TARU PUBLICATIONS
Journal of Statistics and Management Systems cover

Journal of Statistics and Management Systems

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0014·ISSN (Print): 0972-0510

Indexed in ABDC Australia

Powered by:Powered by

Monthly Journal: Publishes peer-reviewed aticles on theoretical and applied statistics and management systems, expoloring industrial statistics, actuarial and decision sciences.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Statistics and Management Systems
Open Access Research Article

Estimation of missing data in intuitionistic fuzzy soft matrix (IFSM) with application in MCDM

, * ,

* Corresponding author · click or hover a name for details

pp. 589–603Vol. 27Issue 3March 2024DOI: 10.47974/JSMS-1022XML
Received:
08 Jun 2022
Accepted:
06 Sep 2022
Published Online:
30 Mar 2024
Article type:
Research Article
Language:
EN
Article no.:
JSMS-1022
Pages:
589–603

Abstract

The theory of fuzzy soft as well as intuitionistic soft set generally depends on complete information. But there are situations in which the complete information is not available due to various different reasons like data erroneous, in sufficiency of data, lacking of evidence and illegibility of data. Missing data restrict fuzzy soft matrix and intuitionistic fuzzy soft matrix and that causes more ambiguous uncertainty in the process of decision making. Thus, estimation of incomplete information data plays an important role in multi criteria decision making process which has been developed recently.  Here, a novel method of missing data estimation in intuitionistic fuzzy soft matrix is described. Firstl, we estimate the missing values using the information given in data. After estimation the missing values in IFSM thus obtained is applied in a multi-criteria decision-making problem with illustration by an example.

Keywords

Fuzzy soft setIncomplete fuzzy soft matrixIntuitionistic fuzzy soft setIncomplete fuzzy soft matrix and multi criteria decision making

