Abstract
Pythagorean fuzzy sets as generalizations of intuitionistic fuzzy sets are effective for dealing with uncertainty information, but little effort has been paid to conflict analysis of Pythagorean fuzzy information systems. In this paper, we present the concepts of the maximum positive alliance, central alliance, and negative alliance with the two thresholds \(\alpha \) and \(\beta \). Then we show how to compute the thresholds \(\alpha \) and \(\beta \) for conflict analysis based on decision-theoretic rough set theory. Finally, we employ several examples to illustrate how to compute the maximum positive alliance, central alliance, and negative alliance from the view of matrix.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Beliakov, G., James, S.: Averaging aggregation functions for preferences expressed as Pythagorean membership grades and fuzzy orthopairs. In: Proceedings of 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 298–305. IEEE (2014)
Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J., Xu, Z.S., Bedregal, B., Montero, J., Hagras, H., Herrera, F., DeBaets, B.: A historical account of types of fuzzy sets and their relationships. IEEE Trans. Fuzzy Syst. 24(1), 179–194 (2016)
Deja, R.: Conflict Analysis, Rough Set Methods and Applications. Studies in Fuzzyness and Soft Comput. Physica, Heidelberg (2000). 491–520
Ju, H.R., Li, H.X., Yang, X.B., Zhou, X.Z.: Cost-sensitive rough set: a multi-granulation approach. Knowl.-Based Syst. (2017). http://dx.doi.org/10.1016/j.knosys.2017.02.019
Kang, X.P., Miao, D.Q.: A variable precision rough set model based on the granularity of tolerance relation. Knowl.-Based Syst. 102, 103–115 (2016)
Khan, M.T., Azam, N., Khalid, S., Yao, J.T.: A three-way approach for learning rules in automatic knowledge-based topic models. Int. J. Approx. Reason. 82, 210–226 (2017)
Lang, G.M., Miao, D.Q., Yang, T., Cai, M.J.: Knowledge reduction of dynamic covering decision information systems when varying covering cardinalities. Inf. Sci. 346–347, 236–260 (2016)
Li, H.X., Zhang, L.B., Zhou, X.Z., Huang, B.: Cost-sensitive sequential three-way decision modeling using a deep neural network. Int. J. Approx. Reason. (2017). http://dx.doi.org/10.1016/j.ijar.2017.03.008
Lin, T.Y.: Granular computing on binary relations analysis of conflict and chinese wall security policy. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS, vol. 2475, pp. 296–299. Springer, Heidelberg (2002). doi:10.1007/3-540-45813-1_38
Liu, G.L.: The axiomatization of the rough set upper approximation operations. Fundam. Informaticae 69(3), 331–342 (2006)
Maeda, Y., Senoo, K., Tanaka, H.: Interval density functions in conflict analysis. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS, vol. 1711, pp. 382–389. Springer, Heidelberg (1999). doi:10.1007/978-3-540-48061-7_46
Pawlak, Z.: Some remarks on conflict analysis. Eur. J. Oper. Res. 166(3), 649–654 (2005)
de Oliveira Silva, L.G., de Almeida-Filho, A.T.: A multicriteria approach for analysis of conflicts in evidence theory. Inf. Sci. 346, 275–285 (2016)
Ramanna, S., Skowron, A.: Requirements interaction and conflicts: a rough set approach. In: Proceedings of IEEE Symposium Series on Foundations of Computational Intelligence (2007)
Reformat, M.Z., Yager, R.R.: Suggesting recommendations using pythagorean fuzzy sets illustrated using netflix movie data. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2014. CCIS, vol. 442, pp. 546–556. Springer, Cham (2014). doi:10.1007/978-3-319-08795-5_56
Sun, B.Z., Ma, W.M., Zhao, H.Y.: Rough set-based conflict analysis model and method over two universes. Inf. Sci. 372, 111–125 (2016)
Skowron, A., Deja, R.: On some conflict models and conflict resolutions. Rom. J. Inf. Sci. Technol. 5(1–2), 69–82 (2002)
Song, J.J., Tsang, E.C.C., Chen, D.G., Yang, X.B.: Minimal decision cost reduct in fuzzy decision-theoretic rough set model. Knowl.-Based Syst. (2017). http://dx.doi.org/10.1016/j.knosys.2017.03.013
Yager, R.R.: Pythagorean membership grades in multicriteria decision making. IEEE Trans. Fuzzy Syst. 22, 958–965 (2014)
Yao, Y.Y.: Probabilistic rough set approximations. Int. J. Approx. Reason. 49, 255–271 (2008)
Zhang, X.L., Xu, Z.S.: Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int. J. Intell. Syst. 29, 1061–1078 (2014)
Acknowledgments
We would like to thank the reviewers very much for their professional comments and valuable suggestions. This work is supported by the National Natural Science Foundation of China (Nos. 61603063, 61673301, 11526039), Doctoral Fund of Ministry of Education of China (No. 20130072130004), China Postdoctoral Science Foundation (No. 2015M580353), China Postdoctoral Science special Foundation (No. 2016T90383).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Lang, G., Miao, D., Zhang, Z., Yao, N. (2017). Conflict Analysis for Pythagorean Fuzzy Information Systems. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10314. Springer, Cham. https://doi.org/10.1007/978-3-319-60840-2_26
Download citation
DOI: https://doi.org/10.1007/978-3-319-60840-2_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-60839-6
Online ISBN: 978-3-319-60840-2
eBook Packages: Computer ScienceComputer Science (R0)