Effectively classifying anomalies in a multi-class setting holds significant importance in domains such as medical datasets, fraud detection, and anomaly detection. This task presents challenges that include efficient training on large datasets, accurate classification in imbalanced scenarios, and sensitivity to high imbalance ratios (IR). This paper introduces a novel approach, the Intuitionistic Fuzzy Twin Support Vector Machine-based Decision Tree (NDT-IFTSVM), aimed at addressing these issues. NDT-IFTSVM integrates IFTSVM and decision tree methodologies, offering an efficient solution for multi-class classification. The proposed algorithm constructs a decision tree comprised of a series of two-class IFTSVMs. To enhance balance and separability, the multi-class method iteratively divides into two sets based on distance between class centres and instance distribution. This recursive process continues until each subset exclusively contains a single class, facilitating effective classification. To handle highly imbalanced datasets, NDT-IFTSVM incorporates a rational weighting strategy. Additionally, we refine NDT-IFTSVM by introducing a regularization term that maximizes the margin between the bounding and proximal hyperplanes, mitigating the impact of noise and outliers. Finally, a coordinate descent system with shrinking by an active set is applied to reduce the computational complexity. Numerical evaluations employ the bootstrap technique with a 95% confidence interval and statistical tests to quantify the significance of performance improvements. Experimental results on 12 datasets demonstrate the efficacy of the proposed method, showcasing promising outcomes compared to other techniques documented in the literature.

The intuitionistic fuzzy twin support vector machine (IFTSVM) merges the idea of the intuitionistic fuzzy set (IFS) with the twin support vector machine (TSVM), which can reduce the negative impact of noise and outliers. However, this technique is not suitable for multi-class and high-dimensional feature space problems. Furthermore, the computational complexity of IFTSVM is high because it uses the membership and non-membership functions to build a score function. We propose a new version of IFTSVM by using relative density information. This idea approximates the probability density distribution in multi-dimensional continuous space by computing the K-nearest-neighbor distance of each training sample. Then, we evaluate all the training points by a one-versus-one-versus-rest strategy to construct the k-class classification hyperplanes. A coordinate descent system is utilized to reduce the computational complexity of the training. The bootstrap technique with a 95 % confidence interval and Friedman test are conducted to quantify the significance of the performance improvements observed in numerical evaluations. Experiments on 24 benchmark datasets demonstrate the proposed method produces promising results as compared with other support vector machine models reported in the literature.

Fuzzy twin support vector machine (FTSVM) is an effective machine learning technique that is able to overcome the negative impact of noise and outliers in tackling data classification problems. In the FTSVM, the degree of membership function in the sample space describes the space between input data and class center, while ignoring the position of input data in the feature space and simply miscalculated the ledge support vectors as noises. This paper presents an intuitionistic FTSVM (IFTSVM) that combines the idea of intuitionistic fuzzy number with twin support vector machine (TSVM). An adequate fuzzy membership is employed to reduce the noise created by the pollutant inputs. Two functions, i.e., linear and nonlinear, are used to formulate two nonparallel hyperplanes. An IFTSVM not only reduces the influence of noises, it also distinguishes the noises from the support vectors. Further, this modification can minimize a newly formulated structural risk and improve the classification accuracy. Two artificial and eleven benchmark problems are employed to evaluate the effectiveness of the proposed IFTSVM model. To quantify the results statistically, the bootstrap technique with the 95% confidence intervals is used. The outcome shows that an IFTSVM is able to produce promising results as compared with those from the original support vector machine, fuzzy support vector machine, FTSVM, and other models reported in the literature.

This paper introduces a new type-2 intuitionistic exponential triangular fuzzy number. Basic generalized exponential triangular intuitionistic fuzzy numbers are formulated by (α,β)-cuts. Some of properties and theorems of this type of fuzzy number with graphical representations have been studied and some examples are given to show the effectiveness of the proposed method. Also, the ranking function of the generalized exponential triangular intuitionistic fuzzy number is computed. This ranking method is based on the centroid concept and Euclidean distance. Based on the ranking method, we develop an approach to solving an intuitionistic fuzzy assignment problem where cost is not deterministic numbers but imprecise ones. Then, we solve an intuitionistic fuzzy transportation problem where transportation cost, source, and demand were generalized type-2 intuitionistic fuzzy numbers by the ranking method for Euclidean distance. Intuitionistic fuzzy set theory has been used for analyzing the fuzzy system reliability. We have taken the intuitionistic fuzzy failure to start of an automobile as known basic fault events such as Ignition failure, Battery internal shortage, Spark plug failure and fuel pump failure using Type-2 Intuitionistic Exponential Triangular Fuzzy Number. Our computational procedure is very simple to implement for calculations in intuitionistic fuzzy failure. The major advantage of using Intuitionistic fuzzy sets over fuzzy sets is that intuitionistic fuzzy sets separate the positive and the negative evidence for the membership of an element in a set. Furthermore, the proposed technique can be suitably utilized to solve the start of an automobile problem, because the result of system failure in this method is significant. Finally, the proposed method has been compared with other existing method through numerical examples.