Jump to ContentJump to Main Navigation
Show Summary Details
In This Section

Journal of Artificial Intelligence and Soft Computing Research

The Journal of Polish Neural Network Society, the University of Social Sciences in Lodz & Czestochowa University of Technology

4 Issues per year

Open Access
Online
ISSN
2083-2567
See all formats and pricing
In This Section

Group Decision Making using Interval-Valued Intuitionistic Fuzzy Soft Matrix and Confident Weight of Experts

Sujit Das
  • Department of Computer Science and Engineering, Dr. B. C. Roy Engineering College, Durgapur-6, India
  • Email:
/ Samarjit Kar
  • Department of Mathematics, National Institute of Technology, Durgapur-9, India
  • Email:
/ Tandra Pal
  • Department of Computer Science and Engineering, National Institute of Technology, Durgapur-9, India
  • Email:
Published Online: 2014-12-30 | DOI: https://doi.org/10.2478/jaiscr-2014-0025

Abstract

This article proposes an algorithmic approach for multiple attribute group decision making (MAGDM) problems using interval-valued intuitionistic fuzzy soft matrix (IVIFSM) and confident weight of experts. We propose a novel concept for assigning confident weights to the experts based on cardinals of interval-valued intuitionistic fuzzy soft sets (IVIFSSs). The confident weight is assigned to each of the experts based on their preferred attributes and opinions, which reduces the chances of biasness. Instead of using medical knowledgebase, the proposed algorithm mainly relies on the set of attributes preferred by the group of experts. To make the set of preferred attributes more important, we use combined choice matrix, which is combined with the individual IVIFSM to produce the corresponding product IVIFSM. This article uses IVIFSMs for representing the experts’ opinions. IVIFSM is the matrix representation of IVIFSS and IVIFSS is a natural combination of interval-valued intuitionistic fuzzy set (IVIFS) and soft set. Finally, the performance of the proposed algorithm is validated using a case study from real life

References

  • [1] D. Molodtsov, Soft set theory - first results, Comput. Math. Appl. vol. 37, no. (4-5), pp. 19-31, 1999 [Crossref]

  • [2] S.R.S. Varadhan, Probability Theory, American Mathematical Society, 2001

  • [3] L. A. Zadeh, Fuzzy sets, Information and Control, vol. 8, pp. 338-353, 1965 [Crossref]

  • [4] Z. Pawlak, Rough sets, International Journal of Computer Science, vol. 11, pp. 341-356, 1982 [Crossref]

  • [5] S. Kar, S. Das, P. K. Ghosh, Applications of neuro fuzzy systems: A brief review and future outline, Applied Soft Computing Journal, vol. 15, pp. 243-259, 2014 [Crossref]

  • [6] N. Cagman, S. Enginoglu, Soft matrix theory and its decision making, Computers and Mathematics with Applications, vol. 59, no. 10, pp. 3308-3314, 2010

  • [7] N. Cagman, S. Enginoglu, Soft set theory and uni- int decision making, European Journal of Operational Research, vol. 207, no. 2, pp. 848-855, 2010 [Web of Science]

  • [8] F. Feng, Y. B. Jun, X. Liu, L. Li, An adjustable approach to fuzzy soft set based decision making, Journal of Computational and Applied Mathematics, vol. 234, no. 1, pp. 10-20, 2010

  • [9] Jiang, Y. Tang, Q. Chen, An adjustable approach to intuitionistic fuzzy soft sets based decision making, Applied Mathematical Modelling, vol. 35, no. 2, pp. 824-836, 2011 10] Z. Kong, L. Gao, L. Wang, Comment on A fuzzy soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics, vol. 223, no. 2, pp. 540-542, 2009 [Crossref]

  • [10] Z. Kong, L. Gao, L. Wang, Comment on A fuzzy soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics, vol. 223, no. 2, pp. 540-542, 2009 [Web of Science]

  • [11] P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Computers and Mathematics with Applications, vol. 44, no. (8-9), pp. 1077-1083, 2002

  • [12] A. R. Roy, P. K. Maji, A fuzzy soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics, vol. 203, no. 2, pp. 412-418, 2007 [Web of Science]

  • [13] Y. Zou, Z. Xiao, Data analysis approaches of soft sets under incomplete information, Knowledge- Based Systems, vol. 21, no. 8, pp. 941-945, 2008

  • [14] Z. Xiao, K. Gong, Y. Zou, A combined forecasting approach based on fuzzy soft sets, Journal of Computational and Applied Mathematics, vol. 228, no. 1, pp. 326-333, 2009

  • [15] J. Kalayathankal and G. S. Singh, A fuzzy soft flood alarm model, Mathematics and Computers in Simulation, vol. 80, no. 5, pp. 887-893, 2010 [Web of Science]

  • [16] D. V. Kovkov, V. M. Kolbanov, D. A. Molodtsov, Soft sets theory-based optimization, Journal of Computer and Systems Sciences International, vol. 46, no. 6, pp. 872-880, 2007

