arXiv subjects

Debjani Chakraborty

Publications and source records attributed to Debjani Chakraborty.

5 recordsLinked to original sources

arXiv2026

Bayesian fuzzy optimization using fuzzy Gaussian process

In many real-life problems, decision-making gets complicated due to dual sources of uncertainty, known as randomness and fuzziness or imprecision, which can be challenging for traditional optimization methods. Most of the existing fuzzy optimization techniques that optimize fuzzy-valued objective functions ignore fuzziness, while the probabilistic optimization techniques ignore randomness. To handle this dual source of uncertainty, Kwakernaak introduced the concept of a fuzzy random variable as ``random variables whose values are not real, but fuzzy numbers". This work aims to derive a theoretical background for the Gaussian fuzzy process and fuzzy acquisition functions, which will be used to develop a novel \emph{Bayesian fuzzy optimization} (BFO) technique that optimizes a fuzzy-values objective function. Based on fuzzy random variables, the Gaussian fuzzy process is developed, which is used as a prior belief about the fuzzy-valued objective function in the BFO. Fuzzy acquisition functions are defined to act as a guide for the search process of BFO with the help of posterior fuzzy mean and fuzzy variance. The proposed method demonstrated effective performance in both fuzzy mean-variance portfolio allocation and Indian temperature data analysis, showing robust predictive accuracy and adaptability. The proposed method can have broader applications in various fields like healthcare, material science, agriculture, etc.

math.GM↗

arXiv2026

MTRBO: Multiple trust-region based Bayesian optimization

Bayesian Optimization (BO) is a popular framework for optimizing black-box functions. Despite its effectiveness, BO is often inefficient for high-dimensional problems due to the exponential growth of the search space, heterogeneity of the objective function, and low sampling budget. To overcome these issues, this work proposes a multiple trust region-based Bayesian optimization technique(MTRBO). A trust region is a localized region within which an optimization model is trusted to approximate the objective function accurately. Assuming a Gaussian process (GP) as a prior belief about the objective function and based on the posterior mean and variance functions, the method adaptively exploits near the promising current solution inside a trust region. Also explores the most uncertain region in the search space inside another trust region. The theoretical global convergence property of the proposed method is established. Then the work is benchmarked against other state-of-the-art trust-region-based Bayesian optimization algorithms, demonstrating superior performance on a variety of non-convex and high-dimensional test functions. The proposed method outperforms others in terms of solution quality within the sampling budget (the number of function evaluations). The proposed method is applied to the portfolio optimization problem to verify its applicability in real-world scenarios.

math.OC↗

arXiv2025

A Fuzzy Geometric Study of Equidistant Sets in Fuzzy Metric Space

In this paper, the fuzzy Hausdorff distance is studied, and also the fuzzy equidistant set for two points of a fuzzy metric space is introduced. Here, the fuzzy metric space has been redefined using recently developed fuzzy geometry, and the equidistant sets have been constructed for two different fuzzy points. Different cases for the equidistant sets have been studied, considering two fuzzy points with separate spreads, externally tangent spreads, partially overlapping spreads, internally tangent spreads, fully overlapping spreads, and sets that coincide with the cores of fuzzy points. The proposed construction provides a graded equidistant set that aligns with the classical midset when the metric is precise. Suitable numerical and pictorial examples are given to support the discussions and studies.

math.GM↗

arXiv2024

Inter Observer Variability Assessment through Ordered Weighted Belief Divergence Measure in MAGDM Application to the Ensemble Classifier Feature Fusion

A large number of multi-attribute group decisionmaking (MAGDM) have been widely introduced to obtain consensus results. However, most of the methodologies ignore the conflict among the experts opinions and only consider equal or variable priorities of them. Therefore, this study aims to propose an Evidential MAGDM method by assessing the inter-observational variability and handling uncertainty that emerges between the experts. The proposed framework has fourfold contributions. First, the basic probability assignment (BPA) generation method is introduced to consider the inherent characteristics of each alternative by computing the degree of belief. Second, the ordered weighted belief and plausibility measure is constructed to capture the overall intrinsic information of the alternative by assessing the inter-observational variability and addressing the conflicts emerging between the group of experts. An ordered weighted belief divergence measure is constructed to acquire the weighted support for each group of experts to obtain the final preference relationship. Finally, we have shown an illustrative example of the proposed Evidential MAGDM framework. Further, we have analyzed the interpretation of Evidential MAGDM in the real-world application for ensemble classifier feature fusion to diagnose retinal disorders using optical coherence tomography images.

cs.AI↗

arXiv2024

Multiscale Color Guided Attention Ensemble Classifier for Age-Related Macular Degeneration using Concurrent Fundus and Optical Coherence Tomography Images

Automatic diagnosis techniques have evolved to identify age-related macular degeneration (AMD) by employing single modality Fundus images or optical coherence tomography (OCT). To classify ocular diseases, fundus and OCT images are the most crucial imaging modalities used in the clinical setting. Most deep learning-based techniques are established on a single imaging modality, which contemplates the ocular disorders to a specific extent and disregards other modality that comprises exhaustive information among distinct imaging modalities. This paper proposes a modality-specific multiscale color space embedding integrated with the attention mechanism based on transfer learning for classification (MCGAEc), which can efficiently extract the distinct modality information at various scales using the distinct color spaces. In this work, we first introduce the modality-specific multiscale color space encoder model, which includes diverse feature representations by integrating distinct characteristic color spaces on a multiscale into a unified framework. The extracted features from the prior encoder module are incorporated with the attention mechanism to extract the global features representation, which is integrated with the prior extracted features and transferred to the random forest classifier for the classification of AMD. To analyze the performance of the proposed MCGAEc method, a publicly available multi-modality dataset from Project Macula for AMD is utilized and compared with the existing models.

eess.IV↗