Total views : 474
Generalization of Rough Topology
Background/Objectives: The essential part of rough set theory is an approximation space. This theory can be defined as lower and upper approximations and these approximations are defined using the equivalence classes. We need to generalize this theory in uncertain environment. Our objective is to propose a generalized rough topology. Methods/ Statistical Analysis: Interior and closure of rough topology are same as lower, upper approximations of a rough set. We will find interior and closure of rough topology and obtain extended rough topology. Findings: In this paper, we have studied rough set topologically and proposed a definition of rough fuzzy topology by considering approximations and boundary. Theorems and propositions related to rough fuzzy topology are proposed in this paper. Application/Improvements: Our rough fuzzy topology can be applied to solve real life issues where decision values are in fuzzy form. An algorithm is proposed for the same.
Lower Approximations, Rough Fuzzy Topology, Rough Set, Rough Topology, Upper Approximations.
- Pawlak Z. Rough Sets. International Journal of Computer and Information Sciences. 1982; 11(5):341–56.
- Zadeh LA. Fuzzy Sets. Information and Control. 1965; 8:338–53.
- Zimmermann HJ. Fuzzy Set Theory and Its Applications. 4th ed. Kluwer. 2001.
- Dubois D, Prade H. Rough Fuzzy Sets and Fuzzy Rough Sets. International Journal of General Systems. 1990; 17(2- 3):191–209.
- Tripathi A, Tyagi K. Approximate equalities using topological space. Int J Granular Computing. Rough sets and intelligence Systems. 2014; 3(4):272–91.
- Lashin E, Kozae FAM, Khadra AA, Medhat T. Rough set theory for topological spaces. International Journal of Approximate Reasoning. 2005; 40(1-2):35–43.
- Thivagar ML, Richard C, Paul NR. Mathematical Innovations of a Modern Topology in Medical Events. International Journal of Information Science. 2012 Feb; 2(4):33–6.
- Qing E, Wang W, Xuan T, Yong H, Sheng LJ. Topology Theory on Rough Sets. IEEE Transactions on systems, Man, and Cybernetics- Part B. 2008; 38(1):68–77.
- Boby P, Sunil M, John J. On rough Topological space. International Journal of Mathematical. 2012; 3(9):3413–21.
- Thuan ND. Covering Rough Sets from a Topological Point of view. International Journal of Computer Theory and Engineering. 2009; 1(5):1793–8201.
- Zheng KQ. On the topological properties of fuzzy rough sets. Hindwai Publishing, 2005; 151(3):601–13.
- Tiwari SP, Shambhu S, Yadav, Vijay K. Fuzzy Closure Spaces vs. Fuzzy Rough Sets. Fuzzy information and engineering. 2014 Mar; 6(1):93–100.
- Weidong T, Jinzhao W, Zheng D. On Fuzzy Rough Sets and Their Topological Structures Hindwai Journal. 2014; 1–17.
- Amgad SS, Abu Donia HM. Generalizations of rough functions in topological spaces by using pre-open sets. Journal of Intelligent Learning Systems and Applications. 2012; 4(2):127–34.
- Cobo L, Castro H, Quintero A. A Location Routing Protocol based on Smart Antennas for Wireless Sensor Networks. Indian Journal of Science and Technology. 2015 Jun; 8(11):1–12. Doi: 10.17485/ijst/2015/v8i11/71788.
- Khameneh AZ, Kilismant A, Salleh RA. An adjustable method for data ranking based on fuzzy soft sets. Indian Journal of Science and Technology. 2015 Sep; 8(21):1–9. Doi: 10.17485/ijst/2015/v8i21/72587.
- Srimani PK, Kot MS. Knowledge Discovery in medical data by using rough set rule induction algorithms. Indian Journal of Science and Technology. 2014 Jan; 7(7):1–11. Doi: 10.17485/ijst/2014/v7i7/44729.
- Pawlak Z. Rough Sets and Fuzzy Sets. Fuzzy Sets and Systems. 1985; 17:99–102.
- Pawlak Z. Rough Sets theory and its applications. Journal of Telecommunications and Information Sciences. 2009; 179:2809–32.
- Pawlak Z. Rough Sets. Theoretical Aspect of Reasoning about Data. Kluwer Academic Publishers Norwell. Dordrecht. 1991. Oct 31.
- Chang CL. Fuzzy topological spaces. Math Anal Appl. 1968; 24(1):182–90.
- Richard J, Qiang S. Rough and Fuzzy Sets for Dimensionality Reduction. 2001.
- Palaniappan N. Fuzzy topology. Narosa Publications. 2002.
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 3.0 License.