New gene selection method improves tumor classification accuracy.
problem Efficiently selecting relevant genes from high-dimensional tumor gene expression data.
method Fuzzy-Rough Set Theory for feature dependency analysis.
result The proposed method outperforms state-of-the-art techniques in tumor classification.
Paper proposes a new classifier for gender detection in mobile telematics.
problem Detecting gender through mobile telematics data.
method Choquet fuzzy integral vertical bagging classifier combining random forest and rough set theory.
result Choquet fuzzy integral vertical bagging classifier outperforms other classifiers.
Fuzzy Rough Set selects key features for phishing detection.
problem Efficient feature selection for phishing detection.
method Fuzzy Rough Set (FRS) theory for feature selection.
result Maximum F-measure of 95% using Random Forest.
Feature selection and attribute reduction are crucial problems, and widely used techniques in the field of machine learning, data mining and pattern recognition to overcome the well-known phenomenon of the Curse of Dimensionality, by either selecting a subset of features or removing unrelated ones. This paper presents …
Unified framework evaluates different nearest neighbor classification methods.
problem Evaluating and comparing classical, fuzzy, and fuzzy rough nearest neighbor classification methods.
method Standardized nearest neighbor weighting with kernel functions applied to distance and/or rank values of nearest neighbors.
result NN, FNN, and FRNN perform best with Boscovich distance, and NN and FRNN perform best with specific combinations of weights and scaling measures.
Fuzzy prediction sets generalize binary predictions to include elements at varying confidence levels.
problem Binary prediction sets are limited; fuzzy prediction sets offer richer guarantees.
method Generalize prediction sets to fuzzy sets, showing they are e-values with merging properties.
result Optimal e-values lead to optimal fuzzy prediction sets, including optimal conformal prediction.
Paper defines kernels for fuzzy sets, useful in machine learning.
problem Uncertainty in data with fuzzy set membership.
method Defined cross product, intersection, non-singleton, and distance-based kernels.
result Kernels improve machine learning tasks with fuzzy data.
In this paper, we have tried to apply the concepts of fuzzy sets to Lie groups and its relative concepts. First, we define a C1 fuzzy submanifold after reviewing C1−fuzzy manifold definition. In main section, we defined the Lie group and some its relative concepts such as fuzzy transformation group,…
Unified probabilistic foundation for fuzzy simplicial sets in dimensionality reduction.
problem Lack of clear probabilistic interpretation in fuzzy simplicial sets.
method Introducing a probabilistic framework explaining fuzzy simplicial sets as marginals of probability measures on simplicial sets.
result Unified probabilistic theoretical foundation for fuzzy simplicial sets.
Enhanced fuzzy system predicts chaotic time series with improved accuracy.
problem Forecasting chaotic time series with high uncertainty.
method Combines evolving fuzzy systems, participatory learning, KRLS, and type-2 fuzzy sets.
result Proposed model outperforms other methods in accuracy and complexity.
Paper investigates differentiable fuzzy implications and their suitability for learning.
problem Analyzing differentiable fuzzy implications and their suitability for learning.
method Investigates the properties of fuzzy implications in a differentiable setting and introduces a new family of fuzzy implications.
result Various fuzzy implications are unsuitable for differentiable learning, and a new family of fuzzy implications is introduced.
A novel weighted feature selection method using fuzzy sets improves classification accuracy and stability.
problem Improving feature selection accuracy and stability in machine learning models.
method Combination of four feature selection methods using fuzzy sets and bootstrap.
result Our method achieved significantly higher stability than individual methods.
A deep convolutional fuzzy system (DCFS) on a high-dimensional input space is a multi-layer connection of many low-dimensional fuzzy systems, where the input variables to the low-dimensional fuzzy systems are selected through a moving window across the input spaces of the layers. To design the DCFS based on input-outpu…
We present a new distributed fuzzy partitioning method to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems. The proposed algorithm builds a fixed number of fuzzy sets for all variables and adjusts their shape and position to the real distribution of training data. A two-step p…
A new fuzzy clustering method using hyperbolic smoothing for large datasets.
problem Building fuzzy clusters for large data sets efficiently.
method A novel smoothing numerical approach to relax the sum-of-squares criterion, converting the problem into a differentiable optimization problem.
result The method produces better fuzzy partitions compared to traditional fuzzy C-means. In a recent paper [1] we introduced the Fuzzy Bayesian Learning (FBL) paradigm where expert opinions can be encoded in the form of fuzzy rule bases and the hyper-parameters of the fuzzy sets can be learned from data using a Bayesian approach. The present paper extends this work for selecting the most appropriate rule b…
Proposes new random models for fuzzy clustering similarity measures.
problem Challenges in choosing a random model for fuzzy clustering similarity measures.
method Introduces three intuitive and explainable random models for fuzzy clusterings.
result Each random model has distinct behavior, emphasizing the importance of accurate model selection.
