
-
Previous Article
Generating geometric body shapes with electromagnetic source scattering techniques
- ERA Home
- This Issue
-
Next Article
High-order energy stable schemes of incommensurate phase-field crystal model
Rough semi-uniform spaces and its image proximities
Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj-211004, India |
In this paper, we introduce the concept of rough semi-uniform spaces as a supercategory of rough pseudometric spaces and approximation spaces. A completion of approximation spaces has been constructed using rough semi-uniform spaces. Applications of rough semi-uniform spaces in the construction of proximities of digital images is also discussed.
References:
[1] |
B. Batíková,
Completion of semi-uniform spaces, Appl. Categ. Structures, 15 (2007), 483-491.
doi: 10.1007/s10485-007-9092-5. |
[2] |
A. D. Concilio, C. Guadagni, J. F. Peters and S. Ramanna,
Descriptive proximities. Properties and interplay between classical proximities and overlap, Math. Comput. Sci., 12 (2018), 91-106.
doi: 10.1007/s11786-017-0328-y. |
[3] |
S. Dev, F. M. Savoy, Y. H. Lee and S. Winkler,
Rough-set-based color channel selection, IEEE Geoscience and Remote Sensing Letters, 14 (2017), 52-56.
doi: 10.1109/LGRS.2016.2625303. |
[4] |
C. J. Henry and S. Ramanna,
Signature-based perceptual nearness: Application of near sets to image retrieval, Math. Comput. Sci., 7 (2013), 71-85.
doi: 10.1007/s11786-013-0145-x. |
[5] |
S. A. Naimpally and B. Warrack, Proximity Spaces, Reprint of the 1970 original [MR0278261].
Cambridge Tracts in Mathematics, 59. Cambridge University Press, Cambridge, 2008.
doi: 10.1017/CBO9780511569364. |
[6] |
Z. Pawlak,
Rough sets, Internat. J. Comput. Inform. Sci., 11 (1982), 341-356.
doi: 10.1007/BF01001956. |
[7] |
A. S. Aguiar Pessoa, S. Stephany and L. M. Garcia Fonseca, Feature selection and image classification using rough sets theory, 2011 IEEE International Geoscience and Remote Sensing Symposium, (2011), 2904–2907.
doi: 10.1109/IGARSS.2011.6049822. |
[8] |
J. F. Peters, Computational Proximity. Excursions in the Topology of Digital Images, Intelligent Systems Reference Library, 102. Springer, [Cham], 2016.
doi: 10.1007/978-3-319-30262-1. |
[9] |
J. F. Peters, Topology of Digital Images: Visual Pattern Discovery in Proximity Spaces, Intell. Syst. Ref. Libr., Springer, 2014.
doi: 10.1007/978-3-642-53845-2. |
[10] |
J. F. Peters, J. Stepaniuk and A. Skowron,
Nearness of visual objects. Application of rough sets in proximity spaces, Fund. Inform., 128 (2013), 159-176.
doi: 10.3233/FI-2013-939. |
[11] |
J. F. Peters and P. Wasilewski,
Foundation of near sets, Inform. Sci., 179 (2009), 3091-3109.
doi: 10.1016/j.ins.2009.04.018. |
[12] |
P. K. Singh and S. Tiwari, A fixed point theorem in rough semi-linear uniform spaces, Submitted. Google Scholar |
[13] |
P. K. Singh and S. Tiwari, Topological structures in rough set theory: A survey, Hacet. J. Math. Stat., (2020), 1–25.
doi: 10.15672/hujms.662711. |
[14] |
S. Tiwari and P. K. Singh,
Čech rough proximity spaces, Mat. Vesnik, 72 (2020), 6-16.
|
[15] |
S. Tiwari and P. K. Singh,
An approach of proximity in rough set theory, Fund. Inform., 166 (2019), 251-271.
