Characterization of rough semiring

Afrika Matematika - Tập 28 - Trang 945-956 - 2017
A. Manimaran1, B. Praba2, V. M. Chandrasekaran1
1School of Advanced Sciences, VIT University, Vellore, India
2SSN College of Engineering, Chennai, India

Tóm tắt

In this paper, we give a characterization of the rough semiring $$(T,\Delta ,\nabla )$$ . The order of a rough semiring is also derived. We present the idea of rough homomorphism on the set of all rough sets for the given information system together with the operations Praba $$\Delta $$ and Praba $$\nabla $$ . We illustrate these concepts through examples.

Tài liệu tham khảo

Bisaria, J., Srivastava, N., Paradasani, K.R.: A rough set model for sequential pattern mining with constraints. (IJCNS) Int. J. Comput. Netw. Secur. 1(2), 16–22 (2009) Chen, D., Chi, D.W., Wang, C.X., Wang, Z.R.: A rough set based hiererchical clustering algorithm for categorical data. Int. J. Inf. Technol. 12(3), 149–159 (2006) Chouchoulas, A., Shen, Q.: Rough set-aided keyword reduction for text categorization. Appl. Artif. Intell. 15, 843–873 (2001) Fiala, N.C.: Semigroup, monoid and group models of groupoid identities, Quasigroups and related systems 16, 25–29 (2008) Howie, J.M.: Fundamentals of Semigroup Theory. Oxford University Press, New York (2003) Krishna, K.V., Chatterjee, N.: Representation of near semirings and approximation of their categories. Southeast Asian Bull. Math. 31, 903–914 (2007) Lee, S.H.: Extending semiring homomorphisms to ring homomorphisms. Commun. Korean Math. Soc. 13(2), 243–249 (1998) Manimaran, A., Praba, B., Chandrasekaran, V.M.: Regular rough \(\nabla \) monoid of idempotents. Int. J. Appl. Eng. Res. 9(16), 3469–3479 (2014) Nasiri, J.H., Mashinchi, M.: Rough set and data analysis in decision tables. J. Uncertain Syst. 3(3), 232–240 (2009) Pawlak, Z.: Rough sets. Int. J. Comput.Inf. Sci. 11, 341–356 (1982) Praba, B., Mohan, R.: Rough lattice. Int. J. Fuzzy Math. Syst. 3(2), 135–151 (2013) Praba, B., Chandrasekaran, V.M., Manimaran, A.: A commutative regular monoid on rough sets. Ital. J. Pure Appl. Math. 31, 307–318 (2013) Praba, B., Chandrasekaran, V.M., Manimaran, A.: Semiring on rough sets. Indian J. Sci. Technol. 8(1), 280–286 (2015) Sai, Y., Nie, P., Xu, R., Huang, J.: A rough set approach to mining concise rules from inconsistent data. IEEE Int. Conf. Granul. Comput. 10(12), 333–336 (2006) Sreenivasulu Reddy, P., Tela, G.Y.: Simple semirings. Int. J. Eng. Invent. 2(7), 16–19 (2013) Vasanthi, T., Sulochana, N.: On the additive and multiplicative structure of semirings. Ann. Pure Appl. Math. 3(1), 78–84 (2013) Venkatalakshmi, C., Vasanthi, T.: Some special classes of semirings. Int. J. Appl. Inf. Syst. 6(8), 27–29 (2014) Wang, Z., Shu, L., Ding, X.: Homomorphisms of approximation spaces. J. Appl. Math. 2012, 1–18 (2012) Xiao, Q.M., Zhang, Z.L.: Rough prime ideals and rough fuzzy prime ideals in semigroups. Inf. Spaces 176, 725–733 (2006) Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965) Zhai, Y.H., Qu, K.S.: On characteristics of information system homomorphisms. Theory Comput. Syst. 44(3), 414–431 (2009)