In this paper we use fuzzy systems theory to convert the technical trading rules commonly used by stock practitioners into excess demand functions which are then used to drive the price dynamics. The technical trading rules are recorded in natural languages where fuzzy words and vague expressions abound. In Part I of t…
This paper solves a coinsurance problem using fuzzy numbers and expected utility operators.
problem Formulating a coinsurance problem in the possibilistic setting of expected utility operators.
method Developed a framework using expected utility operators to model risk aversion and solve the coinsurance problem.
result Various formulas for the optimal T-coinsurance rate are derived for specific utility functions and fuzzy numbers. Introduces fuzzy layers to enhance deep learning performance.
problem Improving deep learning accuracy for complex tasks.
method Incorporates fuzzy methodologies into deep learning architecture.
result Preliminary results show promising performance in semantic segmentation.
Paper simulates LR fuzzy intervals with interval-valued cores.
problem Generating random fuzzy intervals with interval-valued cores.
method Developed algorithms for simulating LR fuzzy numbers with interval-valued cores.
result Numerically efficient algorithm for simulating fuzzy values.
Study compares GFMM neural networks for pattern classification.
problem Pattern classification problems.
method Two algorithms (incremental and agglomerative learning) to train GFMM neural networks.
result GFMM neural networks show strong and weak points on benchmark datasets.
A new hybrid fuzzy-crisp clustering algorithm addresses imbalanced cluster sizes.
problem Imbalanced influence in fuzzy c-means clustering for large vs. small clusters.
method Hybrid fuzzy-crisp algorithm combining linear and quadratic membership functions, setting exact zero membership for sufficiently distant points.
result The hybrid algorithm outperforms conventional fuzzy and crisp clustering methods on imbalanced datasets.
In a context of document co-clustering, we define a new similarity measure which iteratively computes similarity while combining fuzzy sets in a three-partite graph. The fuzzy triadic similarity (FT-Sim) model can deal with uncertainty offers by the fuzzy sets. Moreover, with the development of the Web and the high ava…
A new fuzzy time series method for non-stationary data.
problem Forecasting in non-stationary environments with concept drift.
method Non-Stationary Fuzzy Time Series (NSFTS) with time-varying parameters.
result The method can adapt to dynamic changes in the stochastic process.
Improves k-NN for monotonic data with robustness against noise.
problem Class noise in real-life data violates monotonic constraints in k-NN.
method Monotonic Fuzzy k-NN (MonFkNN) with new fuzzy membership calculation.
result Significant accuracy improvements and robustness against monotonic noise.
The future value of a security is described as a random variable. Distribution of this random variable is the formal image of risk uncertainty. On the other side, any present value is defined as a value equivalent to the given future value. This equivalence relationship is a subjective. Thus follows, that present value…
Fuzzy eIX method evolves classifiers for online data streams.
problem Handling time-varying classifiers in online data streams.
method Develops evolving Internal-eXternal Fuzzy granules for numerical data.
result Fuzzy eIX maintains high accuracy in dynamic scenarios.
A novel weighted distance improves fuzzy c-means clustering accuracy.
problem Improving fuzzy c-means clustering performance with weighted distances.
method Proposed Canberra Weighted Distance to enhance FCM algorithm.
result Experimental results show superior performance of the proposed method.
Impact of chosen behavioural factors on imprecision of present value is discussed here. The formal model of behavioural present value is offered as a result of this discussion. Behavioural present value is described here by fuzzy set. These considerations were illustrated by means of extensive numerical case study. Fin…
Fuzzy clustering with similarity queries improves efficiency and accuracy.
problem Clustering uncertain or vague datasets.
method Semi-supervised active clustering framework with oracle similarity queries.
result Polynomial-time approximation algorithm for fuzzy clustering with few similarity queries.
MBGD-RDA trains TSK fuzzy systems efficiently on big datasets.
problem Training TSK fuzzy systems efficiently on big datasets.
method MBGD-RDA combines mini-batch gradient descent, regularization, AdaBound, and novel techniques for TSK fuzzy systems.
result MBGD-RDA achieves fast convergence and superior generalization on big datasets.
