Fuzzy Decision-Tree-Based Analysis of Databases

2011 ◽  
pp. 760-783
Author(s):  
Malcolm Beynon
Keyword(s):  
Decision Tree ◽  
Decision Trees ◽  
Inductive Learning ◽  
Fuzzy Decision ◽  
Fuzzy Decision Tree ◽  
Fuzzy Environment ◽  
The United Kingdom ◽  
Fuzzy Representation ◽  
Fuzzy Decision Trees ◽  
Low Pay

The general fuzzy decision tree approach encapsulates the benefits of being an inductive learning technique to classify objects, utilising the richness of the data being considered, as well as the readability and interpretability that accompanies its operation in a fuzzy environment. This chapter offers a description of fuzzy decision tree based research, including the exposition of small and large fuzzy decision trees to demonstrate their construction and practicality. The two large fuzzy decision trees described are associated with a real application, namely, the identification of workplace establishments in the United Kingdom that pay a noticeable proportion of their employees less than the legislated minimum wage. Two separate fuzzy decision tree analyses are undertaken on a low-pay database, which utilise different numbers of membership functions to fuzzify the continuous attributes describing the investigated establishments. The findings demonstrate the sensitivity of results when there are changes in the compactness of the fuzzy representation of the associated data.

Induction of fuzzy decision trees and its refinement using gradient projected-neuro-fuzzy decision tree

2014 ◽  
Vol 6 (4) ◽  
pp. 346 ◽  
Author(s):  
Swathi Jamjala Narayanan ◽  
Rajen B. Bhatt ◽  
Ilango Paramasivam ◽  
M. Khalid ◽  
B.K. Tripathy
Keyword(s):  
Decision Tree ◽  
Decision Trees ◽  
Fuzzy Decision ◽  
Fuzzy Decision Tree ◽  
Neuro Fuzzy ◽  
Fuzzy Decision Trees

Utilizing Fuzzy Decision Trees in Decision Making

2011 ◽  
pp. 2024-2030
Author(s):  
Malcolm J. Beynonm
Keyword(s):  
Data Mining ◽  
Decision Making ◽  
Decision Tree ◽  
Decision Trees ◽  
Time Series Data ◽  
Series Data ◽  
Fuzzy Decision ◽  
Fuzzy Environment ◽  
Complex Decision Making ◽  
Fuzzy Decision Trees

The seminal work of Zadeh (1965), namely fuzzy set theory (FST), has developed into a methodology fundamental to analysis that incorporates vagueness and ambiguity. With respect to the area of data mining, it endeavours to find potentially meaningful patterns from data (Hu & Tzeng, 2003). This includes the construction of if-then decision rule systems, which attempt a level of inherent interpretability to the antecedents and consequents identified for object classification (See Breiman, 2001). Within a fuzzy environment this is extended to allow a linguistic facet to the possible interpretation, examples including mining time series data (Chiang, Chow, & Wang, 2000) and multi-objective optimisation (Ishibuchi & Yamamoto, 2004). One approach to if-then rule construction has been through the use of decision trees (Quinlan, 1986), where the path down a branch of a decision tree (through a series of nodes), is associated with a single if-then rule. A key characteristic of the traditional decision tree analysis is that the antecedents described in the nodes are crisp, where this restriction is mitigated when operating in a fuzzy environment (Crockett, Bandar, Mclean, & O’Shea, 2006). This chapter investigates the use of fuzzy decision trees as an effective tool for data mining. Pertinent to data mining and decision making, Mitra, Konwar and Pal (2002) succinctly describe a most important feature of decision trees, crisp and fuzzy, which is their capability to break down a complex decision-making process into a collection of simpler decisions and thereby, providing an easily interpretable solution.

