Related papers: Homomorphisms between fuzzy information systems re…
Zigzag persistent homology is a powerful generalisation of persistent homology that allows one not only to compute persistence diagrams with less noise and using less memory, but also to use persistence in new fields of application.…
While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…
In this paper we provide new several Jackson-type approximations results for continuous fuzzy-number-valued functions which improve several previous ones. We use alternative techniques adapted from Interval Analysis which rely on the…
The theory of fuzzy semigroups is a branch of mathematics that arose in early 90's as an effort to characterize properties of semigroups by the properties of their fuzzy subsystems which include, fuzzy subsemigroups and their alike, fuzzy…
Two main topics are considered: The characterisation of finite homomorphism dualities for relational structures, and the splitting property of maximal antichains in the homomorphism order.
Prediction sets offer a binary inclusion/exclusion for each element at the same fixed confidence level. We generalize to fuzzy prediction sets, which exclude elements at their own data-driven confidence level. Our key insight is that a…
Rule mining algorithms are one of the fundamental techniques in data mining for disclosing significant patterns in terms of linguistic rules expressed in natural language. In this paper, we revisit the concept of fuzzy implicative rule to…
This paper shows that the endograph metric and the $\Gamma$-convergence are compatible on a large class of fuzzy set in $\mathbb{R}^m$.
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
In this paper we introduce some families of fuzzy L-systems and investigate their properties. We further discuss the relationship between fuzzy L languages and the fuzzy languages generated by fuzzy grammar proposed in Ref.[3,5]. A measure…
We prove two results concerning an Ulam-type stability problem for homomorphisms between lattices. One of them involves estimates by quite general error functions; the other deals with approximate (join) homomorphisms in terms of certain…
In this book we study the concepts of Fuzzy Cognitive Maps (FCMs) and their Neutrosophic analogue, the Neutrosophic Cognitive Maps (NCMs).Fuzzy Cognitive Maps are fuzzy structures that strongly resemble neural networks, and they have…
This paper discusses the properties the spaces of fuzzy sets in a metric space equipped with the endograph metric and the sendograph metric, respectively. We first give some relations among the endograph metric, the sendograph metric and…
We briefly review the connection between the fuzzy field theories and matrix models and describe the main features of the models that appear. We summarize the different approaches to their analysis, some of the recent results and the…
The rank-three tensor models, which have a rank-three tensor as their only dynamical variable, may be interpreted as models of dynamical fuzzy spaces. In this interpretation, the generalized Hermiticity condition on the rank-three tensor…
Persistence diagrams concisely represent the topology of a point cloud whilst having strong theoretical guarantees, but the question of how to best integrate this information into machine learning workflows remains open. In this paper we…
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…
The main purpose of this paper is to provide a solution of the consistent fuzzy linear system and a generalized solution of the inconsistent fuzzy linear system involving the core-EP inverse of an associated matrix. Before this can be…
Measuring the similarity of two files is an important task in malware analysis, with fuzzy hash functions being a popular approach. Traditional fuzzy hash functions are data agnostic: they do not learn from a particular dataset how to…
In this study different types of intuitionistic fuzzy continuities (IFCs) and intuitionistic fuzzy boundedness (IFBs) in intuitionistic fuzzy pseudo normed linear spaces are studied. Relations (intra and inter) on intuitionistic fuzzy…