Volume 4, Issue 1, June 2019, Page: 8-20
A Study on Matrices Using Interval Valued Intuitionistic Fuzzy Soft Set and Its Application in Predicting Election Results in India
Somen Debnath, Department of Mathematics, Tripura University, Suryamaninagar, Agartala, India
Received: Feb. 3, 2019;       Accepted: Mar. 8, 2019;       Published: Apr. 2, 2019
DOI: 10.11648/j.dmath.20190401.12      View  179      Downloads  43
Abstract
Nowadays the concept of matrix is used widely in different fields such as engineering, medical, economics, game theory, geology, computer science etc. Matrices are also used in representing the real world data like the population of people, infant mortality rate etc. In economics very large matrices are used for optimization of problems. Matrices play an important role to represent different types of soft set in concise form by which we can easily perform algebraic operations on them. Classical matrices can’t represent all types of uncertainties present in daily life problems. To tackle those problems related to uncertainties fuzzy matrix is introduced in which every member belongs to the unit interval [0, 1]. By combining soft set and fuzzy matrix a new concept fuzzy soft matrix is introduced. Later it has been extended to intuitionistic fuzzy soft matrix, interval-valued fuzzy soft matrix, interval-valued intuitionistic fuzzy soft matrix etc. In this paper we give a brief discussion on different types of interval valued intuitionistic fuzzy soft matrices and apply some new matrix operations on them. Moreover a new methodology has been developed to solve interval valued intuitionistic fuzzy soft set based real life decision making problems which may contain more than one decision maker and put an effort to apply it to a more relevant way in predicting election results in India by using the concept of choice matrix.
Keywords
Soft Set, Fuzzy Soft Set, Fuzzy Soft Matrix, Intuitionistic Fuzzy Soft Set, Choice Matrix
To cite this article
Somen Debnath, A Study on Matrices Using Interval Valued Intuitionistic Fuzzy Soft Set and Its Application in Predicting Election Results in India, International Journal of Discrete Mathematics. Vol. 4, No. 1, 2019, pp. 8-20. doi: 10.11648/j.dmath.20190401.12
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
K. Atanassov, Intuitionisticfuzzy sets, Fuzzy Sets and Systems, 20(1986), 87-96.
[2]
K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31(1989), 343-349.
[3]
N. Cagman, S. Enginoglu, Soft matrix theory and its decision making, Computers and Mathematics with Applications, 59(2010), 3308-3314.
[4]
B. Chetia, P. K. Das, An application of interval valued fuzzy soft sets in medical diagnosis, International Journal of Contemporary Mathematical Sciences, 5(2010), 1887 - 1894.
[5]
J. Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18(1967), 145-174.
[6]
M. Gorzalczan, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems, 21(1987), 1-17.
[7]
H. Hashimoto, Canonical form of a transitive fuzzy matrix, Fuzzy sets and systems, 11(1983), 157-162.
[8]
D. S. Hooda, R. Kumari, On applications of fuzzy soft sets in dimension reduction and medical diagnosis, Advances in Research, 12(2017), 1-9.
[9]
Y. Jiang, Y. Tang, Q. Chen, H. Liu, J. Tung, Interval -valued intuitionistic fuzzy soft sets and their properties, Computers and Mathematics with Applications, 60(2010), 906-918.
[10]
P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, J. Fuzzy Mathematics, 9(2001), 589-602.
[11]
P. K. Maji, R. Biswas, A. R. Roy, Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics, 12(2004), 669-683.
[12]
D. Molodtsov, Soft set theory-first results, Computers and Mathematics with Application, 37(1999), 19-31.
[13]
Z. Pawlak, Rough sets, International Journal of Computing and Information Sciences 11(1982), 341-356.
[14]
P. Rajarajeswari, P. Dhanalakshmi, Interval valued intuitionistic fuzzy soft matrix theory, International Journal of Mathematical Archive, 5(2014), 152-161.
[15]
R. Rathika, S. Subramanian, An application of intuitionistic fuzzy soft matrix theory based on the reference function in decision making problem, International Journal of Pure and Applied Mathematics, 119(2018), 219-234.
[16]
X. B. Yang, T. Y. Lin, J. Y. Yang, Y. Li, D. Yu, Combination of interval-valued fuzzy set and soft set, Computers and Mathematics with Applications, 58(2009), 521-527.
[17]
Y. Yang, J. Chenli, Fuzzy soft matrices and their applications part I, Lecture notes in Computer Science, 7002(2011), 618-627.
[18]
L. A. Zadeh, Fuzzy set, Information and Control, 8(1965), 338-353.
[19]
M. Zulqarnain, M. Saeed, An application of interval valued fuzzy soft matrix in decision making, Science International (Lahore), 28(2016), 2261-2264.
Browse journals by subject