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Original Articles

The axiomatic characterizations on L-fuzzy covering-based approximation operators

, , &
Pages 332-353 | Received 31 Jan 2016, Accepted 24 Feb 2017, Published online: 10 Apr 2017

References

  • Bartl, Eduard, and Michal Krupka. 2016. “Residuated Lattices of Block Relations: Size Reduction of Concept Lattices.” International Journal of General Systems 45: 773–789.
  • Belohlavek, R. 2001. “Fuzzy Closure Operators.” Journal of Mathematical Analysis and Application 262: 473–489.
  • Belohlavek, R. 2002a. “Fuzzy Closure Operators II: Induced Relations, Representation, and Examples.” Soft Computing 7: 53–64.
  • Belohlavek, R. 2002b. Fuzzy Relational Systems. Foundations and Principles. New York: Kluwer Academic Publishers.
  • Belohlavek, R., and T. Funiokova. 2004. “Fuzzy Interior Operators.” International Journal of General Systems 33 (4): 315–330.
  • Belohlavek, R., and J. Konecny. 2011. “Closure Spaces of Isotone Galois Connections and their Morphisms.” Lecture Notes in Articial Intelligence 7106: 182–191.
  • Belohlavek, R., and J. Konecny. 2012. “Concept Lattices of Isotone vs. Antitone Galois Connections in Graded Setting: Mutual Reducibility Revisited.” Information Sciences 199: 133–137.
  • Chen, X. Y., and Q. G. Li. 2007. “Construction of Rough Approximations in Fuzzy Setting.” Fuzzy Sets and Systems 158: 2641–2653.
  • Deng, T., Y. Chen, W. Xu, et al. 2007. “A Novel Approach to Fuzzy Rough Sets Based on a Fuzzy Covering.” Information Sciences 177: 2308–2326.
  • Dubois, D., and H. Prade. 1990. “Rough Fuzzy Sets and Fuzzy Rough Sets.” International Journal of General Systems 17: 191–208.
  • Fang, J. M. 2010. “Stratified L-Ordered Convergence Structures.” Fuzzy Sets and Systems 161: 2130–2149.
  • Georgescu, G., and A. Popescu. 2004. “Non-Dual Fuzzy Connections.” Archive for Mathematical Logic 43 (8): 1009–1039.
  • Goguen, J. A. 1967. “L-Fuzzy Sets.” Journal of Mathematical Analysis and Applications 18: 145–174.
  • Gottwald, S. 2001. A Treatise on Many-Valued Logics. Baldock: Research Studies Press.
  • Guan, L., and G. Wang. 2012. “Generalized Approximations Defined by Non-Equivalence Relations.” Information Sciences 193: 163–179.
  • Hao, J., and Q. G. Li. 2011. “The Relationship Between L-Fuzzy Rough Set and L-Topology.” Fuzzy Sets and Systems 178: 74–83.
  • Hájek, P. 1998. Metamathematics of Fuzzy Logic. Dordrecht: Kluwer Academic Publishers.
  • Høhle, U., and S. E. Rodabaugh. 1999. Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, The Handbooks of Fuzzy Sets Series. Vol. 3. Boston: Kluwer Academic Publishers.
  • Jin, Q., and L. Q. Li. 2013. “On the Second Type of L-Fuzzy Covering Rough Sets.” Information-An International Interdisciplinary Journal 16 (2): 1101–1106.
  • Jin, Q., and L. Q. Li. 2016. “One-Axiom Characterizations on Lattice-Valued Closure (Interior) Operators.” Journal of Intelligent and Fuzzy Systems 31: 1679–1688.
  • Kim, Y. C. 2015. “Join-Meet Approximation Operators and Fuzzy Preorders.” Journal of Intelligent and Fuzzy Systems 28: 1089–1097.
  • Krídlo, Ondrej, Stanislav Krajči, and Lubomir Antoni. 2016. “Formal Concept Analysis of Higher Order.” International Journal of General Systems 45: 116–134.
  • Lai, H., and D. Zhang. 2007. “Fuzzy Preorder and Fuzzy Topology.” Fuzzy Sets and Systems 157: 1865–1885.
  • Lang, G. M., Q. G. Li, and L. K. Guo. 2015. “Homomorphisms-based Attribute Reduction of Dynamic Fuzzy Covering Information Systems.” International Journal of General Systems 44: 791–811.
  • Li, L. Q., Q. Jin, S. Sun, et al. 2012. “The Topological Stuructures Induced by Upper and Lower Approximations of many Valued Approximation Spaces.” Journal of Systems Science and Mathematical Sciences 32: 226–236.
  • Li, L. Q., and Q. G. Li. 2015. “On Enriched L-Topologies: Base and Subbase.” Journal of Intelligent and Fuzzy Systems 28: 2423–2432.
  • Li, L. Q., and Q. Jin. 2012. “On Stratified L-Convergence Spaces: Pretopological Axioms and Diagonal Axioms.” Fuzzy Sets and Systems 204: 40–52.
  • Li, L. Q., Q. Jin, G. W. Meng, et al. 2016. “The Lower and Upper L-Topological (p-Regular) Modifications for Lattice-Valued Convergence Spaces.” Fuzzy Sets and Systems 282: 47–61.
