Abstract
The combination of temporal vague set theory and rough set theory is developed in this paper. The lower and upper approximation operators of a temporal vague set are constructed, which is partitioned by an indiscernibility relation in Pawlak approximation space, and the concept of rough temporal vague sets is proposed as a generalization of rough vague sets. Further properties associated with the lower and upper approximations of temporal vague sets are studied. Finally, the roughness measure of a temporal vague set is defined as an extension of the parameterized roughness measure of a vague set. Meantime, some properties of roughness measure are established.
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References
Gau, W.L., Buehrer, D.J.: Vague sets. IEEE Transactions on Systems, Man and Cybernetics 23, 610–614 (1993)
Pawlak, Z.: Rough sets. Internationtal Journal of Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Rough sets: Theoretical aspects of reasoning about data. Kluwer academic publishers, Dordrecht (1991)
Pawlak, Z.: Rough sets and fuzzy sets. Fuzzy Sets and Systems 17, 99–102 (1985)
Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17, 191–209 (1990)
Dubois, D., Prade, H.: Two fold fuzzy sets and rough sets-some issues in knowledge representation. Fuzzy Sets and Systems 23, 3–18 (1987)
Wygralak, M.: Rough sets and fuzzy sets-some remarks on interrelations. Fuzzy Sets and Systems 29, 241–243 (1989)
Yao, Y.Y.: A comparative study of fuzzy sets and rough sets. Information Sciences 109, 227–242 (1998)
Yao, Y.Y.: Semantics of fuzzy sets in rough set theory. LNCS Transactions on Rough Sets 2, 310–331 (2004)
Yao, Y.Y.: Combination of rough and fuzzy sets based on α-level sets. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis for Imprecise Data, pp. 301–321. Kluwer Academic Publishers, Boston (1997)
Wang, J., Liu, S.Y., Zhang, J.: Roughness of a vague set. International Journal of Computational Cognition 3(3), 83–87 (2005)
Banerjee, M., Sankar, K.P.: Roughness of a fuzzy set. Information Sciences 93, 235–246 (1996)
Eswarlal, T.: Roughness of a Boolean vague set. International Journal of Computational Cognition 6(1), 8–11 (2008)
Gu, S.M., Gao, J., Tian, X.Q.: A fuzzy measure based on variable precision rough sets. In: Cao, B.Y. (ed.) Fuzzy Information and Engineering (ICFIE). ASC, vol. 40, pp. 798–807 (2007)
Huynh, V.N., Nakamori, Y.: A roughness measure for fuzzy sets. Information Sciences 173, 255–275 (2005)
Zhang, X.Y., Xu, W.H.: A Novel Approach to Roughness Measure in Fuzzy Rough Sets. Fuzzy Information and Engineering (ICFIE) ASC 40, 775–780 (2007)
Pattaraintakorn, P., Naruedomkul, K., Palasit, K.: A note on the roughness measure of fuzzy sets. Applied Mathematics Letters 22, 1170–1173 (2009)
Al-Rababah, A., Biswas, R.: Rough vague sets in an approximation space. International Journal of Computational Cognition 6(4), 60–63 (2008)
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Shen, Y. (2010). Rough Temporal Vague Sets in Pawlak Approximation Space. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds) Rough Set and Knowledge Technology. RSKT 2010. Lecture Notes in Computer Science(), vol 6401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16248-0_8
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DOI: https://doi.org/10.1007/978-3-642-16248-0_8
Publisher Name: Springer, Berlin, Heidelberg
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