Fuzzy Decision Trees

2011 ◽  
pp. 696-703
Author(s):  
Malcolm J. Beynon
Keyword(s):  
Artificial Intelligence ◽  
Decision Tree ◽  
Decision Trees ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Entropy Measure ◽  
Fuzzy Decision ◽  
Fuzzy Environment ◽  
Fuzzy Decision Trees

The inductive learning methodology known as decision trees, concerns the ability to classify objects based on their attributes values, using a tree like structure from which decision rules can be accrued. In this article, a description of decision trees is given, with the main emphasis on their operation in a fuzzy environment. A first reference to decision trees is made in Hunt et al. (1966), who proposed the Concept learning system to construct a decision tree that attempts to minimize the score of classifying chess endgames. The example problem concerning chess offers early evidence supporting the view that decision trees are closely associated with artificial intelligence (AI). It is over ten years later that Quinlan (1979) developed the early work on decision trees, to introduced the Interactive Dichotomizer 3 (ID3). The important feature with their development was the use of an entropy measure to aid the decision tree construction process (using again the chess game as the considered problem). It is ID3, and techniques like it, that defines the hierarchical structure commonly associated with decision trees, see for example the recent theoretical and application studies of Pal and Chakraborty (2001), Bhatt and Gopal (2005) and Armand et al. (2007). Moreover, starting from an identified root node, paths are constructed down to leaf nodes, where the attributes associated with the intermediate nodes are identified through the use of an entropy measure to preferentially gauge the classification certainty down that path. Each path down to a leaf node forms an ‘if .. then ..’ decision rule used to classify the objects. The introduction of fuzzy set theory in Zadeh (1965), offered a general methodology that allows notions of vagueness and imprecision to be considered. Moreover, Zadeh’s work allowed the possibility for previously defined techniques to be considered with a fuzzy environment. It was over ten years later that the area of decision trees benefited from this fuzzy environment opportunity (see Chang and Pavlidis, 1977). Since then there has been a steady stream of research studies that have developed or applied fuzzy decision trees (FDTs) (see recently for example Li et al., 2006 and Wang et al., 2007). The expectations that come with the utilisation of FDTs are succinctly stated by Li et al. (2006, p. 655); “Decision trees based on fuzzy set theory combines the advantages of good comprehensibility of decision trees and the ability of fuzzy representation to deal with inexact and uncertain information.” Chiang and Hsu (2002) highlight that decision trees has been successfully applied to problems in artificial intelligence, pattern recognition and statistics. They go onto outline a positive development the FDTs offer, namely that it is better placed to have an estimate of the degree that an object is associated with each class, often desirable in areas like medical diagnosis (see Quinlan (1987) for the alternative view with respect to crisp decision trees). The remains of this article look in more details at FDTs, including a tutorial example showing the rudiments of how an FDT can be constructed.

A Fuzzy Decision Tree Analysis of Traffic Fatalities in the US

2009 ◽  
pp. 201-217
Author(s):  
Malcolm J. Beynon
Keyword(s):  
Decision Tree ◽  
Decision Trees ◽  
Decision Rules ◽  
Decision Tree Analysis ◽  
Fuzzy Decision ◽  
Fuzzy Decision Tree ◽  
Traffic Fatalities ◽  
Tree Analysis ◽  
The Us ◽  
Fuzzy Decision Trees

This chapter considers the role of fuzzy decision trees as a tool for intelligent data analysis in domestic travel research. It demonstrates the readability and interpretability the findings from fuzzy decision tree analysis can pertain, first presented in a small problem allowing the fullest opportunity for the analysis to be followed. The investigation of the traffic fatalities in the states of the US offers an example of a more comprehensive fuzzy decision tree analysis. The graphical representations of the fuzzy based membership functions show how the necessary linguistic terms are defined. The final fuzzy decision trees, both tutorial and US traffic fatalities based, show the structured form the analysis offers, as well as more readable decision rules contained therein.

Fuzzy Decision Trees

2011 ◽  
pp. 382-390
Author(s):  
Malcolm J. Beynon
Keyword(s):  
Decision Tree ◽  
Decision Trees ◽  
Binary Tree ◽  
Fuzzy Decision ◽  
Data Set ◽  
Fuzzy Environment ◽  
Id3 Algorithm ◽  
Backtrack Algorithm ◽  
The 1960S ◽  
Fuzzy Decision Trees

