Decision-theoretic Rough Sets-based Three-way Approximations of Interval-valued Fuzzy Sets

• Autorzy: Lang G. , Yang T.

Identyfikatory

DOI

10.3233/FI-2015-1287

• Języki publikacji: EN

Abstrakty

EN

In practical situations, interval-valued fuzzy sets are of interest because fuzzy sets of this kind are frequently encountered. In this paper, motivated by the needs for solving imprecise problems, we generalize the concept of shadowed sets for understanding interval-valued fuzzy sets and provide a solution to compute a pair of thresholds by searching for a balance of uncertainty. Then we present three-way approximations of interval-valued fuzzy sets and a formulation for calculating the pair of thresholds using single-valued loss functions. We also compute three-way approximations of interval-valued fuzzy sets using interval-valued loss functions. Afterwards, we employ several examples to illustrate that how to take an action for an object with an interval-valued membership grade using an interval-valued loss function.

Słowa kluczowe

EN

decision-theoretic rough sets; interval-valued fuzzy sets; interval-valued loss function; Shadowed sets

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2015
• Tom: Vol. 142, nr 1-4
• Strony: 117--143
• Opis fizyczny: Bibliogr. 65 poz., tab.

Twórcy

autor

Lang G.

• School of Mathematics and Computer Science Changsha University of Science and Technology Changsha, Hunan 410114, P.R. China

autor

Yang T.

• College of Science Central South University of Forestry and Technology Changsha, Hunan 410004, P.R. China
• College of Information System and Management National University of Defense Technology