doi: 10.3233/FI-2019-1802. |
[16] |
M. Vlach, Algebraic and topological aspects of rough set theory, Fourth International Workshop on Computational Intelligence and Application-IEEE, SMC, (2008), 23–30. Google Scholar |
[17] |
M. Wolski,
Granular computing: Topological and categorical aspects of near and rough set approaches to granulation of knowledge, Lecture Notes in Comput. Sci., 7736 (2013), 34-52.
doi: 10.1007/978-3-642-36505-8_3. |
[18] |
M. Wolski,
Perception and classification. A note on near sets and rough sets, Fund. Inform., 101 (2010), 143-155.
doi: 10.3233/FI-2010-281. |
[19] |
W. Z. Wu and J. S. Mi, Some mathematical structures of generalized rough sets in infinite universes of discourse, Lecture Notes in Comput. Sci., 6499 (2011), 175-206. Google Scholar |
[20] |
Y. Y. Yao,
Relational interpretations of neighborhood operators and rough set approximation operators, Inform. Sci., 111 (1998), 239-259.
doi: 10.1016/S0020-0255(98)10006-3. |
show all references
References:
[1] |
B. Batíková,
Completion of semi-uniform spaces, Appl. Categ. Structures, 15 (2007), 483-491.
doi: 10.1007/s10485-007-9092-5. |
[2] |
A. D. Concilio, C. Guadagni, J. F. Peters and S. Ramanna,
Descriptive proximities. Properties and interplay between classical proximities and overlap, Math. Comput. Sci., 12 (2018), 91-106.
doi: 10.1007/s11786-017-0328-y. |
[3] |
S. Dev, F. M. Savoy, Y. H. Lee and S. Winkler,
Rough-set-based color channel selection, IEEE Geoscience and Remote Sensing Letters, 14 (2017), 52-56.
doi: 10.1109/LGRS.2016.2625303. |
[4] |
C. J. Henry and S. Ramanna,
Signature-based perceptual nearness: Application of near sets to image retrieval, Math. Comput. Sci., 7 (2013), 71-85.
doi: 10.1007/s11786-013-0145-x. |
[5] |
S. A. Naimpally and B. Warrack, Proximity Spaces, Reprint of the 1970 original [MR0278261].
Cambridge Tracts in Mathematics, 59. Cambridge University Press, Cambridge, 2008.
doi: 10.1017/CBO9780511569364. |
[6] |
Z. Pawlak,
Rough sets, Internat. J. Comput. Inform. Sci., 11 (1982), 341-356.
doi: 10.1007/BF01001956. |
[7] |
A. S. Aguiar Pessoa, S. Stephany and L. M. Garcia Fonseca, Feature selection and image classification using rough sets theory, 2011 IEEE International Geoscience and Remote Sensing Symposium, (2011), 2904–2907.
doi: 10.1109/IGARSS.2011.6049822. |
[8] |
J. F. Peters, Computational Proximity. Excursions in the Topology of Digital Images, Intelligent Systems Reference Library, 102. Springer, [Cham], 2016.
doi: 10.1007/978-3-319-30262-1. |
[9] |
J. F. Peters, Topology of Digital Images: Visual Pattern Discovery in Proximity Spaces, Intell. Syst. Ref. Libr., Springer, 2014.
doi: 10.1007/978-3-642-53845-2. |
[10] |
J. F. Peters, J. Stepaniuk and A. Skowron,
Nearness of visual objects. Application of rough sets in proximity spaces, Fund. Inform., 128 (2013), 159-176.
doi: 10.3233/FI-2013-939. |
[11] |
J. F. Peters and P. Wasilewski,
Foundation of near sets, Inform. Sci., 179 (2009), 3091-3109.
doi: 10.1016/j.ins.2009.04.018. |
[12] |
P. K. Singh and S. Tiwari, A fixed point theorem in rough semi-linear uniform spaces, Submitted. Google Scholar |
[13] |
P. K. Singh and S. Tiwari, Topological structures in rough set theory: A survey, Hacet. J. Math. Stat., (2020), 1–25.
doi: 10.15672/hujms.662711. |
[14] |
S. Tiwari and P. K. Singh,
Čech rough proximity spaces, Mat. Vesnik, 72 (2020), 6-16.