  • [17] M. M. Mushrif, S. Sengupta, A. K. Ray, Texture classification using a novel, soft set theory based classification algorithm, in P. J. Narayanan, S. K. Nayar, H. Y. Shum (Eds.), Proceedings of the 7th Asian Conference on Computer Vision, 2006, Lecture Notes in Computer Science, vol. 3851, pp. 246-254

  • [18] P. K. Maji, R. Biswas, A. R. Roy, Soft sets theory, Comput. Math. Appl., vol. 45, pp. 555-562, 2003 [Crossref]

  • [19] P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, J. Fuzzy Math., vol. 9, no. 3, pp. 589-602, 2001

  • [20] X. B. Yang, T. Y. Lin, J. Y. Yang, Y. Li, D. Y. Yu, Combination of interval-valued fuzzy set and soft set, Comput. Math. Appl., vol. 58, pp. 521-527, 2009 [Web of Science]

  • [21] P. K. Maji, More on intuitionistic fuzzy soft sets, in H. Sakai, M. K. Chakraborty, A. E. Hassanien, D. Slezak, W. Zhu (Eds.), Proceedings of the 12th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2009), Lecture Notes in Computer Science, vol. 5908, pp. 231-240

  • [22] P.K. Maji, R. Biswas, A.R. Roy, Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics vol. 9, no. 3, pp. 677-692, 2001

  • [23] P.K. Maji, A.R. Roy, R. Biswas, On intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics, vol. 12, no. 3, pp. 669-683, 2004

  • [24] P.K. Maji, An application of intuitionistic fuzzy soft sets in a decision making problem, in IEEE International Conference on Progress in Informatics and Computing (PIC), vol. 1, December 10-12, 2010, pp. 349-351

  • [25] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 20, pp. 87- 96, 1986 [Crossref]

  • [26] Y. Jiang, Y. Tang, Q. Chen, H. Liu, J. Tang, Interval-valued intuitionistic fuzzy soft sets and their properties, Comput. Math. Appl., vol. 60, pp. 906-918, 2010 [Web of Science] [Crossref]

  • [27] F. Feng, Y. Li, V. Leoreanu-Fotea, Application of level soft sets in decision making based on intervalvalued fuzzy soft sets, Comput. Math. Appl., vol. 60, pp. 1756-1767, 2010 [Crossref]

  • [28] H. Qin, X. Ma, T. Herawan, J. M. Zain, An adjustable approach to interval-valued intuitionistic fuzzy soft sets based decision making, in N. T. Nguyen, C. G. Kim, and A. Janiak (Eds.), Proceedings of ACIIDS, 2011, LNAI, vol. 6592, pp. 80-89, Springer-Verlag Berlin Heidelberg

  • [29] Z. Zhang, C. Wang, D. Tian, K. Li, A novel approach to interval-valued intuitionistic fuzzy soft set based decision making, Applied Mathematical Modelling, vol. 38, no. 4, pp. 1255-1270, 2014 [Crossref] [Web of Science]

  • [30] J. Mao, D. Yao, C. Wang, Group decision making methods based on intuitionistic fuzzy soft matrices, Applied Mathematical Modelling, vol. 37, pp. 6425-6436, 2013 [Web of Science]

  • [31] S. Das, S. Kar, Group decision making in medical system: An intuitionistic fuzzy soft set approach, Applied Soft Computing, 24. pp. 196-211, 2014, http://dx.doi.org/10.1016/j.asoc.2014.06.050 [Web of Science] [Crossref]

  • [32] S. Das, M. B. Kar, T. Pal, S. Kar, Multiple Attribute Group Decision Making using Interval-Valued Intuitionistic Fuzzy Soft Matrix, Proc. of IEEE International Conference on Fuzzy Systems (FUZZIEEE), Beijing, July 6-11, 2014, pp. 2222 - 2229, doi: 10.1109/FUZZ-IEEE.2014.6891687 [Crossref]

  • [33] S. Das, M. B. Kar, S. Kar, Group Multi Criteria Decision Making using Intuitionistic Multi Fuzzy Sets, Journal of Uncertainty Analysis and Applications, 1:10, 2013, doi:10.1186/2195-5468-1-10 [Crossref]

  • [34] S. Das, S. Kar, Intuitionistic Multi Fuzzy Soft Set and its Application in Decision Making, in P. Maji et al. (Eds.), Proceedings of Fifth International Conference on Pattern Recognition and Machine Intelligence (PReMI), 2013, Lecture Notes in Computer Science, vol. 8251, pp. 587-592

  • [35] S. Das, S. Kar, The Hesitant Fuzzy Soft Set and its Application in Decision Making, in Proceedings of International Conference on Facets of Uncertainties and Applications (ICFUA), 2013, Lecture Notes in Computer Science, Springer, unpublished

  • [36] S. Chen, J. Tan, Handling multi criteria fuzzy decision-making problems based on vague set theory, Fuzzy Sets and Systems, vol. 67, no.2, pp. 163-172, 1994

About the article

Published Online: 2014-12-30

Published in Print: 2014-01-01



Citation Information: Journal of Artificial Intelligence and Soft Computing Research, ISSN (Online) 2083-2567, DOI: https://doi.org/10.2478/jaiscr-2014-0025. Export Citation

© 2015. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Comments (0)

Please log in or register to comment.
Log in