Abstract
In granular computing, information granularity and hierarchical structures are the two main issues that are relevant in investigating the uncertainty measure and structure of all types of granular spaces. To represent and analyze granular structures for neighborhood-based granular space, a distance-based information granularity and the corresponding hierarchical structures of neighborhood-based granular space are discussed in this paper. First, we propose the representation and operations of neighborhood-based granular structures and examine four hierarchical structures of neighborhood-based granular space. Second, a distance between two neighborhood-based granular structures is introduced to differentiate them; this distance is used to establish the axiomatic approach of information granularity of neighborhood-based granular space. Third, the representation and operations of fuzzy neighborhood-based granular structures, a distance between two fuzzy neighborhood-based granular structures, a distance-based information granularity, and a distance-based hierarchical structure for fuzzy neighborhood-based granular space, are studied. Fourth, a novel distance is developed in multi-granulation neighborhood-based granular space. Using this distance, information granularity and a hierarchical structure for multi-granulation neighborhood-based granular space are provided. Finally, distance, information granularity, and hierarchical structure are examined in multi-granulation fuzzy neighborhood-based granular space. The presented distance between two neighborhood granular structures is an effective tool for representing information granularity and constructing hierarchical structures in neighborhood-based granular spaces.
Similar content being viewed by others
References
Abo-Tabl EA (2011) A comparison of two kinds of definitions of rough approximations based on a similarity relation. Inf Sci 181:2587–2596
Chen DG, Zhang XX, Li WL (2015) On measurements of covering rough sets based on granules and evidence theory. Inf Sci 317:329–348
Chen YM, Wu KS, Chen XH, Tang CH, Zhu QX (2014) An entropy-based uncertainty measurement approach in neighborhood systems. Inf Sci 279:239–250
Cornelis C, Medina J, Verbiest N (2014) Multi-adjoint fuzzy rough sets: definition, properties and attribute selection. Int J Approx Reason 55:412–426
D’eer L, Restrepo M, Cornelis C, Gómez J (2016) Neighborhood operators for covering-based rough sets. Inf Sci 336:21–44
Gacek A (2013) Granular modelling of signals: a framework of granular computing. Inf Sci 221:1–11
Hu QH, Yu DR, Xie ZX, Liu JF (2006) Fuzzy probabilistic approximation spaces and their information measures. IEEE Trans Fuzzy Syst 14:191–201
Hu QH, Zhang L, Zhang D, Pan W, An S, Pedrycz W (2011) Measuring relevance between discrete and continuous features based on neighborhood mutual information. Expert Sys App 38:10737–10750
Huang B, Zhuang YL, Li HX (2013) Information granulation and uncertainty measures in interval-valued intuitionistic fuzzy information systems. Eur J Oper Res 231:162–170
Huang B, Guo CX, Li HX, Feng GF, Zhou XZ (2016) Hierarchical structures and uncertainty measures for intuitionistic fuzzy approximation space. Inf Sci 336:92–114
Liang JY, Qian YH (2008) Information granules and entropy theory in information systems. Sci China Ser F Inf Sci 9:1–18
Liang JY, Li R, Qian YH (2012) Distance: a more comprehensible perspective for measures in rough set theory. Knowl Based Syst 27:126–136
Lin GP, Liang JY, Qian YH (2015a) Uncertainty measures for multigranulation approximation space. Int J Uncert Fuzzi Knowl Based Syst 23:443–457
Lin GP, Liang JY, Qian YH (2015b) An information fusion approach by combining multigranulation rough sets and evidence theory. Inf Sci 314:184–199
Lin GP, Qian YH, Li JJ (2012) NMGRS: neighborhood-based multigranulation rough sets. Int J Approx Reason 53:1080–1093
Lin YJ, Li JJ, Lin PR, Lin GP, Chen JK (2014) Feature selection via neighborhood multi-granulation fusion. Knowl Based Syst 67:162–168
Ma ZM, Mi JS (2015) A comparative study of MGRSs and their uncertainty measures. Fundam Inf 142:161–181