Subject Classifications

15B15 Fuzzy Matrices

References

[1] Almedia R.J., Kaymak U. and Sousa J. A New Approach to Dealing with Missing Values in Data Driven Fuzzy Modeling, IEEE International Conference on Fuzzy Systems, (2010), DOI: http://10.1109/FUZZY.2010.5584894. 
[2] Atanassov, Krassimir T. Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20, 87-96 (1986).
[3] Burillo P. and Bustince H. Construction Theorem for Intuitionistic Fuzzy Sets, Fuzzy Sets and System, 84, 271-281 (1996).
[4] Cagman N., and Enginoglo S. Fuzzy Soft Matrix Theory and its Application in Decision Making, International Journal of Fuzzy Systems, 9, 109-119 (2012).
[5] Chen D., Tsang E.C.C., Yeung D.S. and Wang X. The Parameterization Reduction of Soft Sets and its Application, Computer and Mathematics with Applications, 49, 757-763 (2005).
[6] Das S., Ghosh S., Kar S. and Pal T. An Algorithmic Approach for Predicting Unknown Information in Incomplete Fuzzy Soft Set, Arabian Journal of Science and Engineering, (2017), DOI: https://10.1007/s13369-017-2591-2. 
[7] De S.K., Biswas R. and Roy A.R. An Application of Intuitionistic Fuzzy Sets in Medical Diagnosis, Fuzzy Sets and Systems, 117, 209-213 (2001).
[8] Deli I. and Cagman N. Intuitionistic Fuzzy Soft Set Theory and its Decision Making, Applied Soft Computing, 28, 109-113 (2015). 
[9] Deng T., and Wang X. An Object-Parameter Approach to Predicting Unknown Data in Incomplete Fuzzy Soft Sets, Applied Mathematical Modelling, 37, 4139-4146 (2013).
[10] Feng F., Jun Y.B., Liu X.F. and Li L.F. An Adjustable Approach to Fuzzy Soft Set Based Decision Making, Computational and Applied Mathematics, 234, 10-20 (2010).
[11] Hooda D.S. and Barak M.S. Estimation of Missing Data in Design of Experiment and Contingency Table, SN Applied Sciences (2019), DOI: https://doi.org/10.1007/s42452-019-0692-0.
[12] Hooda D.S. and Barak M.S. Estimation of Missing Values in fuzzy Matrices and Interval Valued Fuzzy Matrices, Life Cycle Reliability and Safety Engineering (2020), DOI:https://10.1007/s41872-020-00116-1.   
[13] Hooda D.S. Maximum Entropy Method for Estimation of Missing Data, International Encyclopaedia of Statistics Sciences, Springer-Verlag Berlin Heidelberg (2011), DOI: https://10.1007/978-642-04898-2-622. 
[14] Hooda D.S., Kumari R. and Sharma D.K. Intuitionistic Fuzzy Soft Set Theory and its Application in Medical Diagnosis, International Journal of Statistics in Medical Research, 7, 70-76 (2018). 
[15] Jalilul I.M.M. and Roy T.K. Intuitionistic Fuzzy Soft Matrix Theory, Mathematics and Statistics, 1, 43-49 (2013). 
[16] Kandasamy W.B.V., Smarandache F. and Kandasamy L. Elementary Fuzzy Matrix Entropy Theory and Fuzzy Models for Social Scientists, Automation Los Angles, USA, (2007), DOI: https://10.6084/M9.FIGSHARE.101549. 
[17] Kirisci M. Medical Decision-Making with Respect to the Fuzzy Soft Sets, Journal of Interdisciplinary Mathematics, 23 (2020), 767-776.
[18] Liu H. and Wang G. Multi-Criteria Decision-Making Methods Based on Intuitionistic Fuzzy Sets, European Journal of Operational Research, 179, 220-233 (2007). 
[19] Maji P.K. and Roy A.R. Soft Set Theory, Computer and Mathematics with Applications, 45, 555-562 (2003).
[20] Maji P.K., Biswas R. and Roy A.R. Intuitionistic Fuzzy Soft Sets, The Journal of Fuzzy Mathematics, 9, 677-692 (2001).
[21] Meenakshi A. and Kaliraja M. An Application of Interval Valued Fuzzy Matrices in Medical Diagnosis, International Journal of Mathematical Analysis, 5, 1791-1802 (2011).
[22] Molodtsov D. Soft Set Theory-First Results, Computer and Mathematics with Applications, 37, 19-31 (1999).
[23] Phaengtan K., Aimcharoen N. and Suebsan P. Partial Average of Fuzzy Soft Sets in Decision-Making Problems, 
Journal of Interdisciplinary Mathematics, 24, 1035-1052 (2021). DOI: https://10.1080/09720502.2021.1881223. 
[24] Qin H., Ma X., Herawan T., Zhan J.M.A Novel Data Filling Approach for an Incomplete Soft Set, International Journal of Applied Mathematics and Computer Sciences, 22, 817-828 (2012).
[25] Quinlan J.R. Unknown Attribute Values in Induction, In Proceedings of the 6th International Machine Learning Workshop, San Mateo, Canada,  164-168 (1989).
[26] Si A., Kolya A.K. and Adhikari S.K. Interpolation Based Data Filling Approach of Incomplete Fuzzy Soft Set, International Journal of Scientific Research and Management, 5, 6552-6560 (2017).
[27] Song Y., Wang X., Quan W. and Xue A. A Novel Similarity Measure on Intuitionistic Fuzzy Sets with its Applications, Appl. Intell., 42, 252-261 (2015). 
[28] Szmidt E. and Kacprzyk J. An Application of Intuitionistic Fuzzy Set Similarity Measures to a Multi Criteria Decision Making Problem, Artificial Intelligence and Soft Computing- ICAISC, 4029, 314-323 (2006), DOI: https://doi.org/10.1007/11785231_34 .
[29] Thiesson B. Accelerated Quantification of Bayesian Network with Incomplete Data, In – The First International Conference on Knowledge Discovery and Data Mining, Montreal, Canada, 306-311 (1995).
[30] Xu Z. and Yager R. Some Geometric Aggregation Operators Based on Intuitionistic Fuzzy Sets, International Journal of General System, 35, 417-433 (2006). 
[31] Yan Z. and Zhi X. Data Analysis Approach of Soft Sets under Incomplete Information, Knowledge – Based Systems, 21, 941-945 (2008).
[32] Yates F. The Analysis of Replicated Experiments when the Field Results are Incomplete, Empire Journal of Experimental Agriculture, 1, 129-142 (1933).
[33] Zadeh L.A. Fuzzy Sets, Information and Control, 8, 338-353 (1965).

Views: 204Downloads: 52Citations: 0