The first (crisp) decision tree techniques were introduced in the 1960s (Hunt, Marin, & Stone, 1966), their appeal to decision makers is due in no part to their comprehensibility in classifying objects based on their attribute values (Janikow, 1998). With early techniques such as the ID3 algorithm (Quinlan, 1979), the general approach involves the repetitive partitioning of the objects in a data set through the augmentation of attributes down a tree structure from the root node, until each subset of objects is associated with the same decision class or no attribute is available for further decomposition, ending in a number of leaf nodes. This article considers the notion of decision trees in a fuzzy environment (Zadeh, 1965). The first fuzzy decision tree (FDT) reference is attributed to Chang and Pavlidis (1977), which defined a binary tree using a branch-bound-backtrack algorithm, but limited instruction on FDT construction. Later developments included fuzzy versions of crisp decision techniques, such as fuzzy ID3, and so forth (see Ichihashi, Shirai, Nagasaka, & Miyoshi, 1996; Pal & Chakraborty, 2001) and other versions (Olaru & Wehenkel, 2003).

Dynamic programming based fuzzy partition in fuzzy decision tree induction

2020 ◽  
Vol 39 (5) ◽  
pp. 6757-6772
Author(s):  
Yashuang Mu ◽  
Lidong Wang ◽  
Xiaodong Liu
Keyword(s):  
Dynamic Programming ◽  
Decision Tree ◽  
Decision Trees ◽  
Dynamic Programming Algorithm ◽  
Fuzzy Decision ◽  
Fuzzy Decision Tree ◽  
Fuzzy Partition ◽  
Decision Tree Induction ◽  
Fuzzy Partitions ◽  
Fuzzy Decision Trees

Fuzzy decision trees are one of the most popular extensions of decision trees for symbolic knowledge acquisition by fuzzy representation. Among the majority of fuzzy decision trees learning methods, the number of fuzzy partitions is given in advance, that is, there are the same amount of fuzzy items utilized in each condition attribute. In this study, a dynamic programming-based partition criterion for fuzzy items is designed in the framework of fuzzy decision tree induction. The proposed criterion applies an improved dynamic programming algorithm used in scheduling problems to establish an optimal number of fuzzy items for each condition attribute. Then, based on these fuzzy partitions, a fuzzy decision tree is constructed in a top-down recursive way. A comparative analysis using several traditional decision trees verify the feasibility of the proposed dynamic programming based fuzzy partition criterion. Furthermore, under the same framework of fuzzy decision trees, the proposed fuzzy partition solution can obtain a higher classification accuracy than some cases with the same amount of fuzzy items.

scholarly journals IIVFDT: IGNORANCE FUNCTIONS BASED INTERVAL-VALUED FUZZY DECISION TREE WITH GENETIC TUNING

2012 ◽  
Vol 20 (supp02) ◽  
pp. 1-30 ◽  
Author(s):  
J. SANZ ◽  
H. BUSTINCE ◽  
A. FERNÁNDEZ ◽  
F. HERRERA
Keyword(s):  
Decision Tree ◽  
Fuzzy Sets ◽  
Decision Trees ◽  
Lateral Position ◽  
Superior Performance ◽  
Fuzzy Decision ◽  
Fuzzy Decision Tree ◽  
Genetic Tuning ◽  
Fuzzy Decision Trees ◽  
Interval Valued

The choice of membership functions plays an essential role in the success of fuzzy systems. This is a complex problem due to the possible lack of knowledge when assigning punctual values as membership degrees. To face this handicap, we propose a methodology called Ignorance functions based Interval-Valued Fuzzy Decision Tree with genetic tuning, IIVFDT for short, which allows to improve the performance of fuzzy decision trees by taking into account the ignorance degree. This ignorance degree is the result of a weak ignorance function applied to the punctual value set as membership degree. Our IIVFDT proposal is composed of four steps: (1) the base fuzzy decision tree is generated using the fuzzy ID3 algorithm; (2) the linguistic labels are modeled with Interval-Valued Fuzzy Sets. To do so, a new parametrized construction method of Interval-Valued Fuzzy Sets is defined, whose length represents such ignorance degree; (3) the fuzzy reasoning method is extended to work with this representation of the linguistic terms; (4) an evolutionary tuning step is applied for computing the optimal ignorance degree for each Interval-Valued Fuzzy Set. The experimental study shows that the IIVFDT method allows the results provided by the initial fuzzy ID3 with and without Interval-Valued Fuzzy Sets to be outperformed. The suitability of the proposed methodology is shown with respect to both several state-of-the-art fuzzy decision trees and C4.5. Furthermore, we analyze the quality of our approach versus two methods that learn the fuzzy decision tree using genetic algorithms. Finally, we show that a superior performance can be achieved by means of the positive synergy obtained when applying the well known genetic tuning of the lateral position after the application of the IIVFDT method.

