Feature Selection Based on Variable Precision Fuzzy Discriminant Index

Fuzzy Random Forest: Integrating Fuzzy Set Theory for Enhanced Imbalanced Classification

Standard Random Forest algorithms assume crisp class boundaries and precise feature values, limitations that become critical when dealing with ambiguous or overlapping data patterns common in imbalanced datasets. This paper presents Fuzzy Random Forest (FRF), a novel ensemble method that integrates fuzzy set theory into the tree construction process. Unlike existing methods that rely on crisp partitions, FRF extends the classical Gini impurity and Shannon entropy to fuzzy-valued impurity measures. Rather than counting instances as belonging entirely to one class, FRF weights each instance’s contribution to a node by its fuzzy membership degree, so that the resulting fuzzy class probabilities, and the fuzzy impurity and information-gain measures built from them, capture the ambiguity of borderline cases instead of forcing a crisp assignment. We provide complete mathematical derivations, including proofs of boundedness, crisp reduction, and membership conservation properties. Empirical evaluation on eight imbalanced datasets demonstrates that FRF consistently outperforms standard Random Forest, with particularly notable performance on datasets with high uncertainty and ambiguous class boundaries. On a credit risk dataset (80% non-default, 20% default), FRF achieves exceptional precision (0.99) for minority class predictions while maintaining 89.00% overall accuracy. Statistical validation using McNemar’s Test confirms FRF’s superiority over standard Random Forest, with a chi-square statistic of 100.0 (p less than 0.0001), a 20.6% improvement in information gain, and a 42.9% reduction in entropy reduction variance. FRF is particularly suited for applications requiring high precision in minority class identification and interpretable fuzzy decision rules, such as medical diagnosis, fraud detection, and credit risk assessment where regulatory compliance demands transparent decision-making.

Ordinal Selection Fuzzy Rough Sets: A Dominance Relation-Driven Feature-Instance Bidirectional Selection Method

Ordinal classification involves predicting labels with a natural ordering, yet the presence of feature redundancy and noisy instances can distort the ordinal relationships that fuzzy rough set models rely on. Most existing approaches tackle feature selection in isolation, overlooking how these two factors interact to degrade both the quality of selected features and the integrity of retained instances. This work introduces Ordinal Selection Fuzzy Rough Sets (OSFRS), a framework that couples feature and instance selection through dominance relations rather than treating them as separate stages. The method begins by constructing a normalized dominance-based fuzzy lower approximation to quantify feature importance, alongside an ordinal discriminability index that explicitly encodes the ordering among decision classes. Rather than evaluating all instances uniformly, the method suppresses noisy samples by measuring differences in order fuzziness -- instances near decision boundaries are retained while those far from boundaries or exhibiting high ambiguity are deprioritized. A dual-criterion selection strategy then jointly optimizes ordinal discriminability and ranked feature importance, yielding a compact feature subset and a refined instance set in a single pass. Evaluation on nine UCI ordinal datasets shows that OSFRS achieves comparable classification consistency without statistically significant loss, while achieving higher reduction rates than competing methods, with no selection failures across any dataset.

An integrated multi criteria decision making framework for hyperbolic fuzzy sets based on a robust logarithmic score function for enhanced healthcare decision support

An Enhanced Adaptive Fuzzy Membership Function for Intuitionistic Fuzzy Sets

The Enhanced Adaptive Fuzzy Membership Function proposed in this article provides a new approach to determine the membership/non-membership levels in an uncertainty interval, which consist of lower bound and upper bound. Proposed for addressing the intuitionistic fuzzy systems, the EAFMF essentially accommodates membership, non-membership as well as hesitancy measures and thus expresses a broader spectrum of uncertainty. Symmetrical architecture is well capable to represent skewness, nonlinearity and expanded fuzzification regions as compared with rectangle type membership functions. The centroid method applied in our model gives a more stable and representative solution for the crisp outputs computed from the uncertainty interval LB-UB. The proposed approach is well suited to the needs of such applications as medical diagnosis, preventive maintenance, and support for decision making where an accurate reading and interpretation of indecisive information plays a crucial role.

Uncertainty-Aware Feature Selection Framework Based on Three-Way Decision Theory for Explainable Machine Learning

Feature selection is a critical stage in machine learning because it improves predictive performance, reduces computational complexity, and enhances model interpretability. However, many existing feature selection methods rely on binary selection strategies that either retain or discard features based on fixed relevance thresholds. This approach can be inadequate when features contain uncertainty, instability, redundancy, or borderline predictive value. To address this limitation, this article proposes an uncertainty-aware feature selection framework based on three-way decision theory for explainable machine learning. The proposed framework classifies features into three decision regions: accepted features, rejected features, and deferred features. Accepted features are considered highly relevant and reliable, rejected features are removed due to low relevance or high redundancy, while deferred features are subjected to further evaluation because of uncertain or inconsistent importance. By integrating uncertainty measurement with feature relevance scoring, the framework provides a more flexible and transparent alternative to conventional two-way feature selection. The framework also supports explainability by providing clear justification for why each feature is selected, rejected, or deferred. This makes it particularly useful for high-dimensional and high-stakes machine learning applications where model transparency, reliability, and decision accountability are important. The proposed approach is expected to improve feature selection stability, reduce uncertainty in selected feature subsets, and enhance the interpretability of machine learning models.

A granular-ball intuitionistic fuzzy twin support vector machine with RVFL-based feature enhancement for imbalance learning