Uncertainty measurement for neighborhood based soft covering rough graphs with applications
- 20 Downloads
Soft set theory and rough set theory are two newer tools to discuss uncertainty. Soft graphs are a nice way to depict certain information. In order to discuss uncertainty in soft graphs, a new type of graphs called neighborhood based soft covering rough graphs is introduced. We have discussed the uncertainty measures associated with neighborhood based soft covering rough graphs such as roughness measure, entropy measure and granularity. Some important properties of these uncertainty measures are investigated and the relationships between such measures are established. These properties will help to understand the essence of uncertainty measurement and in measuring the quality of a decision rule.
KeywordsSoft set theory Uncertainty measure Soft graph Soft covering rough graph Information entropy Granularity
Mathematics Subject Classification08A72 54A40 03B52 20N25
C. Park was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2017R1D1A1B04032937). The authors are thankful to the reviewers and the editors for their close attention and constructive suggestions to improve the quality of the manuscript.
Compliance with ethical standards
Conflict of interest
The authors of this paper declare that they have no conflict of interest.
- 11.Chitcharoen, D., Pattaraintakorn, P.: Towards theories of fuzzy set and rough set to flow graphs. IEEE Int. Conf. Fuzzy Syst. 4630596, 1675–1682 (2008)Google Scholar
- 12.Dai, J., Wang, W., Xu, Q.: An uncertainty measure for incomplete decision tables and its applications. IEEE Trans. Syst., Man, Cyber. Part B Cybern. (2012). https://doi.org/10.1109/TSMCB.2012.2228480
- 16.Euler, L.: Solutio problematis ad geometriam situs pertinentis, Commentarii Academiae Scientiarum Imperialis Petropolitanae 8:128–140 (1736)Google Scholar
- 17.Faizi, S., Sałabun, W., Rashid, T., Wa̧tróbski, J., Zafar, S.: Group decision-making for hesitant fuzzy sets based on characteristic objects method, Symmetry 9 (2017), 9:8, 17 pagesGoogle Scholar
- 21.Feng, H., Wang, G., Huang, H., Wu, Y.: Incremental Attribute Reduction Based on Elementary Sets. Fuzzy Sets, Data Mining and Granular-Soft Computing. International Workshop on Rough Sets, pp. 185–193. Springer, Berlin (2005)Google Scholar
- 22.Firouzian, S., Jouybari, M.N.: Coloring fuzzy graphs and traffic light problem. TJMCS 2, 431–435 (2011)Google Scholar
- 36.Molodtsov, D.: The Theory of Soft Sets. URSS, Moscow (2004). (in Russian)Google Scholar
- 38.Noor, R., Irshad, I., Javaid, I.: Soft rough graphs (2017). arXiv preprint arXiv:1707.05837
- 46.Rolka, L., Rolka, A.M.: Labeled fuzzy rough sets versus fuzzy flow graphs. In: IJCCI- Proceedings of the 8th International Joint Conference on Computational Intelligence, 2016. pp. 115–120Google Scholar
- 48.Shah, N., Hussain, A.: Neutrosophic soft graphs. Neutrosoph. Sets Syst. 11, 31–44 (2016)Google Scholar
- 49.Shah, N., Rehman, N., Shabir, M., Ali, M.I.: Another approach to roughness of soft graphs with applications in decision making. Symmetry (2018). https://doi.org/10.3390/sym10050145
- 53.Tozlu, N., Yuksel, S., Simsekler, T.H.: A topological approach to soft covering approximation space (2015). arXiv preprint arXiv:1503.07896
- 54.West, D.B.: Introduction to Graph Theory, vol. 2. Prentice hall, Upper Saddle River (2001)Google Scholar
- 59.Yao, Y.Y.: On Generalizing Pawlak Approximation Operators, International Conference on Rough Sets and Current Trends in Computing. Springer, Berlin (1998)Google Scholar