Unknown Values Estimation in Incomplete Fuzzy Soft and Interval Valued Soft Matrices
Keywords:Fuzzy soft set, Interval-valued Fuzzy soft set, Estimation, Fuzzy Soft Matrices and Dimension Reduction.
In day-to-day problems, incomplete information due to unknown values in data is the cause of the loss of information which leads to uncertainly, ambiguity and vagueness. There are many reasons for unknown values in data, like errors in data collection, lack of data information, inappropriate technique, and illegibility of data which cause incompleteness in data. Thus, estimating the unknown values in data of various information systems is an important area of research. In this communication, the definitions of incomplete Fuzzy soft and interval-valued fuzzy soft matrices are given with application in numerical problems. An algorithm is proposed for unknown values estimation in an incomplete fuzzy soft matrix and applied in solving a numerical problem. An application of an incomplete fuzzy soft matrix after inserting the unknown values in dimension reduction is studied. The unknown values in the incomplete interval-valued fuzzy soft matrix are also estimated and applied in the multi-criteria decision-making method.
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(2005), 757-763.
Cagman N., Enginoglu S. Soft Matrices and its Decision Making, Computer and Mathematics with Applications, 59(2010), 3308-3314.
Cagman N., and Enginoglo S. Fuzzy Soft Matrix Theory and its Application in Decision Making, International Journal of Fuzzy Systems, 9(2012), 109-119.
Celik Y. and Yamak S. Fuzzy Soft Set Theory Applied to Medical Diagnosis using Fuzzy Arithmetic Operations, Journal of Inequalities and Applications, DOI: https://doi.org/10.1186/1029-242x-2013.
Deng T. and Wang X. An Object-Parameter Approach to Predicting Unknown Data in Incomplete Fuzzy Soft Sets, Applied Mathematical Modelling,37(2013), 4139-4146.
Dong Y. and Xiao Z. A Group Decision Making Method Based on Dempster-Shafer Fuzzy Soft Sets under Incomplete Information, International Journal of Hybrid Information Technology, 8(2015), 287-296.
Das S., Ghosh S. and Pal T. An Algorithmic Approach for Predicting Unknown Information in Incomplete Fuzzy Soft Set, Arabian Journal for Sciences and Engineering, 42(2017), 3563-3571.
Hooda D.S. and Jain D. Measures of Information on Fuzzy Soft Matrix and Fuzzy Binary Relation, Journal of Combinatories, Information and System Sciences, 37(2012), 1-18.
Hooda D.S. and Kumari R. On Application of Fuzzy Soft Set in Dimension Reduction and Medical Diagnosis, Advance in research, 12(2017), 1-9.
Hooda D.S. and Barak M.S. Estimation of Missing Data in Design of Experiment and Contingency Table, SN Applied Sciences, DOI: https://doi.org/10.1007/s42452-019-0692-0, 2019.
Hooda D.S. and Barak M.S. Estimation of Missing Values in Fuzzy Matrix and Interval Valued Fuzzy Matrix, Life Cycle of Reliability and Safety Engineering, DOI: https://doi.org/10.1007/s41872-020-00116, 2020.
Jun Y.B. and Song S.Z. Soft Sub-algebra and Soft Ideals of BCK/BCI- Algebras Related to Fuzzy Set Theory, Mathematical Communication, 14(2009), 271-281.
Kandasamy W.B.V., Smarandache F. and Kandasamy L. Fuzzy Matrix Entropy Theory and Fuzzy Models for Social Scientists, Automation Los Angles, USA, DOI: 10.6084/M9.FIGSHARE.101549/.2007.
Kong Z., Gao L. and Wang L.S. The Normal Parameter Reduction of Soft Set and its Algorithm, Computer and Mathematics with Application, 56(2008), 3029-3037.
Kong Z.,Gao L. and Wang L.S. Comment on “A Fuzzy Soft Set Theoretic Approach to Decision Making Problems”, Journal ofComputational and Applied Mathematics,223(2009), 540-542.
Kalayathankal S.J. and Singh S. A fuzzy Soft Flood Alarm Model, Mathematics and Computers in Simulation, 80(2010), 887-893.
Kalaichelvi A. and Malini P.H. Applications of Fuzzy Soft Sets to Investment Decision Making Problems, International Journal of Mathematical Sciences and Applications, 3(2011), 1583-1586.
Khan M.S., Algaradi M.A, Abdul Wahab A.W. and Herawan T. An Alternative Data Filling Approach for Predicting of Missing Data in Soft Sets (ADFIS), Springer Plus, 5(2016), 1348.
Molodtsov D.A. Soft Set Theory- First Result, Computers and Mathematics with Applications, 37(1999), 19-31.
Maji P.K., Biswas R. and Roy A.R. Fuzzy Soft Sets, Journal of Fuzzy Mathematics, 9(2001), 589-602.
Maji P.K., Biswas R. and Roy A.R. An Application of Soft Set in Decision Making Problem, Computer and Mathematics with Application, 44(2002), 1077-1083.
Maji P.K., Roy A.R. and Biswas R. On Intuitionistic Fuzzy Soft Set, Journal of Fuzzy Mathematics, 12(2004), 669-683.
Ma X., Sulaiman N., Qin H., Herawan T. and Zain J.M. A New Efficient Normal Parameter Reduction Algorithm of Soft Sets, Computer and Mathematics with Applications, 62(2011), 599-598.
Qin H., Ma X., Herawan T. and Zain J.M. Data Filling Approach of Soft Sets under Incomplete Information, In: Nguyen, N.T., Kim, C. G. Janiak, A. (eds) ACIIDS 2011, LNAI, 6592(2011), 302-311.
Tanay B. and Kandemir M.B. Topological Structure of Fuzzy Soft Set, Computer and Mathematics with Application, 61(2011), 2952-2957.
Wang L. and Qin K. Incomplete Fuzzy Soft Set and their Application to Decision Making. DOI: 103390/Sym11040535.
Zadeh L A. Fuzzy sets. Information and Control, 8(1965), 338-353.
Zou Y. and Xiao Z. Data Analysis Approach of Soft Sets under Incomplete Information, Knowledge-Based System, 21(2008), 941-945.
How to Cite
Copyright (c) 2021 D. S. Hooda, Seema Singh, S. C. Malik
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.