Pedrycz A, Hirota K, Pedrycz W, Dong FY (2012) Granular representation and granular computing with fuzzy sets. Fuzzy Sets Syst 203:17–32
Pedrycz W, Chen SM (2011) Granular computing and intelligent systems: design with information granules of higher order and higher type. Springer, Heidelberg
Pedrycz W, Chen SM (2015a) Information granularity, big data, and computational intelligence. Springer, Heidelberg
Pedrycz W, Chen SM (2015b) Granular computing and decision-making: interactive and iterative approaches. Springer, Heidelberg
Pedrycz W, Succi G, Sillitti A, Iljazi J (2015) Data description: a general framework of information granules. Knowl Based Syst 80:98–108
Qian YH, Dang CY, Liang JY, Wu WZ (2012) Partial ordering of information granulations: a further investigation. Expert Syst 29:3–24
Qian YH, Liang JY, Lin GP, Dang CY (2015) Fuzzy granular structure distance. IEEE Trans Fuzzy Syst 23:2245–2259
Qian YH, Liang JY, Wu WZ, Dang CY (2011) Information granularity in fuzzy binary GrC model. IEEE Trans Fuzzy Syst 2:253–264
Qian YH, Liang JY, Yao YY, Dang CY (2010) MGRS: a multi-granulation rough set. Inf Sci 180:949–970
Qian YH, Zhang H, Li FJ, Hu QH, Liang JY (2014) Set-based granular computing: a lattice model. Int J Approx Reason 55:834–852
Restrepo M, Cornelis C, Gómez J (2014) Partial order relation for approximation operators in covering based rough sets. Inf Sci 284:44–59
She YH, He XL (2012) On the structure of the multigranulation rough set model. Knowl Based Syst 36:81–92
Skowron A, Stepaniuk J, Swiniarski R (2012) Modeling rough granular computing based on approximation spaces. Inf Sci 184:20–43
Sun BZ, Ma WM, Chen DG (2014) Rough approximation of a fuzzy concept on a hybrid attribute information system and its uncertainty measure. Inf Sci 284:60–80
Wang GY, Ma XA, Yu H (2015) Monotonic uncertainty measures for attribute reduction in probabilistic rough set model. Int J Approx Reason 59:41–67
Wang GY, Yang J, Xu J (2017) Granular computing:from granularity optimization to multi-granularity joint problem solving. Granul Comput 2:105–120
Xu WH, Zhang XY, Zhang WX (2009) Knowledge granulation, knowledge entropy and knowledge uncertainty measure in ordered information systems. Appl Soft Comput 9:1244–1251
Yang XB, Qi Y, Yu HL, Song XN, Yang JY (2014) Updating multigranulation rough approximations with increasing of granular structures. Knowl Based Syst 64:59–69
Yang XB, Qi Y, Yang JY (2012a) On characterizing hierarchies of granulation structures via distances. Fundam Inf 122:1–16
Yang XB, Qian YH, Yang JY (2012b) Hierarchical structures on multigranulation spaces. J Comput Sci Tech 27:1169–1183
Yao YY (2001) Information granulation and rough set approximation. Int J Intell Syst 16:87–104
Yao YY (2016) A triarchic theory of granular computing. Granul Comput 1(2):1–13
Yao YY, Yao BX (2012) Covering based rough set approximations. Inf Sci 200:91–107
Yao YY (1998) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 111:239–259
Yao YY, Zhao LQ (2012) A measurement theory view on the granularity of partitions. Inf Sci 213:1–13
Yu ZM, Bai XL, Yun ZQ (2013) A study of rough sets based on 1-neighborhood systems. Inf Sci 248:103–113
Zadeh L (1998) Some reflections on soft computing, granular computing and their roles in the conception, design and utilization of information/intelligent systems. Soft Comput 2:23–25
Zhang XH, Miao DQ, Liu CH, Le ML (2016) Constructive methods of rough approximation operators and multigranulation rough sets. Knowl Based Syst 91:114–125
Acknowledgements
The authors would also like to thank the EssayStar Company (http://essaystar.com/) for their assistance in improving the English language of this paper. We appreciate the support provided by the Natural Science Foundation of China (Grant nos. 61473157, 71671086, 61170105, and 71201076) and the Priority Academic Program Development of Jiangsu Higher Education Institutions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Huang, B., Li, H. Distance-based information granularity in neighborhood-based granular space. Granul. Comput. 3, 93–110 (2018). https://doi.org/10.1007/s41066-017-0058-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41066-017-0058-1