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\title{Decision Tree Construction: A Continues Label Support Degree Based Approach}
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             \author[1]{  N.Madhuri}

             \author[2]{  T.Nagalakshmi}

             \author[3]{sujatha  dandu}

             \affil[1]{  Auroras Technological and Research Institute (JNTU)}

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\date{\small \em Received: 25 October 2011 Accepted: 22 November 2011 Published: 2 December 2011}

\maketitle


\begin{abstract}
        


Data mining and classification systems utilize decision tree algorithms since they  proffer rapid speediness, advanced exactness and also simple organization of those algorithms.  An ideal decision can be built only when the appropriate attributes are chosen. This paper  focuses on throwing light on choosing characteristics based on the theory of attribute support  degree on account   of which a unique decision tree construction algorithm is proposed on the  basis of rough set and granular computing theory. It is henceforth proved that the decision tree  proposed by the new approach yields far more better results in terms of precision and  consistency as compared to the decision trees yielded by ID3, C4.5 and DTBAS.    

\end{abstract}


\keywords{rough set: decision tree: granular computing: attribute support degree: attribute  selection.}

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\let\tabcellsep& 	 	 		 
\section[{INTRODUCTION}]{INTRODUCTION}\par
ecision sets can be denoted using tree structures with the help of decision tree which is a unique, spontaneous, data illustration scheme and also a competent classifier. Quinlan et al \hyperref[b0]{[1]} proposed ID3, decision tree algorithm and hence has been persistently augmented which have been advanced to C4.5 \hyperref[b1]{[2]}. The preeminent attribute is chosen as the existing attribute which is then recursively inflates the decision tree branches unless and until the conditional statement is achieved, which ultimately makes use of top-down greedy algorithms. There are different classification schemes that can be achieved concerning different solutions which poses two issues \hyperref[b2]{[3]} in decision tree construction. Choosing characteristics for crafting new branches in a tree is one issue while the other one is pruning which is all about omitting and decreasing the tree. DTBAS \hyperref[b11]{[10]} considered the Assortment of attribute as main concern, which was refined and improved by considering assortment of continuous labels also that is discussed in this paper.\par
Z. Pawlak et al \hyperref[b3]{[4]} recommended rough set theory which is an expansion of set theory for studying intelligent systems which is followed up by inadequate and partial data information. There is a thriving submission of the rough set theory in the disciplines of data mining, pattern recognition, machine learning, decision analysis etc in recent times. Models are categorized into various resembling classes that houses imperceptible objects in terms of few attributes. Issues pertaining to feature selection, data reduction and pattern extraction can be amicably taken care of such that it can liberate the system of redundant data in systems containing null values or missing data.\par
Lin et al \hyperref[b4]{[5]} proposed the expression of Granular Computing which spans itself covering all aspects of concerning theories, tactics, practices and means essential in solving a problem that makes use of granules. Granular Computing has witnessed vast inputs from different practices such as fuzzy sets, rough sets, shadowed sets, probabilistic sets etc.\par
A crucial step that needs to be taken care of while building a decision tree is choosing characteristics of nodes of a tree that houses minimum number of branches. Decision tree based on continuous label support degree (DTBLSD) algorithm is introduced which is considered as a splitting criterion on account of rough set theory and granular computing. Trial results have approved the usage of DTBLSD algorithm that assures and provides uncomplicated structures and superior categorization accuracy.\par
