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A fuzzy clustering algorithm for multidimensional data is proposed in this article. The data is described by vectors whose components are linguistic variables defined in an ordinal scale. The obtained results confirm the efficiency of the…
This article deals with the complexity involved in fuzzy derivatives when both input and output are from nonempty, convex, and compact fuzzy space. Consider a fuzzy valued mapping, and for fuzzy differentiation of fuzzy valued function, we…
In this paper, we mainly discuss the constructions and the characteristics of betweenness relations and fuzzy betweenness relations in KM-fuzzy metric spaces. And the family of betweenness relations induced by a KM-fuzzy metric form a nest…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
Data privacy and silos are nontrivial and greatly challenging in many real-world applications. Federated learning is a decentralized approach to training models across multiple local clients without the exchange of raw data from client…
The concept of uncertainty is posed in almost any complex system including parallel robots as an outstanding instance of dynamical robotics systems. As suggested by the name, uncertainty, is some missing information that is beyond the…
Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines…
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…
Federated Learning (FL) is an evolving paradigm that enables multiple parties to collaboratively train models without sharing raw data. Among its variants, Vertical Federated Learning (VFL) is particularly relevant in real-world,…
Time-varying classifiers, namely, evolving classifiers, play an important role in a scenario in which information is available as a never-ending online data stream. We present a new unsupervised learning method for numerical data called…
Fuzzy metric spaces, grounded in t-norms and membership functions, have been widely proposed to model uncertainty in machine learning, decision systems, and artificial intelligence. Yet these frameworks treat uncertainty as an external…
Bisimulations have been widely used in many areas of computer science to model equivalence between various systems, and to reduce the number of states of these systems, whereas uniform fuzzy relations have recently been introduced as a…
We introduce non-commutative algebras, which can be associated with the function algebra of functions on a finite or half-finite cylinder. The algebras, which depend on a deformation parameter, are crossed product algebras of a partial…
The integration of different learning paradigms has long been a focus of machine learning research, aimed at overcoming the inherent limitations of individual methods. Fuzzy rule-based models excel in interpretability and have seen…
The involvement of uncertainty of varying degrees when the total of the membership degree exceeds one or less than one, then the newer mathematical paradigm shift, Fuzzy Theory proves appropriate. For the past two or more decades, Fuzzy…
Modeling relations between components of 3D objects is essential for many geometry editing tasks. Existing techniques commonly rely on labeled components, which requires substantial annotation effort and limits components to a dictionary of…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…
Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…
Fuzzy clustering algorithms can be roughly categorized into two main groups: Fuzzy C-Means (FCM) based methods and mixture model based methods. However, for almost all existing FCM based methods, how to automatically selecting proper…
The AI community is increasingly focused on merging logic with deep learning to create Neuro-Symbolic (NeSy) paradigms and assist neural approaches with symbolic knowledge. A significant trend in the literature involves integrating axioms…