Shadowed sets of dynamic fuzzy sets
Tóm tắt
In practical situations, fuzzy sets with time-varying membership degrees are frequently encountered. In this paper, we interpret dynamic fuzzy sets by means of shadowed sets. We provide an analytic solution to computing the pair of thresholds by searching for a balance of uncertainty in the framework of shadowed sets. Subsequently, we construct errors-based three-way approximations of shadowed sets and present an alternative decision-theoretic formulation for calculating the pair of thresholds. Finally, we employ several examples to illustrate how to calculate thresholds for making a decision by means of dynamic loss functions.
Tài liệu tham khảo
Banerjee M, Pal SK (1996) Roughness of a fuzzy set. Inf Sci 93:235–246
Cattaneo G, Ciucci D (2003) Shadowed sets and related algebraic structures. Fundam Inform 55:255–284
Cattaneo G, Ciucci D (2003) An algebraic approach to shadowed sets. Electron Notes Theor Comput Sci 82:64–75
Cattaneo G, Ciucci D (2008) Theoretical aspects of shadowed sets. In: Pedrycz W, Skowron A, Kreinovich V (eds) Handbook of granular computing. Wiley, New York, pp 603–628
Chakrabarty K, Biswas R, Nanda S (1998) Nearest ordinary set of a fuzzy set: a rough theoretic construction. Bull Pol Acad Sci Tech Sci 46:105–114
Chanas S (2001) On the interval approximation of a fuzzy number. Fuzzy Sets Syst 122:353–356
Deng XF, Yao YY (2014) Decision-theoretic three-way approximations of fuzzy sets. Inf Sci 279:702–715
Deng XF, Yao YY (2013) Mean-value-based decision-theoretic shadowed sets. In: Pedrycz W, Reformat MZ (eds) Proceedings of 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS). IEEE Press, New York, pp 1382–1387
Dubois D, Prade H (1980) Fuzzy sets and fuzzy rough sets: theory and applications. Academic Press, New York
Feng T, Mi JS (2016) Variable precision multigranulation decision-theoretic fuzzy rough sets. Knowl Based Syst 91:93–101
Grzegorzewski P (2002) Nearest interval approximation of a fuzzy number. Fuzzy Sets Syst 130:321–330
Hu BQ (2014) Three-way decisions space and three-way decisions. Inf Sci 281:21–52
Hu BQ, Wong H, Yiu KFC (2016) The aggregation of multiple three-way decision spaces. Knowl Based Syst 98:241–249
Grzegorzewski P (2013) Fuzzy number approximation via shadowed sets. Inf Sci 225:35–46
Klir GJ, Bo Y (1995) Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall, Upper Saddle River
Lang GM, Yang T (2015) Decision-theoretic rough sets-based three-way approximations of interval-valued fuzzy sets. Fundamenta Informaticae 142:117–143
Li HX, Zhou XZ (2011) Risk decision making based on decision-theoretic rough set: a three-way view decision model. Int J Comput Intell Syst 4:1–11
Li JH, Huang CC, Qi JJ, Qian YH, Liu WQ (2016) Three-way cognitive concept learning via multi-granularity. Inf Sci. doi:10.1016/j.ins.2016.04.051
Liang DC, Liu D, Pedrycz W, Hu P (2013) Triangular fuzzy decision-theoretic rough sets. Int J Approx Reason 54:1087–1106
Liang DC, Liu D (2014) Systematic studies on three-way decisions with interval-valued decision-theoretic rough sets. Inf Sci 276:186–203
Liu D, Li TR, Liang DC (2012) Interval-valued decision-theoretic rough sets. Comput Sci 39(7):178–181
Liu D, Yao YY, Li TR (2011) Three-way investment decisions with decision-theoretic rough sets. Int J Comput Intell Syst 4:66–74
Liu D, Li TR, Liang DC (2013) Three-way decisions in dynamic decision-theoretic rough sets. Lect Notes Comput Sci 8171:291–301
Liu D, Liang DC, Wang CC (2016) A novel three-way decision model based on incomplete information system. Knowl Based Syst 91:32–45
Ma XA, Wang GY, Yu H, Li TR (2014) Decision region distribution preservation reduction in decision-theoretic rough set model. Inf Sci 278:614–640
Min F, Xu J (2016) Semi-greedy heuristics for feature selection with test cost constraints. Granul Comput 1(3):199–211
Mitra S, Kundu PP (2011) Satellite image segmentation with shadowed C-means. Inf Sci 181:3601–3613
Nasibov EN, Peker S (2008) On the nearest parametric approximation of a fuzzy number. Inf Sci 159:1365–1375
Pedrycz W (1998) Shadowed sets: representing and processing fuzzy sets. IEEE Trans Syst Man Cybern Syst 28:103–109
Pedrycz W (1999) Shadowed sets: bridging fuzzy and rough sets. In: Pal SK, Skowron A (eds) Rough fuzzy hybridization: a new trend in decision-making. Springer, Singapore, pp 179–199
Pedrycz W (2004) Fuzzy clustering with a knowledge-based guidance. Pattern Recogn Lett 25:469–480
Pedrycz W (2005) Interpretation of clusters in the framework of shadowed sets. Pattern Recogn Lett 26:2439–2449
Pedrycz W (2009) From fuzzy sets to shadowed sets: interpretation and computing. Int J Intell Syst 24:48–61
Pedrycz A, Dong F, Hirota K (2009) Finite cut-based approximation of fuzzy sets and its evolutionary optimization. Fuzzy Sets Syst 160:3550–3564
Sang YL, Liang JY, Qian YH (2016) Decision-theoretic rough sets under dynamic granulation. Knowl Based Syst 91:84–92
Skowron A, Jankowski A, Dutta S (2016) Interactive granular computing. Granul Comput 1(2):95–113
Solana-Cipres C, Fernandez-Escribano G, Rodriguez-Benitez L, Moreno-Garcia J, Jimenez-Linares L (2009) Real-time moving object segmentation in H.264 compressed domain based on approximate reasoning. Int J Approx Reason 51:99–114
Lopes NV, Couto P, Jurio A, Melo-Pinto P (2013) Hierarchical fuzzy logic based approach for object tracking. Knowl Based Syst 54:255–268
Wang GY, Ou JP, Wang PZ (1988) Dynamic fuzzy sets. Fuzzy Syst Math 2(1):1–8
Wang L, Wang J (2012) Feature weighting fuzzy clustering integrating rough sets and shadowed sets. Int J Pattern Recognit Artif Intell 26(04):1250010
Yao YY (2008) Probabilistic rough set approximations. Int J Approx Reason 49:255–271
Yao YY (2010) Three-way decisions with probabilistic rough sets. Inf Sci 180:341–353
Yao YY (2011) Two semantic issues in a probabilistic rough set model. Fundamenta Informaticae 108:249–265
Yao YY (2003) Probabilistic approaches to rough sets. Expert Syst 20:287–297
Yao YY (2011) The superiority of three-way decision in probabilistic rough set models. Inf Sci 181(6):1080–1096
Yu H, Jiao P, Yao YY, Wang GY (2016) Detecting and refining overlapping regions in complex networks with three-way decisions. Inf Sci 373:21–41
Zadeh LA (1965) Fuzzy sets. Inf. Control 8:338–353
Zadeh LA (2008) Is there a need for fuzzy logic? Inf Sci 178:2751–2779
Zhang HR, Min F (2016) Three-way recommender systems based on random forests. Knowl Based Syst 91:275–286
Zhou J, Pedrycz W, Miao DQ (2011) Shadowed sets in the characterization of rough-fuzzy clustering. Pattern Recogn 44:1738–1749