  • Li, T., Yee Leung, and W. Zhang. 2008. “Generalized Fuzzy Rough Approximation Operators Based on Fuzzy Coverings.” International Journal of Approximate Reasoning. 48: 836–856.
  • Liu, G., and Y. Sai. 2009. “A Comparison of Two Types of Rough Sets Induced by Coverings.” International Journal of Approximate Reasoning 50: 521–528.
  • Liu, G. 2013. “The Relationship Among Different Covering Approximations.” Information Sciences 250: 178–183.
  • Ma, Z. M., and B. Q. Hu. 2013. “Topological and Lattices Structures of L-Fuzzy Rough Sets Determined by Lower and Upper Sets.” Information Sciences 218: 194–204.
  • Ma, Z., J. Li, and J. Mi. 2015. “Some Minimal Axiom Sets of Rough Sets.” Information Sciences 312: 40–54.
  • Mi, J., and W. Zhang. 2004. “An Axiomatic Characterization of a Fuzzy Generalization of Rough Sets.” Information Sciences 160: 235–249.
  • Morsi, N. N., and M. M. Yakout. 1998. “Axiomatics for Fuzzy Rough Set.” Fuzzy Sets and Systems 100: 327–342.
  • Pawlak, Z. 1982. “Rough Sets.” International Journal of Computer and Information Sciences 11: 341–356.
  • Qin, K., Z. Pei, J. L. Yang, et al. 2013. “Approximation Operators on Complete Completely Distributive Lattices.” Information Sciences 247: 123–130.
  • Radzikowska, A. M., and E. E. Kerre. 2004. “Fuzzy Rough Sets Based on Residuated Lattices.” Transactions on Rough Sets II, in: LNCS 3135: 278–296.
  • She, Y. H., and G. J. Wang. 2009. “An Axiomatic Approach of Fuzzy Rough Sets Based on Residuated Lattices.” Computers and Mathematics with Applications 58: 189–201.
  • Syau, Y. R., and E. Lin. 2014. “Neighborhood Systems and Covering Approximation Spaces.” Knowledge-based Systems 66: 61–67.
  • Tiwari, S. P., and A. K. Srivastava. 2013. “Fuzzy Rough Sets, Fuzzy Preorders and Fuzzy Topologies.” Fuzzy Sets and Systems 210: 63–68.
  • Wang, C. Y., and B. Q. Hu. 2013. “Fuzzy Rough Sets Based on Generalized Residuated Lattices.” Information Sciences 248: 31–49.
  • Wang, Z., Y. Wang, and K. Tang. 2014. “Some Properties of L-Fuzzy Approximation Spaces Based on Bounded Integral Residuated Lattices.” Information Sciences 278: 110–126.
  • Wu, W. Z., and W. Zhang. 2004. “Constructive and Axiomatic Approaches of Fuzzy Approximation Operators.” Information Sciences 159: 233–254.
  • Wu, W. Z., Y. Leung, and J. S. Mi. 2005. “On Characterizations of L-Fuzzy Rough Approximation Operators.” Fuzzy Sets and Systems 154: 76–102.
  • Yang, X. 2007. “Minimization of Axiom Sets on Fuzzy Approximation Operators.” Information Sciences 177: 3840–3854.
  • Yang, X., and T. Li. 2006. “The Minimization of Axiom Sets Characterizing Generalized Approximation Operators.” Information Sciences 176: 887–889.
  • Yao, Y., and B. Yao. 2012. “Covering Based Rough Set Approximations.” Information Sciences 200: 91–107.
  • Yao, Y. 1996. “Two Views of the Theory of Rough Sets in Finite Universes.” International Journal of Approximation Reasoning 15: 291–317.
  • Yao, Y. 1998. “Constructive and Algebraic Methods of the Theory of Rough Sets.” Information Sciences 109: 21–47.
  • Yao, Y. 2006. “Neighborhood Systems and Approximate Retrieval.” Information Sciences 176: 3431–3452.
  • Zhang, D. 2007. “An Enriched Category Approach yo many Valued Topology.” Fuzzy Sets and Systems 158: 349–366.
  • Zhang, Y., J. Li, and W. Wu. 2010. “On Axiomatic Characterizations of Three Pairs of Covering Based Approximation Operators.” Information Sciences 180: 274–287.
  • Zhang, Y., and M. Luo. 2011. “On Minimization of Axiom Sets Characterizing Covering-based Approximation Operators.” Information Sciences 181: 3032–3042.
  • Zhang, Y., C. Li, M. Lin, et al. 2015. “Relationships Between Generalized Rough Sets Based on Covering and Reflexive Neighborhood System.” Information Sciences 319: 56–67.
  • Zhao, F. F., and L. Q. Li. 2016. “Reduction of Rough Set Based on Generalized Neighborhood System Operator.” Journal of Mathematics and Informatics 6: 67–72.
  • Zhao, X. R., and B. Q. Hu. 2015. “Fuzzy Variable Precision Rough Sets Based on Residuated Lattices.” International Journal of General Systems 44: 743–765.
  • Zhu, W., and F. Wang. 2007. “On Three Types of Covering-based Rough Sets.” IEEE Transactions on Knowledge and Data Engineering 19: 1131–1144.
  • Zhu, W. 2009. “Relationship Between Generalized Rough Sets Based on Binary Relation and Covering.” Information Sciences 179: 210–225.

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