Related papers: Approximating approximate reasoning: Fuzzy sets an…

Risk specialists are trying to understand risk better and use complex models for risk assessment, while many risks are not yet well understood. The lack of empirical data and complex causal and outcome relationships make it difficult to…

Inspired by a mathematical riddle involving fuses, we define the "fusible numbers" as follows: $0$ is fusible, and whenever $x,y$ are fusible with $|y-x|<1$, the number $(x+y+1)/2$ is also fusible. We prove that the set of fusible numbers,…

Fuzzy Rule-Based Classification Systems (FRBCSs) have the potential to provide so-called interpretable classifiers, i.e. classifiers which can be introspective, understood, validated and augmented by human experts by relying on fuzzy-set…

Feature selection is a vital technique in machine learning, as it can reduce computational complexity, improve model performance, and mitigate the risk of overfitting. However, the increasing complexity and dimensionality of datasets pose…

Can a deep neural network be approximated by a small decision tree based on simple features? This question and its variants are behind the growing demand for machine learning models that are *interpretable* by humans. In this work we study…

In the intricate field of medical diagnostics, capturing the subtle manifestations of diseases remains a challenge. Traditional methods, often binary in nature, may not encapsulate the nuanced variances that exist in real-world clinical…

Many classification problems consider classes that form a hierarchy. Classifiers that are aware of this hierarchy may be able to make confident predictions at a coarse level despite being uncertain at the fine-grained level. While it is…

Recently, Hierarchical Clustering (HC) has been considered through the lens of optimization. In particular, two maximization objectives have been defined. Moseley and Wang defined the \emph{Revenue} objective to handle similarity…

The conventional clustering algorithms have difficulties in handling the challenges posed by the collection of natural data which is often vague and uncertain. Fuzzy clustering methods have the potential to manage such situations…

In this paper, a new interval type-2 fuzzy neural network able to construct non-separable fuzzy rules with adaptive shapes is introduced. To reflect the uncertainty, the shape of fuzzy sets considered to be uncertain. Therefore, a new form…

We prove that the space of intuitionistic fuzzy values (IFVs) with a linear order based on a score function and an accuracy function has the same algebraic structure as the one induced by a linear order based on a similarity function and an…

In this article, the theory of hierarchical evolutive systems of Ehresmann and Vandremeersch [Bull. Math. Bio. 49, 13-50 (1987)] is improved by considering the categories of the theory as fuzzy sets whose elements are the composite objects…

Inconsistency in prediction problems occurs when instances that relate in a certain way on condition attributes, do not follow the same relation on the decision attribute. For example, in ordinal classification with monotonicity…

Many state-of-the-art technologies developed in recent years have been influenced by machine learning to some extent. Most popular at the time of this writing are artificial intelligence methodologies that fall under the umbrella of deep…

For a given partially ordered set (poset) and a given family of mappings of the poset into itself, we study the problem of the description of joint fixed points of this family. Well-known Tarski's theorem gives the structure of the set of…

In this paper, we extend the notions of statistically convergence of order $\beta $ and strong Ces\`{a}ro summability of order $\beta ,$ and introduce the notions $f-$statistically convergence of order $\beta $ and strong Ces\`{a}ro…

We propose a nearest neighbor based clustering algorithm that results in a naturally defined hierarchy of clusters. In contrast to the agglomerative and divisive hierarchical clustering algorithms, our approach is not dependent on the…

This paper introduces techniques to integrate WordNet into a Fuzzy Logic Programming system. Since WordNet relates words but does not give graded information on the relation between them, we have implemented standard similarity measures and…

The problem of minimizing finite fuzzy interpretations in fuzzy description logics (FDLs) is worth studying. For example, the structure of a fuzzy/weighted social network can be treated as a fuzzy interpretation in FDLs, where actors are…

In this paper, we modify some previous definitions of fuzzy Turing machines to define the notions of accepting and rejecting degrees of inputs, computationally. We use a BFS-based search method and obtain an upper level bound to guarantee…