Bibliografia

• [1] Azam, N., Yao, J.T.: Game-theoretic rough sets for recommender systems, Knowledge-Based Systems, 72, 2014, 96-107.
• [2] Banerjee, M., Pal, S.K.: Roughness of a fuzzy set, Information Sciences, 93, 1996, 235-246.
• [3] Cattaneo, G., Ciucci, D.: Shadowed sets and related algebraic structures, Fundamenta Informaticae, 55, 2003, 255-284.
• [4] Cattaneo, G., Ciucci, D.: An algebraic approach to shadowed sets, Electronic Notes in Theoretical Computer Science, 82, 2003, 64-75.
• [5] Cattaneo, G., Ciucci, D.: Theoretical aspects of shadowed sets, W. Pedrycz, A. Skowron, V. Kreinovich (Eds.), Handbook of Granular Computing, John Wiley and Sons, New York, 2008, pp. 603-628.
• [6] Chakrabarty, K., Biswas, R., Nanda, S.: Nearest ordinary set of a fuzzy set: a rough theoretic construction, Bulletin of the Polish Academy of Sciences: Technical Sciences, 46, 1998, 105-114.
• [7] Chanas, S.: On the interval approximation of a fuzzy number, Fuzzy Sets and Systems, 122, 2001, 353-356.
• [8] Chen, M., Miao, D.Q.: Interval set clustering, Expert Systems with Applications, 38(4), 2011, 2923-2932.
• [9] Cheng, Y., Miao, D.Q., Fen, Q.R.: Positive approximation and converse approximation in interval-valued fuzzy rough sets Information Sciences, 181(11), 2011, 2086-2110.
• [10] Deng, X.F., Yao, Y.Y.: Decision-theoretic three-way approximations of fuzzy sets, Information Sciences, 279, 2014, 702-715.
• [11] Deng, X.F., Yao, Y.Y.: Mean-value-based decision-theoretic shadowed sets, W. Pedrycz, M.Z. Reformat (Eds.), Proceedings of 2013 Joint IFSA World Congress and NAFIPS AnnualMeeting (IFSA/NAFIPS), IEEE Press, New York, 2013, 1382-1387.
• [12] Deng, X.F., Yao, Y.Y.: A multifaceted analysis of probabilistic three-way decisions, Fundamenta Informaticae, 132(3), 2014, 291-313.
• [13] Dubois, D., Prade, H.: Fuzzy Sets and Fuzzy Rough Sets: Theory and Applications, Academic Press, New York (1980).
• [14] Grzegorzewski, P.: Nearest interval approximation of a fuzzy number, Fuzzy Sets and Systems, 130, 2002, 321-330.
• [15] Grzegorzewski, P.: Fuzzy number approximation via shadowed sets, Information Sciences, 225, 2013, 35-46.
• [16] Hu, B.Q.: Three-way decisions space and three-way decisions, Information Sciences, 281, 2014, 21-52.
• [17] Jia, X.Y., Liao, W.H., Tang, Z.M., Shang, L.: Minimum cost attribute reduction in decision-theoretic rough set models, Information Sciences, 219, 2013, 151-167.
• [18] Jia, X.Y., Tang, Z.M., Liao, W.H., Shang, L.: On an optimization representation of decision-theoretic rough set model, International Journal of Approximate Reasoning, 55(1), 2014, 156-166.
• [19] Klir, G.J., Bo, Y.: Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, New Jersey,1995.
• [20] Li, H.X., Zhou, X.Z.: Risk decision making based on decision-theoretic rough set: a three-way view decision model, International Journal of Computational Intelligence Systems, 4, 2011, 1-11.
• [21] Li, Y., Zhang, Z.H., Chen, W.B., Min, F.: TDUP: an approach to incremental mining of frequent itemsets with three-way-decision pattern updating, International Journal ofMachine Learning and Cybernetics, 2015, 1-13.
• [22] Liang, D.C., Liu, D.: Systematic studies on three-way decisionswith interval-valued decision-theoretic rough sets, Information Sciences 276, 2014, 186-203.
• [23] Liang, D.C., Liu, D.: Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets, Information Sciences, 300, 2015, 28-48.
• [24] Liang, D.C., Liu, D., Pedrycz, W., Hu, P.: Triangular fuzzy decision-theoretic rough sets, International Journal of Approximate Reasoning, 54, 2013, 1087-1106.
• [25] Liang, D.C., Pedrycz,W., Liu, D., Hu, P.: Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making, Applied Soft Computing, 29, 2015, 256-269.
• [26] Liu, D., Li, T.R., Ruan, D.: Probabilistic model criteria with decision-theoretic rough sets, Information Sciences, 181(17), 2011, 3709-3722.
• [27] Liu, D., Li, T.R., Liang, D.C.: Interval-valued decision-theoretic rough sets, Computer Science, 39(7), 2012, 178-181.
• [28] Liu, D., Li, T.R., Liang, D.C.: Three-Way Decisions in Dynamic Decision-Theoretic Rough Sets, Lecture Notes in Computer Science, 8171, 2013, 291-301.
• [29] Liu, D., Li, T.R., Zhang, J.B.: Incremental updating approximations in probabilistic rough sets under the variation of attributes, Knowledge-based Systems, 73, 2015, 81-96.
• [30] Liu, D., Liang, D.C., Wang, C.C.: A novel three-way decision model based on incomplete information system, Knowledge-Based Systems, 2015, http://dx.doi.org/10.1016/j.knosys.2015.07.036.
• [31] Liu, D., Yao, Y.Y., Li, T.R.: Three-way investment decisions with decision-theoretic rough sets, International Journal of Computational Intelligence Systems, 4, 2011, 66-74.