The rest of the paper is organized as follows: Section 2 discusses concepts relevant to rough set theory and granular computing. Section 3 gives a basic introduction to our new method and presents a simple example. Experimental comparison of the proposed method with 103 and C4.S is given in section 4. The final section concludes the research work of this paper. 
\section[{II. BASIC CONCEPT}]{II. BASIC CONCEPT}\par
Few fundamental concepts of rough set theory \hyperref[b6]{[6,}\hyperref[b7]{7]} and granular computing \hyperref[b9]{[8]} are first initiated for ease of demonstration. Definition 1 (Information System) : An information system can be labeled as wherein U is a finite set of object known as the universe; , which is a non-vacant finite group of attributes; C and D depict set of condition and decision attributes respectively as also , which says that is a value set of the attribute a and Where is the cardinal number of .( I ) 2011 December ( , , , ) S U A V f = A C D = U , a v v a A = ? ? U a v\par
When in an equivalence relation R, the granular degree of R reaches the minimum size ; When R is a domain relation, the granular degree of R attains the maximum size Definition 5 : Assume R is knowledge of repository , the granular degree of basic knowledge is defined asIII. 
\section[{PROPOSED ALGORITHM}]{PROPOSED ALGORITHM}\par
This section aims at familiarizing the algorithm of building a decision tree on the basis of attribute support degree. 
\section[{a) The Principle of Label and Attribute Selection}]{a) The Principle of Label and Attribute Selection}\par
The label that represents least average uncertainty is supposed to be chosen as the test label and then choose attribute with less uncertainty as test attribute from the class represented by the selected label, which because it makes apt decisions when compared to existing test attribute selection in different decision tree algorithms. ( Attribute Support Degree ) Let be an information system is a label contains subset of attributes represented as . Attribute support degree can be denoted as follows based on the definitions mentioned above. 
\section[{Where}]{Where}\par
denotes the cardinal number of . 
\section[{Global}]{Global}I ) 2011 December ( f U A V = × ? ( , ) a f u a V ? a A ? , u U ? ( ( )) X BND X ( , , , ) S U A V f = R A ? X U ? ( ) R X ( ) R X ( ) BND X ( ) R X Ji(x), ( ) R X ( ) BND X ( ) \{ | [ ] \}....(1) R R X x U x X = ? ? ( ) \{ | [ ] \}...(2) ( ) ( ) ( )....(3) R R X x U x X BND X R X R X ? = ? ? ? = ? ( , , , ) S U A V f = P A ? ( ) \{( , ) | , ( , ) ( . )....(4) a IND P x y U U P f x a f y a = ? × ? ? = ( ) U IND P ( , ) K U R = R U U ? × ( ) GD R 2 | | | | ( ) ...(5) | | | | R R GD R U U U = = × | | R R U U ? × 2 | | / | | 1/ | | U U U = 2 2 | | / | | 1 U U = ( , ) K U R = , 1 2 / \{ , ,..., \} n U R X X X = 2 1 2 | | ( ) ...(6) | | n i i i x GD X U = = ? 1 2 \{ , ,.... \} ls a a a | | 1 ( ) ( ) ....(7) | | l i i uc uc a avg l l = = ? ( ) uc avg l l l ( ) i uc a i a l ( , , , ) S U A V f = , A C D = U l Q C ? ( ) | ( ) | ( , ) ...(8) ( ) ( ) GD Q D IND QUD S Q D GD Q IND Q = = U | ( ) | IND Q ( ) IND Q U U ? ×\par
Decision Tree Construction: A Continues Label Support Degree Based Approach\par
. Definition 5 states that whenever we get the relations among them, namely, when GD(R) is smaller, the distinguishable degree is stronger and S(Q,D) is greater, thereby Q is better sets of test attribute of D. On the contrary, the smaller S(Q,D) is, the worse we get Q as sets of test attribute of D. 
\section[{b) The Description of DTBLSD}]{b) The Description of DTBLSD}\par
