Learning with uncertainty by Xizhao Wang, Junhai Zhai

By Xizhao Wang, Junhai Zhai

Learning with uncertainty covers a wide variety of eventualities in desktop studying, this booklet generally specializes in: (1) choice tree studying with uncertainty, (2) Clustering less than uncertainty setting, (3) energetic studying in accordance with uncertainty criterion, and (4) Ensemble studying in a framework of uncertainty. The ebook begins with the advent to uncertainty together with randomness, roughness, fuzziness and non-specificity after which comprehensively discusses a few key matters in studying with uncertainty, corresponding to uncertainty illustration in studying, the effect of uncertainty at the functionality of studying method, the heuristic layout with uncertainty, and so forth.

Most contents of the booklet are our examine ends up in fresh many years. the aim of this publication is to aid the readers to appreciate the effect of uncertainty on studying techniques. It comes with many examples to facilitate figuring out. The ebook can be utilized as reference publication or textbook for researcher fellows, senior undergraduates and postgraduates majored in desktop technology and know-how, utilized arithmetic, automation, electric engineering, etc.

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15) are defined on fuzzy partition; the equivalent definitions on universe are given as follows. 16) y∈U F ∈U /P μPX (x) = sup min μF (x), sup min μF (y), μX (y) F ∈U /P . 15 Suppose that P and Q are two fuzzy attributes in a given FDT . 19) X ∈U /Q and τP (Q) = x∈U where |U | is the cardinality of the universe U . 16 The truth degree of the fuzzy set P with respect to the fuzzy set Q is defined by β = T (P, Q) = τP (Q) . 2 Generating Fuzzy Decision Tree with Fuzzy Rough Set Technique This section introduces the algorithm for generating fuzzy decision trees based on the significance of fuzzy conditional attribute with respect to fuzzy decision attribute.

First, for each conditional attribute A, calculate its information gain. 246. 029 Because the information gain of conditional attribute Outlook is the maximum, Outlook is selected as the extended attribute. Decision Tree with Uncertainty ■ 21 S = {D1, D2, D3, . . 2 Partition data set with attribute Outlook. Step 2: Partition the data set of instances. The conditional attribute Outlook is selected as the extended attribute for the root of the decision tree. According to its values, the data set of instances is partitioned into three subsets.

88). 873). 83). 92). 3 Fuzzy Decision Tree Based on Fuzzy Rough Set Techniques In this section, we introduce an algorithm of induction of fuzzy decision tree with fuzzy rough set technique [12]. In the presented algorithm, the expanded attributes are selected by using significance of fuzzy conditional attributes with respect to fuzzy decision attributes [13–16]. We first review the basic concepts of fuzzy rough sets and then introduce the algorithm. 1 Fuzzy Rough Sets A DT [17] refers to a four-tuple DT = U , A ∪ C, V , f , where U = {x1 , x2 , .

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