Constructing Fuzzy Type-I Decision Tree Using Fuzzy Type-II Ambiguity Measure from Fuzzy Type-II Datasets

A computational intelligence technique for the effective diagnosis of diabetic patients using principal component analysis (PCA) and modified fuzzy SLIQ decision tree approach

Medical errors are considered as the leading cause of death and injury. Breast cancer becomes one of the leading causes of death among women, not only in the Philippines but worldwide. In this paper, data mining was used to predict the stage of breast cancer using a hybrid of fuzzy logic and decision tree. This aims to help experts to make decisions rather than replacing them. The result will only give an expert a recommendation, but the final decision is still on the hands of the experts. Feature selection was used to determine the best attribute in the dataset from Surveillance Epidemiology and End Results (SEER). The data set consists of incidence from 1975 to 2016, but the study limits the analysis from 2010 to 2016. Different cleaning and preprocessing of data are conducted. After thorough preprocessing of data, six (6) attributes are selected, and one (1) target class. Performance comparison shows that the fuzzy decision tree achieved a higher accuracy of 99.96%, sensitivity of 99.26% and specificity of 99.98% than the decision tree classification technique. The simulation result shows a correctly classified instance of 165,124, which is equivalent to 99.97% and only 351 incorrect classified instances or 0.21%. Thus, a fuzzy decision tree is more robust than the traditional decision tree classifier for predicting the stage of breast cancer.

This paper introduces a novel Fuzzy Numeric Inference Strategy (FNIS) which induces fuzzy trees that can be applied to data domains where the outcome can be either numeric or discrete. The methodology applies the principles of fuzzy theory to pre-generated crisp decision trees in order to soften th e sharp decision boundaries that are inherent in such induction techniques. Introducing fuzziness around a tree node allows classification knowledge to be represented more naturally and in-line with human thinking thus creating more robust trees when handling imprecise or conflicting information. The FNIS methodology first extrapolates rules from crisp decision trees. Each attribute is then fuzzified using a Genetic Algorithm (GA) to determine the size of the fuzzy partitions around each tree node automatically. A fuzzy decision tree is then created using a one-to-one mapping and a genetically optimised pre-selected fuzzy inference technique is used to combine all information throughout the tree. FNIS uses two strategies for defuzzification, depending on the type of the outcome variable. For discrete values the traditional centre of gravity approach is adopted, whilst for predicting numeric outcomes a novel method of defuzzification is proposed. CHAID is a successfully proven algorithm for inducing decision trees which can solve both classification and regression problems. It is used to illustrate the creation of fuzzy trees through the proposed strategy. A series of experiments is carried out to compare the performance of crisp trees with FNIS induced fuzzy trees, using real world datasets. The results are shown to compare favourably with other fuzzy and crisp decision tree algorithms. The fuzzy trees are also shown to be more robust leading to improved classification/prediction over crisp trees.

Explainable Artificial Intelligence (XAI) is expected to play a key role in the design phase of next generation cellular networks. As 5G is being implemented and 6G is just in the conceptualization stage, it is increasingly clear that AI will be essential to manage the ever-growing complexity of the network. However, AI models will not only be required to deliver high levels of performance, but also high levels of explainability. In this paper we show how fuzzy models may be well suited to address this challenge. We compare fuzzy and classical decision tree models with a Random Forest (RF) classifier on a Quality of Experience classification dataset. The comparison suggests that, in our setting, fuzzy decision trees are easier to interpret and perform comparably or even better than classical ones in identifying stall events in a video streaming application. The accuracy drop with respect to RF classifier, which is considered to be a black-box ensemble model, is counterbalanced by a significant gain in terms of explainability.

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.

The fuzzy ID3 is tailored for inducing fuzzy decision trees from the fuzzy decision tables with fuzzy condition attributes and fuzzy decision attribute. In fuzzy ID3, average fuzzy classification entropy is used as heuristic for selecting the expanded attributes, while fuzzy confidence degree is used as termination conditions of leaf nodes. When fuzzy ID3 is applied to induce fuzzy decision tree from fuzzy decision tables with continuous-valued conditional attributes and fuzzy-valued decision attribute, it is necessary for fuzzy ID3 to fuzzify the continuous-valued conditional attributes, but it is difficult to determine the fuzzy membership degree. In this paper, an induction method of fuzzy decision trees named TRFDT is proposed, TRFDT can directly induce fuzzy decision tree from fuzzy decision tables with continuous-valued conditional attributes and fuzzy-valued decision attribute. Tolerance rough fuzzy dependence is employed to select expanded attributes, Kosko fuzzy entropy is used as termination condition of leaf nodes. An example is presented to illustrate the induction process of fuzzy decision tree.

The objective of the classification is to assign a class label to a data sample based on previous, learned experience. Despite the long tradition of classification algorithms research, there is not a unique technique that yields the best classification performance in all scenarios. Many real-world problems are uncertain. In this case, the crisp classification can be difficult to perform. The usage of fuzzy logic can be useful to describe real-world problems with higher accuracy. In this paper, we describe and compare algorithms of Fuzzy Decision Trees (FDTs), which are an extension of traditional decision trees. These algorithms are popular for their easy understandability and interpretability. But today there are many algorithms for FDT induction. These algorithms differ in many aspects. The most common difference is in information measures for selecting splitting attributes. Generally, the goal of decision tree induction is to create the smallest tree which is the most accurate as possible. In this paper, we use various information measures to induct FDTs and compare the accuracy and size of obtained FDTs. In comparison, information measures that are based on a generalization of the Shannon entropy and cumulative mutual information are included. The comparison shows that FDTs based on the cumulative mutual information acquired the best results. These results will also be included in a course on data mining that is taught at Faculty of Management Science and Informatics of University of Zilina.

