An Efficient Approach for Fuzzy Decision Reduct Computation
Fuzzy rough sets is an extension of classical rough sets for feature selection in hybrid decision systems. However, reduct computation using the fuzzy rough set model is computationally expensive. A modified quick reduct algorithm (MQRA) was proposed in l
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Abstract. Fuzzy rough sets is an extension of classical rough sets for feature selection in hybrid decision systems. However, reduct computation using the fuzzy rough set model is computationally expensive. A modified quick reduct algorithm (MQRA) was proposed in literature for computing fuzzy decision reduct using Radzikowska-Kerry fuzzy rough set model. In this paper, we develop a simplified computational model for discovering positive region in Radzikowska-Kerry’s fuzzy rough set model. Theory is developed for validation of omission of absolute positive region objects without affecting the subsequent inferences. The developed theory is incorporated in MQRA resulting in algorithm Improved MQRA (IMQRA). The computations involved in IMQRA are modeled as vector operations for obtaining further optimizations at implementation level. The effectiveness of algorithm(s) is empirically demonstrated by comparative analysis with several existing reduct approaches for hybrid decision systems using fuzzy rough sets. Keywords: Fuzzy rough sets, Hybrid decision systems, Reduct, Quick Reduct, Fuzzy decision reduct.
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Introduction
Rough sets [38], developed by Prof. Z. Pawlak [39], has emerged as an important soft computing paradigm being applied for several data mining and machine learning applications [20,40]. Feature selection using reduct based on rough set principles is extensively employed in several application domains [5,20,35]. Rough sets provide a non invasive data mining approach for knowledge discovery in databases (KDD) [11,50]. The process of knowledge discovery in a given decision system primarily consists of reduct computation as the preprocessing step for dimensionality reduction. But classical rough sets are applicable to decision (or information) systems with qualitative attributes. Hybrid decision systems contain a mixture of qualitative and quantitative attributes and occur frequently in real world decision systems. The classical definitions of rough sets are based on an indisernibility relation, which is an equivalence relation. Hence under indiscernibility relation using a quantitative attribute, two objects will be unrelated even though they have near values on J.F. Peters and A. Skowron (Eds.): Transactions on Rough Sets XVII, LNCS 8375, pp. 82–108, 2014. c Springer-Verlag Berlin Heidelberg 2014
An Efficient Approach for Fuzzy Decision Reduct Computation
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a real-values scale. A reduct computed thus would contain primary key like attributes and leads to classifiers with less generalization capacity. Hence classical rough sets cannot be applied directly to hybrid decision systems for reduct computation. Traditionally indiscernibility relation using quantitative attribute was defined after discretization. The process of discretization converts a quantitative attribute into a qualitative attribute. A discretization algorithm places cuts in the domain of quantitative attribute and divides the continuous domain into non overlapping intervals (bins). Two objects having values in the same interval are assigned th
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