• [32] Ma, X.A., Wang, G.Y., Yu, H., Li, T.R.: Decision region distribution preservation reduction in decisiontheoretic rough set model, Information Sciences, 278, 2014, 614-640.
• [33] Mitra, S., Kundu, P.P.: Satellite image segmentation with shadowed C-means, Information Sciences, 181, 2011, 3601-3613.
• [34] Moore, R., Lodwick,W.: Interval analysis and fuzzy set theory, Fuzzy Sets and Systems, 135, 2003, 5-9.
• [35] Nasibov, E.N., Peker, S.: On the nearest parametric approximation of a fuzzy number, Information Sciences, 159, 2008, 1365-1375.
• [36] Pedrycz, W.: Shadowed sets: representing and processing fuzzy sets, IEEE Transactions on Systems Man Cybernetics-Systems, 28, 1998, 103-109.
• [37] Pedrycz, W.: Shadowed sets: bridging fuzzy and rough sets, S.K. Pal, A. Skowron (Eds.), Rough Fuzzy Hybridization: A New Trend in Decision-Making, Springer, Singapore, 1999, 179-199.
• [38] Pedrycz, W.: Fuzzy clustering with a knowledge-based guidance, Pattern Recognition Letters, 25, 2004, 469-480.
• [39] Pedrycz, W.: Interpretation of clusters in the framework of shadowed sets, Pattern Recognition Letters, 26, 2005, 2439-2449.
• [40] Pedrycz, W.: From fuzzy sets to shadowed sets: Interpretation and computing, International Journal of Intelligent Systems, 24, 2009, 48-61.
• [41] Pedrycz, A., Dong, F., Hirota, K.: Finite cut-based approximation of fuzzy sets and its evolutionary optimization, Fuzzy Sets and Systems, 160, 2009, 3550-3564.
• [42] Qian, Y.H., Liang, J.Y., Dang, C.Y.: Interval ordered information systems, Computers and Mathematics with Applications, 56, 2008, 1994-2009.
• [43] Qian, Y.H., Zhang, H., Sang, Y.L., Liang, J.Y.: Multigranulation decision-theoretic rough sets, International Journal of Approximate Reasoning, 55(1), 2014, 225-237.
• [44] Sang, Y.L., Liang, J.Y., Qian, Y.H.: Decision-theoretic rough sets under dynamic granulation, Knowledge-Based Systems, 2015, doi: http://dx.doi.org/10.1016/j.knosys.2015.08.001.
• [45] Sengupta, A., Pal, T.K.: On comparing interval numbers, European Journal of Operational Research, 127, 2000, 28-43.
• [46] Slezak, D., Ziarko, W.: The investigation of the Bayesian rough set model, International Journal of Approximate Reasoning, 40, 2005, 81-91.
• [47] Turksen, I.B.: Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems, 20(2), 1986, 191-210.
• [48] Wang, L., Wang, J.: Feature weighting fuzzy clustering integrating rough sets and shadowed sets, International Journal of Pattern Recognition and Artificial Intelligence, 26(4), 2012, http://dx.doi.org/10.1142/S0218001412500103.
• [49] Yao, Y.Y.: Probabilistic rough set approximations, International Journal of Approximate Reasoning, 49, 2008, 255-271.
• [50] Yao, Y.Y.: Three-way decisions with probabilistic rough sets, Information Sciences, 180, 2010, 341-353.
• [51] Yao, Y.Y.: Two semantic issues in a probabilistic rough set model, Fundamenta Informaticae, 108, 2011, 249-265.
• [52] Yao, Y.Y.: Probabilistic approaches to rough sets, Expert Systems, 20, 2003, 287-297.
• [53] Yao, Y.Y.: The superiority of three-way decision in probabilistic rough set models, Information Sciences, 181(6), 2011, 1080-1096.
• [54] Yao, J.T., Azam, N.: Web-based medical decision support systems for three-way medical decision making with game-theoretic rough sets, IEEE Transaction on Fuzzy Systems, 23(1), 2014, 3-15.
• [55] Yang, X.P., Yao, J.T.: Modelling multi-agent three-way decisions with decision-theoretic rough sets, Fundamenta Informaticae, 115(2-3), 2012, 157-171.
• [56] Yu, H., Liu, Z.G., Wang, G.Y.: An automatic method to determine the number of clusters using decision theoretic rough set, International Journal of Approximate Reasoning, 55(1), 2014, 101-115.
• [57] Ziarko, W.: Probabilistic approach to rough set, International Journal of Approximate Reasoning, 49, 2008, 272-284.
• [58] Zadeh, L.A.: Fuzzy sets, Information and Control, 8, 1965, 338-353.
• [59] Zadeh, L.A.: Is there a need for fuzzy logic? Information Sciences, 178, 2008, 2751-2779.
• [60] Zhao, X.R., Hu, B.Q.: Fuzzy and interval-valued fuzzy decision-theoretic rough set approaches based on fuzzy probability measure, Information Sciences, 298, 2015, 534-554.
• [61] Zhou, J., Pedrycz, W., Miao, D.Q.: Shadowed sets in the characterization of rough-fuzzy clustering, Pattern Recognition, 44, 2011, 1738-1749.
• [62] Zhou, J., Miao, D.Q.: _−Interval attribute reduction in variable precision rough set model, Soft Computing, 15(8), 2011, 1643-1656.
• [63] Zhou, Y., Su, H.B., Zhang, H.T.: A novel data selection method based on shadowed sets, Procedia Engineering, 15, 2011, 1410-1415.
• [64] Zhou, B., Yao, Y.Y., Luo, J.G.: Cost-sensitive three-way email spam filtering, Journal of Intelligent Information Systems, 42(1), 2014, 19-45.
• [65] Zhou, B.: Multi-class decision-theoretic rough sets, International Journal of Approximate Reasoning, 55(1), 2014, 211-224.