
[27]
B.C. Cuong, "Picture fuzzy sets first results"Part 1, in preprint of seminar on neuro-fuzzy systems with applications., Institute of Mathematics: Hanoi, May 2013.
[28]
T. Mahmood, U. Kifayat, Q. Khan, and N. Jan, "An approach toward decision making and medical diagnosis problems using the concept of spherical fuzzy sets", Neural Comput. Appl., vol. 31, no. 11, pp. 7041-7053, November 2019.
[29]
P. Thirunavukarasu, R. Suresh, and V. Ashokkumar, "Theory of complex fuzzy soft set and its applications", Int. J. Innov. Res. Sci. Eng. Technol., vol. 3, no. 10, pp. 13-18, 2017.
[30]
L.A. Zadeh, "Fuzzy sets", Inf. Control, vol. 8, pp. 338-353, 1965.

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