Paper proposes a classifier using fuzzy sets for data simplification.
problem Data simplification and handling uncertainty in real-world applications.
method Multi-resolution hierarchical granular representation (MRHGRC) using hyperbox fuzzy sets.
result High accuracy at low granularity with reduced data size.
We introduce a notion of p-rough integrator on any Banach manifolds, for any p≥1, which plays the role of weak geometric Holder p-rough paths in the usual Banach space setting. The awaited results on rough differential equations driven by such objects are proved, and a canonical representation is given if the man…
A new adaptive binarization technique using fuzzy integrals improves image quality.
problem Improving image thresholding quality.
method FLAT (Fuzzy Local Adaptive Thresholding) based on fuzzy integrals.
result The proposed FLAT method produces better image quality than traditional algorithms and neural networks.
SESSC clusters fuzzy rules for TSK classifiers, improving performance with label info.
problem Lack of supervised clustering for TSK fuzzy classifiers.
method SESSC integrates within-cluster compactness, between-cluster separation, and label information.
result SESSC initialization outperforms other clustering methods, especially for small rule numbers.
Paper explores rough path theory for frictionless markets, linking NCFL to unbiased rough integrators.
problem Tackles the limits of rough path theory in frictionless markets.
method Investigates the capacity of rough path theory to support No Free Lunch markets.
result Establishes a 'Rough Kreps-Yan' theorem linking NCFL to unbiased rough integrators.
The main objective is to present a some variant of the Black - Litterman model. We consider the canonical case when priori return is determined by means such excess return from the CAPM market portfolio which is derived using reverse optimization method. Then the a priori return is at risk quantified uncertainty. On th…
The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.
problem Approximating functionals of non-geometric rough paths.
method Extending rough paths with time and quadratic variation terms, proving uniform approximation.
result Linear functionals of extended signatures uniformly approximate continuous functionals.
This paper explores fuzzy systems' equivalence to neural networks and other machine learning methods.
problem Designing optimal fuzzy systems and overcoming challenges.
method Comparative analysis of Takagi-Sugeno-Kang fuzzy systems with neural networks, mixture of experts, CART, and stacking ensemble regression.
result Functional equivalence between fuzzy systems and machine learning methods.
Model rough volatility using RDEs with correlated Brownian motion and fractional Brownian motion.
problem Modeling rough volatility with correlated stochastic processes.
method Developed a method to lift Brownian motion and rough paths, applying it to fractional Brownian motion to model rough volatility.
result Calibrated a new rough volatility model to market data.
Fuzzy ROC handles indeterminate data points in ROC analysis.
problem Handling indeterminate data points in ROC analysis.
method Extends ROC visualization to indeterminate data, addressing sensitivity and specificity bounds.
result Visual summarization of possibilities from different indeterminacy zones.
Distributional (or distribution-valued) data are a new type of data arising from several sources and are considered as realizations of distributional variables. A new set of fuzzy c-means algorithms for data described by distributional variables is proposed. The algorithms use the L2 Wasserstein distance between dist…
Proposes a new gauge theory for fuzzy geometries using finite-dimensional algebras.
problem Modeling fuzzy geometries in noncommutative geometry.
method Introduces a Yang-Mills-Higgs matrix model based on gauge matrix spectral triples.
result States Yang-Mills-Higgs theory as an explicit random multimatrix model.
Fuzzy clustering reduces text data dimensions effectively.
problem Sparsity and high dimensionality in document-term frequency matrices.
method Fuzzy clustering applied as a new unsupervised feature transformation method.
result Fuzzy clustering outperforms PCA and SVD in reducing text data dimensions.
New cluster validity index detects optimal number of clusters and secondary options.
problem Determining the optimal number of clusters in fuzzy clustering.
method Correlation-based fuzzy cluster validity index (WP index) using fuzzy c-means algorithm.
result WP index outperforms existing indexes in detecting optimal number of clusters and secondary options.
A new fuzzy k-means algorithm for high-dimensional data with variable feature weights.
problem Clustering high-dimensional data with varying feature significance.
method Proposes a modified fuzzy k-means algorithm using two entropy terms to weight features.
result Improved clustering performance on various datasets compared to state-of-the-art methods.
We propose a mathematical model for the word-of-mouth communications among stock investors through social networks and explore how the changes of the investors' social networks influence the stock price dynamics and vice versa. An investor is modeled as a Gaussian fuzzy set (a fuzzy opinion) with the center and standar…