Fuzzy Decision Rule Construction Using Fuzzy Decision Trees

2010 ◽  
pp. 104-124
Author(s):  
Malcolm J. Beynon ◽  
Paul Jones
Keyword(s):  
Decision Trees ◽  
Decision Rules ◽  
Activity Levels ◽  
Fuzzy Decision ◽  
Data Set ◽  
Online Activity ◽  
Fuzzy Environment ◽  
E Learning ◽  
Fuzzy Decision Trees ◽  
University Course

This chapter considers the soft computing approach called fuzzy decision trees (FDT), a form of classification analysis. The consideration of decision tree analysis in a fuzzy environment brings further interpretability and readability to the constructed ‘if .. then ..’ decision rules. Two sets of FDT analyses are presented, the first on a small example data set, offering a tutorial on the rudiments of one FDT technique. The second FDT analysis considers the investigation of an e-learning database, and the elucidation of the relationship between weekly online activity of students and their final mark on a university course module. Emphasis throughout the chapter is on the visualization of results, including the fuzzification of weekly online activity levels of students and overall performance.

The Exposition of Fuzzy Decision Trees and Their Application in Biology

2011 ◽  
pp. 375-394
Author(s):  
Malcolm J. Beynon ◽  
Kirsty Park
Keyword(s):  
Decision Trees ◽  
Decision Rules ◽  
Linguistic Variables ◽  
Membership Functions ◽  
Fuzzy Decision ◽  
Decision Tree Classification ◽  
Fuzzy Environment ◽  
Technical Details ◽  
Fuzzy Decision Trees ◽  
Visual Results

This chapter employs the fuzzy decision tree classification technique in a series of biological based application problems. With its employment in a fuzzy environment, the results, in the form of fuzzy ‘if .. then ..’ decision rules, bring with them readability and subsequent interpretability. The two contrasting applications considered concern, the age of abalones and the lengths of torpor bouts of hibernating Greater Horseshoe bats. Emphasis is on the visual results presented, including the series of membership functions used to construct the linguistic variables representing the considered attributes and the final fuzzy decision trees constructed. Technical details presented further offer the opportunity to readers to future employ the technique in other biological applications.

An Improved Second Order Training Algorithm for Improving the Accuracy of Fuzzy Decision Trees

2016 ◽  
Vol 5 (4) ◽  
pp. 96-120 ◽  
Author(s):  
Swathi Jamjala Narayanan ◽  
Rajen B. Bhatt ◽  
Ilango Paramasivam
Keyword(s):  
Decision Tree ◽  
Second Order ◽  
Fuzzy Decision ◽  
Fuzzy Decision Tree ◽  
Neuro Fuzzy ◽  
Selection Threshold ◽  
Induction Process ◽  
Fuzzy Partitions ◽  
Fuzzy Decision Trees ◽  
Interpretable Classification

Fuzzy decision tree (FDT) is a powerful top-down, hierarchical search methodology to extract human interpretable classification rules. The performance of FDT depends on initial fuzzy partitions and other parameters like alpha-cut and leaf selection threshold. These parameters are decided either heuristically or by trial-and-error. For given set of parameters, FDT is constructed using any standard induction algorithms like Fuzzy ID3. Due to the greedy nature of induction process, there is a chance of FDT resulting in poor classification accuracy. To further improve the accuracy of FDT, in this paper, the authors propose the strategy called Improved Second Order- Neuro- Fuzzy Decision Tree (ISO-N-FDT). ISO-N-FDT tunes parameters of FDT from leaf node to roof node starting from left side of tree to its right and attains better improvement in accuracy with less number of iterations exhibiting fast convergence and powerful search ability.

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