The basic notion of DTBLSD expresses the point that whenever label support degree with association of label level attribute support degree is made use of as a customary for choosing a test attribute concerning every node in the decision tree. The attribute reduction set assists in selecting a condition attribute that possesses the highest degree of label level attribute which can be put to use at the root of the decision tree. There will be a testing of the remaining condition attributes on each and every branch of the root node S (Q,D) D using Q can be estimated with the help of a measure addition of new sub-trees to every division until the leaf is reached.\par
According to the above idea, using the S(Q,D) as the splitting criterion, we propose our algorithm DTBLSD. Current sample set is depicted by T, set of labels depicted by L, condition attribute set of a label is depicted by the . depicts the number of attributes in the condition attribute set of label . All attributes of the condition attribute set are discrete and continuous values are discretized by continuous labeling. Following are the specific steps of the algorithm.\par
Algorithm : A decision tree is created by DTBLSD (T, attribute list) that using the given training data. The top-down recursive divide and conquer approach for construction of a decision tree wherein the recursion related division takes place only when any one criterion mentioned below is gratified. A common class contains : 
\section[{Input}]{Input}\par
1. AII specimens for a specific branch which restores a leaf that is termed with the concerned class.\par
Here, a large case of voting is provisioned to change the present working node into a leaf that is termed with the concerned class that in in demand from amongst various specimens. 2. In addition, there are no more specimen test attributes and the class division specimens can be placed wherein a leaf is generated and termed with the most featured class in specimens.\par
IV. 
\section[{EXPERIMENTS a) Example Analysis}]{EXPERIMENTS a) Example Analysis}\par
Table  {\ref 1} showcases a data tuple training group originated from All Electronics customer records that are implemented using polic mentioned in reference \hyperref[b6]{(6)}. The first step is to estimate the degree of attribute support for each situational attribute or characteristic. ( ) 
\section[{U IND al}]{U IND al}\par
= \{ \{l,2,8,9, 11 \},\{3,7,12,13\},\{ 
\section[{U IND az}]{U IND az}\par
= \{ \{1, 2, 3, 13\},\{4, 8, 10, 11, 12, 14\}, \{\par
(U IND a = \{\{1, 2, 3, 4, 8, 12, 14\}, \{5\textbf{3)} 
\section[{U IND a}]{U IND a}\par
= \{ \{l,3,4,5,8,9,10,13\},\{2,6,7,11,12,14\}\};\par
( )  Table  {\ref I} : Training data tuple from the AIIElectronics customer database Notations used in example descriptions: Age???, Income???, Student???, Credit???, Buy?? is selected as the min root of the decision tree and is tagged with age since is the maximum extent of a degree from amongst all the condition attributes as also various number of divisions which are branched in reference to a range of different attributes. In case where age=1, all the specimens that are grouped into this should belong to the same class and hence a leaf should be generated at the end of every division and should be tagged with d=yes. The figure above depicts the final decision tree that is built by DTBLSD.U IND d = \{ \{1 ,2,\textbf{6,8,14 \},\{3,4,5,7,9, 10, 11,12, 13\}\}; ( , )} 
\section[{b) Experimentl Comparison}]{b) Experimentl Comparison}\par
Experimental comparison of DTBLSD with respect to ID3 \hyperref[b0]{[1]}, C4.5 \hyperref[b1]{[2]} and DTBAS \hyperref[b11]{[10]} is discussed in this section. The real datasets that are used in this are approved from University of California, Irvine (UCI), and is known as the machine learning database repository where C++ design language is implemented to form the requisite algorithm. WEKA 3.7 is used for successful accomplishment of ID3 \hyperref[b0]{[1]} and C4.5 \hyperref[b1]{[2]} which is a compilation of machine learning algorithms used for data mining generated and procured by  {\ref Frank}      