Decision bees have been widely and successfully used in machine learning. However, they have suffered from overfitting in noisy domains. This problem has been remedied, in C4.5 for example, by tree pruning, resulting in improved performance. More recently, fuzzy representations have been combined with decision trees. How does the performance of fuzzy decision trees compare to that of pruned decision trees? The authors propose a comparative study of pruned decision trees and fuzzy decision trees. Further, for continuous inputs, they explore different ways: (1) for selecting the granularity of the fuzzy input variables; and (2) for defining the membership functions of the fuzzy input values. We carry out an empirical study using 12 data sets. The results show that a fuzzy decision tree constructed using FID3, combined with fuzzy clustering (to build membership functions) and cluster validity (to decide on granularity), is superior to pruned decision trees.

This paper proposes an integrated approach utilizing Fuzzy Logic and Decision Tree algorithms to diagnose early-stage faults in power transformers based on Dissolved Gas Analysis (DGA) test results of transformer insulation oil. Overcoming limitations in conventional methods such as Duval Triangle, Key Gas Analysis, Rogers Ratio, IEC Ratio, and Doernenburg Ratio, our Fuzzy Logic and Decision Tree models address issues like inaccurate diagnosis, inconsistent diagnosis, lack of decisions or out-of-code results, and time-intensive manual calculations for large DGA datasets. The Decision Tree algorithm, a machine learning technique is applied to categorize faults into thermal and electrical types. Trained with over 300 DGA samples from transformers with known faults, the models exhibit robust performance during testing with different datasets. Notably, the Duval Triangle decision tree model attains the highest accuracy among the ten developed models, achieving a 98% accuracy rate when tested with 50 samples with known faults. Moreover, Decision Tree models for KGA, Doernenburg, Rogers, and IEC also demonstrate substantial prediction accuracy at 92%, 86%, 92%, and 90% respectively underscoring the efficacy of artificial intelligence methods over traditional approaches.

Automatic image annotation based on traditional association rules exists the problem of "sharp boundary", which makes classification more fuzzy and inaccurate. Moreover, with the development of multimedia technology, the storage of image information is expanded quickly, massive image data will produce many redundant association rules, which will greatly decrease the accuracy and efficiency of image classification. In order to solve these two problems, this paper proposed an automatic image annotation model based on fuzzy association rules and decision tree. This approach firstly obtains association rules which represent the correlations between image features and high-level semantic concepts of training images. Then, the decision tree is added to reduce the unnecessary rules. As a result, algorithm complexity and time cost are reduced to a large degree. Experiments are based on two datasets Corel5k and IAPR-TC12. Experiments show the proposed method performs well in comparison with other automatic annotation method.

Because of the inability to take a multi-pass scanning algorithm for random access to fast data streams and traditional data mining algorithms can’t sample all samples of the data stream, research of data stream mining algorithm based on fuzzy decision tree theory that fuzzy decision tree combines the understandability of decision tree and the ability of representation of fuzzy set to deal with the fuzziness and uncertainty information is very valuable to improve the accuracy of data mining. This paper presents a fuzzy decision tree data mining strategy based on hybrid partitioning standard for the problem that the method has a low accuracy when we deal with low-membership samples with missing values by dividing the samples into leaf nodes according to their membership. The multivariate branch fuzzy decision tree data stream mining strategy based on hybrid partitioning standard(MHFlexDT) is used to construct the multivariate branch fuzzy tree structure. The data fitting problem is solved by adding temporary branches to the uncertain data. At the same time, the decision tree depth is effectively limited by using the McDiarmid bound threshold. The experimental results show that MHFlexDT strategy compared with fuzzy decision tree data mining strategy is more effective in large-scale data stream mining to reduce system computation, control decision tree depth, and ensure a high accuracy when we deal with missing values, data over-fitting and noisy data problems.

The construction of decision trees is an efficient tool for inductive learning, and fuzzy decision trees are particularly interesting because they enable the user to take into account imprecise descriptions of the cases, or heterogeneous values (symbolic, numerical, or fuzzy). However, since the method to construct a fuzzy decision tree is not unique, in this paper, a comparative study is presented to point out differences between three methods. This study focus on differences between methods when ranking attributes during the construction of a fuzzy decision tree. The aim is to enable the reader to understand what kind of fuzzy decision tree is obtained by each method.

Decision trees are a popular form of classification models. It is well known that classical trees lack the ability of modelling vagueness. By connecting fuzzy systems and classical decision trees, we try to achieve classifiers that can model vagueness and are comprehensible. We discuss the core problem of how to compute the information measure used in the induction of fuzzy trees and propose some improvements. In addition, we consider fuzzy rule bases derived from fuzzy decision trees and present some heuristic strategies to prune them. We report the results of experiments in which we compare our approach to other well-known classification methods.

A hybrid model combining case-based reasoning and fuzzy decision tree for medical data classification

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.