Fuzzy decision tree for breast cancer prediction

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

One of the most tools of data mining techniques is decision trees for both learning and reasoning from the crisp dataset. In a case of fuzzy dataset, the fuzzy decision tree must be established to extracted fuzzy rules. The paper illustrates an approach to establish fuzzy type-I decision tree from fuzzy type-II dataset using the ambiguity measure in fuzzy type-II form.

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.

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.

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.

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.

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.

Purpose: The TARGIT-A trial of kilovoltage intraoperative radiation therapy (IORT) versus external beam radiation therapy (EBRT) demonstrated a significant reduction in non-breast cancer mortality (nBCM) in women that received IORT, largely attributed to an increase in cardiac mortality in patients that received EBRT. Further, If EBRT does result in excess nBCM due to cardiac or other causes, then treatment with lumpectomy (Lump) alone or mastectomy (Mast) alone should result in lower rates of nBCM rates compared to Lump+EBRT. Our primary objective was to determine whether Lump+EBRT results in increased nBCM compared to Lump+IORT in women with early-stage breast cancer (BC) with a hypothesis that the two approaches should result in equivalent nBCM. We also tested the hypotheses that Lump+EBRT should have the same rates of nBCM as Lump alone or Mast alone. Materials/Methods: We used the Surveillance Epidemiology and End Results (SEER) database to identify women with early-stage BC treated with Lump alone, Lump+EBRT, Lump+IORT, or Mast alone from 2000-2016. SEER does not distinguish between kilovoltage IORT and electron IORT. We included patients with characteristics similar to the TARGIT-A study: age≥45 years; ductal carcinoma in situ (DCIS) or T1; lymph-node negative. We excluded patients that: received chemotherapy; received postmastectomy radiation therapy; had unknown cause of death; and had ≤1 month of follow-up. The primary endpoint was nBCM which is captured in the SEER database (patients were censored if they were alive or dead due to cancer at last follow-up). Cox-proportional hazards multivariate regression models were used to compare nBCM between Lump+EBRT and Lump+IORT adjusting for confounders that were statistically significant on univariate analysis. We secondarily compared nBCM in the Lump+EBRT vs. Lump population and Lump+EBRT vs. Mast population. Results: We identified 219,470 women that met the inclusion criteria: 121,776 Lump+EBRT; 1,735 Lump+IORT; 41,900 Lump; 54,059 Mast. Median follow-up time was 61 months for the entire cohort (IQR, 30-99 months) but was shorter for Lump+IORT patients (29 months) compared to the other groups (63 months Lump+EBRT; 62 months Mast; 57 months Lump). There were a total of 16,640 nBCM events: 6,210 Lump+EBRT; 5,708 Lump; 4,704 Mast; 18 Lump+IORT. The 5-year cumulative incidence of nBCM was 3.1% for Lump+EBRT vs. 1.6% for Lump+IORT (p=0.034). After adjustment for potential confounders (age, tumor location, marital status, race/ethnicity, DCIS vs. invasive, tumor grade, hormone receptor status, and receipt of axillary surgery), patients treated with Lump+IORT had a 38% relative reduction in the risk of nBCM compared to those treated with Lump+EBRT (HR=0.62, 95% CI 0.39-0.99, p=0.045). Other factors associated with increased nBCM included older age, divorced/single/widowed status (vs. married), Black race, high tumor grade, receipt of axillary lymph node dissection (vs. sentinel lymph node biopsy), no axillary surgery (vs. sentinel node biopsy), and ER-/PR- disease (vs. ER+ or PR+). In contrast, patients treated with Lulmp+EBRT had lower nBCM compared to those that received Lump alone (adjusted HR=0.55, 95% CI 0.53-0.57, p<0.0001) and compared to those that received Mast alone (adjusted HR=0.59, 95% CI 0.56-0.61, p<0.0001). Conclusion: In summary, contrary to our hypothesis, we found that Lump+IORT was associated with lower nBCM compared to Lump+EBRT possibly reflecting underlying selection bias. However, Lump+EBRT was not associated with an increased nBCM relative to patients treated with Lump alone or Mast alone. This suggests that the underlying mechanism for the reduced nBCM seen in patients treated with IORT in the TARGIT-A trial and this SEER analysis is not due to the potentially harmful effects of EBRT. Citation Format: Jose G Bazan, Jay Fisher, Sachin Jhawar, Erin Healy, Sasha Beyer, Julia R. White. Impact of intraoperative radiation therapy and external beam radiation therapy on non-breast cancer mortality in early-stage breast cancer [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P3-19-09.

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.

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.

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

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.

Adjuvant Chemotherapy Administration and Survival Outcomes in Lymphoma Survivors with Common Solid Tumors: A Population-Based Study

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.

Background: More than half of cancer patients will receive radiotherapy during the treatment of their cancer; however, a rare and fatal treatment complication is radiation induced sarcoma (RIS). Notably, a large percentage of RIS patients are breast cancer survivors. Previous studies have investigated the incidence of all secondary cancers due to radiotherapy but have not noted the incidence of RIS in a contemporary population-based cohort in the US. To evaluate the relative risk of RIS, we examined data from the Surveillance, Epidemiology, and End Results (SEER) database. We hypothesized that breast cancer would have a higher incidence of RIS compared to 17 other primary cancer sites. Methods: This was a retrospective cohort study that examined SEER registries from 1973 and 2013. We included patients aged 18 years or older who were diagnosed with a primary cancer. We excluded patients with missing information on initial radiotherapy treatment or stage and those who died less than two years from the date of their primary cancer diagnosis. RIS was defined as those who developed a secondary sarcoma near the site of their original malignancy and after a 24-month latency period. Results: Our study included 1,745,867 patients with an average age of 60 years and mean follow up time of 9.2 years. Breast cancer comprised the largest number with 693,701 patients of which 161 (0.02%) had a secondary sarcoma. Prostate cancer comprised the second largest group with 594,271 patients of which 75 (0.01%) had a secondary sarcoma. Of the 359 patients with secondary sarcomas, 242 (67.4%) had RIS. Breast cancer had the highest number of RIS patients at 126 (52.1%) compared to all combined non-breast cancer sites at 116. Interestingly, 172 (71.1%) RIS patients were females, which correlated with the attributable RIS cases from breast and uterine cancer. The relative risk of RIS in breast cancer versus 17 other primary cancer sites was 1.21 (CI: 1.01-1.45, p <0.03, adjusted for age at primary diagnosis, gender, and latency). Conclusions: This study confirms the low incidence of RIS in breast cancer, which has been demonstrated to be around 0.03% - 0.2% in the literature. Our results suggest that breast cancer portends a somewhat higher risk for RIS compared to 17 primary solid malignancies. Although some of the risk is attributable to the high incidence rate of breast cancer, breast cancer patients had a higher relative risk of RIS than other solid tumors after adjusting for covariates. Female gender may be associated with an increased risk for RIS compared to males. Further investigations should be performed to confirm these epidemiological findings given that radiation fields, doses, intention to cure, margin status and systemic therapy are not recorded in SEER. Nonetheless, this study is hypothesis generating in that the majority of RIS cases in solid tumors are attributable to breast cancer in this large population-based series. Citation Format: Snow AE, Struycken LC, Koc M, Greco JP, Zhu Y, In GK, Dorff TB, Lang JE. Incidence of radiation induced sarcoma attributable to radiotherapy in adults: A population-based study of the SEER cancer registry across 17 primary tumor sites [abstract]. In: Proceedings of the 2018 San Antonio Breast Cancer Symposium; 2018 Dec 4-8; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2019;79(4 Suppl):Abstract nr P3-12-14.