\section[{CONCLUSION}]{CONCLUSION}\par
The paper first focuses on explaining the basic notion of label support degree and attribute support degree \hyperref[b11]{[10]} and selecting it as a basic decisive factor on the basis of degree of involvement between condition attribute and decision attribute accordingly where a unique decision algorithm tree based on continuous label support degree and label level attribute support degree (DTBLSD) is recommended. Accordingly a suitable methodology is devised which is flexible enough to accommodate and provides lower complexity and high level of accuracy as compared to other algorithm generating methods. A disadvantage identified in \hyperref[b11]{[10]} is issues pertaining to adjustment with adaptability of samples, which has been overcome successfully in our model.\begin{figure}[htbp]
\noindent\textbf{6}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Definition 6 :}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_4}}\end{figure}
  \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.03774131274131274\textwidth}P{0.21496138996138994\textwidth}P{0.16245173745173747\textwidth}P{0.12142857142857141\textwidth}P{0.07548262548262548\textwidth}P{0.21003861003861005\textwidth}P{0.02789575289575289\textwidth}}
\tabcellsep U\tabcellsep age\tabcellsep income\tabcellsep student\tabcellsep credit\tabcellsep buy\\
\tabcellsep 1\tabcellsep <=30\tabcellsep high\tabcellsep no\tabcellsep fair\tabcellsep No\\
\tabcellsep 2\tabcellsep <=30\tabcellsep high\tabcellsep no\tabcellsep \multicolumn{2}{l}{excellent No}\\
\tabcellsep 3\tabcellsep 31<=age<=40\tabcellsep high\tabcellsep no\tabcellsep fair\tabcellsep yes\\
\tabcellsep 4\tabcellsep >40\tabcellsep medium\tabcellsep no\tabcellsep fair\tabcellsep yes\\
\tabcellsep 5\tabcellsep >40\tabcellsep low\tabcellsep yes\tabcellsep fair\tabcellsep yes\\
2011 December\tabcellsep 6 7 8 9 10\tabcellsep >40 31<=age<=40 <=30 <=30 >40\tabcellsep low low medium low medium\tabcellsep yes yes no yes yes\tabcellsep \multicolumn{2}{l}{excellent No excellent Yes fair No fair Yes fair Yes}\\
\tabcellsep 11\tabcellsep <=30\tabcellsep medium\tabcellsep yes\tabcellsep \multicolumn{2}{l}{excellent Yes}\\
\tabcellsep 12\tabcellsep 31<=age<=40\tabcellsep medium\tabcellsep no\tabcellsep \multicolumn{2}{l}{excellent Yes}\\
\tabcellsep 13\tabcellsep 31<=age<=40\tabcellsep high\tabcellsep yes\tabcellsep fair\tabcellsep Yes\\
\tabcellsep 14\tabcellsep >40\tabcellsep medium\tabcellsep no\tabcellsep \multicolumn{2}{l}{excellent No}\\
\tabcellsep 1 a\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep 1 ( , ) S a d\tabcellsep \tabcellsep \tabcellsep \\
I )\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
(\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Global\tabcellsep \multicolumn{2}{l}{that involved the 10 fold cross estimation to calculate}\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \multicolumn{2}{l}{classification authenticity. All experiments were}\tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{II} \par 
\begin{longtable}{P{0.22417582417582418\textwidth}P{0.1401098901098901\textwidth}P{0.1541208791208791\textwidth}P{0.16346153846153846\textwidth}P{0.16813186813186812\textwidth}}
\tabcellsep \tabcellsep ?\tabcellsep DTBA\tabcellsep DTBLS\\
Dataset\tabcellsep ID3\tabcellsep ? C4.5\tabcellsep S\tabcellsep D\\
ZOO\tabcellsep 0.899\tabcellsep 0.901\tabcellsep 0.911\tabcellsep 0.914\\
Lymphograph\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
y\tabcellsep 0.75\tabcellsep 0.791\tabcellsep 0.765\tabcellsep 0.767\\
Iris\tabcellsep 0.932\tabcellsep 0.936\tabcellsep 0.943\tabcellsep 0.947\\
Monk\tabcellsep 0.637\tabcellsep 0.6\tabcellsep 0.821\tabcellsep 0.824\\
Breas t cancer\tabcellsep 0.9\tabcellsep 0.9\tabcellsep 0.912\tabcellsep 0.916\\
Sick\tabcellsep 0.931\tabcellsep 0.937\tabcellsep 0.955\tabcellsep 0.959\end{longtable} \par
 
\caption{\label{tab_3}Table II :}\end{figure}
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