On the interior and closure operators of fuzzifying neighborhood systems
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Neighborhood systems present a general model for the theory of granular computing. Consistent functions can be used to study the communication between neighborhood systems. In this paper, we propose the extended notions of system consistent (sys-consistent) functions and granule consistent (gra-consistent) functions for fuzzifying neighborhood systems. The definition of the transformation of a fuzzifying neighborhood system by a mapping is presented. Then, the structure preservation properties for interior and closure operators of fuzzifying neighborhood systems are investigated.
Abstract
Neighborhood systems present a general model for the theory of granular computing. Consistent functions can be used to study the communication between neighborhood systems. In this paper, we propose the extended notions of system consistent (sys-consistent) functions and granule consistent (gra-consistent) functions for fuzzifying neighborhood systems. The definition of the transformation of a fuzzifying neighborhood system by a mapping is presented. Then, the structure preservation properties for interior and closure operators of fuzzifying neighborhood systems are investigated.
참고문헌 (28)
- Z. Pawlak, "Rough sets", International Journal of Computer and Information Sciences, 11(5), pp.341~356 (1982)
- J. H. Dai, "Rough set model for cognitive expectation embedded interval-valued decision systems", Chinese Journal of Electronics, 27(4), pp.675~679 (2018)
- K. B. Aviso, "Prediction of CO2 storage site integrity with rough set-based machine learning", Clean Technologies and Environmental Policy, 21(8), pp.1655~1664 (2019)
- J. B. Zhang, "Composite rough sets for dynamic data mining", Inform. Sci, 257, pp.81~100 (2014)
- M. M. Day, "Convergence, closure, and neighborhoods", Duke Math. J, 11, pp.181~199 (1944)
- T. Y. Lin, "Chinese Wall security policy-an aggressive model", Proceedings of the Fifth Annual Computer Security Applications Conference (1989)
- T. Y. Lin, "Neighborhood systems and approximation in relational databased and knowledge bases", Proceedings of the Forth International Symposium on Methodologies of Intelligent Systems (1989)
- T. Y. Lin, "Granular mathematics-foundation and current state", Proceedings of the 2011 IEEE International Conference on Granular Computing, pp.4~12 (2011)
- D. A. Molodtsov, "Soft set theory-rst results", Comput. Math. Appl, 37, pp.19~31 (1999)
- G. Senel, "Soft topology generated by L-soft sets", Journal of New Theory, 4(24), pp.88~100 (2018)
- G. Senel, "A New Approach to Hausdor Space Theory via the Soft Sets", Mathematical Prob-lems in Engineering, 9, pp.1~6 (2016)
- G. Senel, "Soft topological subspaces", Annals of Fuzzy Mathematics and In-formatics, 10(4), pp.525~535 (2015)
- G. Senel, "Soft closed sets on soft bitopological space", Journal of New Results in Science, 3(5), pp.57~66 (2014)
- G. Senel, "Distance and similarity measures for octahedron sets and their application to MCGDM problems", Mathematics, 8, pp.1690~ (2020)
- 이정곤, "Octahedron topological spaces", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 22(1), pp.77~101 (2021), 기초자연과학연구소[DOI]
- N. Subramanian, "Wijsman rough convergence of triple sequences", Matematychni Studii, 48(2), pp.171~179 (2017)
- B. Hazarika, "Generalized ideal limit point and cluster point of double sequences in intuitionitic fuzzy 2- normed linear spaces", Ann. Fuzzy Math. Inform, 9(6), pp.941~955 (2015)
- Z. Y. Xiu, "m-fuzzifying cotopological spaces and m-fuzzifying convex spaces as m-fuzzifying closure spaces", J. Intell. Fuzzy Syst, 33, pp.613~620 (2017)
- Z. Y. Xiu, "Base axioms and subbase axioms in m-fuzzifying convex spaces", Iran. J. Fuzzy Syst, 15(2), pp.75~87 (2018)
- M. Diker, "A category approach to relation preserving functions in rough set theory", Int. J. Approx. Reason, 56, pp.71~86 (2015)
- J. W. Grzymala-Busse, "On rough sets and information system homo-morphism", Bull. Pol. Acad. Sci., Tech. Sci, 36(3), pp.233~239 (1988)
- W. Pedrycz, "Granular worlds: representation and communication problems", Int. J. Intell. Syst, 15(11), pp.1015~1026 (2000)
- P. Zhu, "Some improved results on communication between information systems", Inf. Sci, 180(18), pp.3521~3531 (2010)
- C. Wang, "Communicating between information systems", Inf. Sci, 178(16), pp.3228~3239 (2008)
- P. Zhu, "A unied denition of consistent functions", Fundam. Inform, 135(3), pp.331~340 (2014)
- C. J. Liau, "On consistent functions for neighborhood systems", International Journal of Approximate Reasoning, 121, pp.39~58 (2020)
- L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)
- L. Q. Li, "A rough set model based on fuzzifying neighborhood systems", Soft Computing, 24(8), pp.6085~6099 (2020)
