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).

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-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.

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.

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.

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

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.

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.

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 Application of Fuzzy Decision Tree Algorithm Based on Mobile Computing in Sports Fitness Member Management

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Zhu Gu ◽  
Chaohu He
Keyword(s):  
Decision Tree ◽  
Mobile Computing ◽  
Classification Accuracy ◽  
Decision Tree Algorithm ◽  
Fuzzy Decision ◽  
Fuzzy Decision Tree ◽  
Data Set ◽  
Tree Algorithm ◽  
Id3 Algorithm ◽  
Fitness Industry

After the reform and the opening, the economy of our country has developed rapidly, and the living conditions of the people have become better and better. As a result, they have a lot of time to pay attention to their health, which has promoted the rapid development of the sports and fitness industry in my country. In response to the increasing development of the sports and fitness sector of my country, the current state of the administration of members of the sports fitness industry does not keep pace with the development of the sports and fitness industry of my country. Based on this, this article uses a fuzzy decision tree algorithm to establish a decision tree based on the characteristics of customer data and loses existing customers. Analyzing the situation is of strategic significance for improving the competitiveness of the club. This article selects the 7 most commonly used data sets from the UCI data set as the initial experimental data for model training in three different formats and then uses the data of a specific club member to conduct experiments, using these data files as training samples to construct a vague analysis of the decision tree to overturn the customer to analyze the main factors of customer change. Experiments show that the fuzzy decision tree ID3 algorithm based on mobile computing has the highest accuracy in the Iris data set, reaching 97.8%, and the accuracy rate in the Wine data set is the smallest, only 65.2%. The mobile computing-based fuzzy decision tree ID3 algorithm proposed in this paper obtained the highest correct rate (86.32%). This shows that, compared to traditional analysis methods, the blurred decision tree obtained for churn client analysis has the advantages of high classification accuracy and is understandable so that ideal classification accuracy can be achieved when the tree is small.

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