|
[15] |
S. Tiwari and P. K. Singh,
An approach of proximity in rough set theory, Fund. Inform., 166 (2019), 251-271.
doi: 10.3233/FI-2019-1802. |
[16] |
M. Vlach, Algebraic and topological aspects of rough set theory, Fourth International Workshop on Computational Intelligence and Application-IEEE, SMC, (2008), 23–30. Google Scholar |
[17] |
M. Wolski,
Granular computing: Topological and categorical aspects of near and rough set approaches to granulation of knowledge, Lecture Notes in Comput. Sci., 7736 (2013), 34-52.
doi: 10.1007/978-3-642-36505-8_3. |
[18] |
M. Wolski,
Perception and classification. A note on near sets and rough sets, Fund. Inform., 101 (2010), 143-155.
doi: 10.3233/FI-2010-281. |
[19] |
W. Z. Wu and J. S. Mi, Some mathematical structures of generalized rough sets in infinite universes of discourse, Lecture Notes in Comput. Sci., 6499 (2011), 175-206. Google Scholar |
[20] |
Y. Y. Yao,
Relational interpretations of neighborhood operators and rough set approximation operators, Inform. Sci., 111 (1998), 239-259.
doi: 10.1016/S0020-0255(98)10006-3. |


[1] |
Alexander A. Davydov, Massimo Giulietti, Stefano Marcugini, Fernanda Pambianco. Linear nonbinary covering codes and saturating sets in projective spaces. Advances in Mathematics of Communications, 2011, 5 (1) : 119-147. doi: 10.3934/amc.2011.5.119 |
[2] |
Ademir Fernando Pazoto, Lionel Rosier. Uniform stabilization in weighted Sobolev spaces for the KdV equation posed on the half-line. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1511-1535. doi: 10.3934/dcdsb.2010.14.1511 |
[3] |
Alexandre B. Simas, Fábio J. Valentim. $W$-Sobolev spaces: Higher order and regularity. Communications on Pure & Applied Analysis, 2015, 14 (2) : 597-607. doi: 10.3934/cpaa.2015.14.597 |
[4] |
Xue-Ping Luo, Yi-Bin Xiao, Wei Li. Strict feasibility of variational inclusion problems in reflexive Banach spaces. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2495-2502. doi: 10.3934/jimo.2019065 |
[5] |
Lucas C. F. Ferreira, Jhean E. Pérez-López, Élder J. Villamizar-Roa. On the product in Besov-Lorentz-Morrey spaces and existence of solutions for the stationary Boussinesq equations. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2423-2439. doi: 10.3934/cpaa.2018115 |
[6] |
Mao Okada. Local rigidity of certain actions of solvable groups on the boundaries of rank-one symmetric spaces. Journal of Modern Dynamics, 2021, 17: 111-143. doi: 10.3934/jmd.2021004 |
[7] |
Johannes Kellendonk, Lorenzo Sadun. Conjugacies of model sets. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3805-3830. doi: 10.3934/dcds.2017161 |
[8] |
Xinyuan Liao, Caidi Zhao, Shengfan Zhou. Compact uniform attractors for dissipative non-autonomous lattice dynamical systems. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1087-1111. doi: 10.3934/cpaa.2007.6.1087 |
[9] |
Emma D'Aniello, Saber Elaydi. The structure of $ \omega $-limit sets of asymptotically non-autonomous discrete dynamical systems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 903-915. doi: 10.3934/dcdsb.2019195 |
[10] |
Elena K. Kostousova. External polyhedral estimates of reachable sets of discrete-time systems with integral bounds on additive terms. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021015 |
Impact Factor: 0.263
Tools
Metrics
Other articles
by authors
[Back to Top]