We deal with the higher degree multivariate fuzzy transforms (F-transforms with polynomial components) in the case when generalized fuzzy partition of the Cartesian product of intervals is given by multivariate B-splines. The aim of this paper is to generalize the technique of modified F-transform introduced...

Data stream analysis is growing in popularity in the last years since several application domains require to continuously and quickly analyse data produced by sensors with the aim of, for instance, reacting immediately when problems arise, or detecting new trends. The specificity of these domains imposes...

In fuzzy cognitive maps (FCMs) based modelling paradigm, the complex system's behaviour is gathered by the causal connections acting between its main characteristics or subsystems. The system is represented by a weighted, directed digraph, where the nodes represent specific subsystems or features, while...

The aim of this contribution is to establish the interrelationship between L-fuzzifying approximation spaces based on reflexive L-fuzzy relations and L-fuzzifying pretopological spaces. This connection is established in the category theoretic setup.

Recently, we have introduced six types of composition of crisp ternary relations. These compositions are close in spirit to the definition of the composition of binary relations. In this note, we extend these notions to the fuzzy setting. Based on these types of composition, we introduce several types...

In this paper, we develop a topological view point on the subject of mathematical morphology. We shaw that erosion can be interpreted as a certain remote fuzzy interior operator; in its turn dilation can be interpreted as a remote fuzzy closure operator. Further, we introduce two kinds (upper and lower)...

The dramatic success of Artificial Intelligence applications has been accompanied by more complexity, which makes its comprehension for final users more difficult and damages trustworthiness as a result. Within this context, the emergence of Explainable AI aims to make intelligent systems decisions and...

Convexity of preferences is a canonical assumption in economic theory. In this paper we consider a generalized definition of convex preferences that relies on the abstract notion of convex space.

Following R. Wille's lead and suggestion we set out to design a new kind of view onto a formal context analogous but different to Formal Concept Analysis (FCA) and Formal Independent Analysis (FIA). In this instance, we choose to analyse the information in the incidence table in terms of the partitions...

Accurate, well-timed, and efficient delivery operations is a must for supply chains and logistics providers’ survival in a digitally enhanced business environment. Sustainability, mobility and livability related objectives of Smart City Logistics (SCL) address the reduction of trucks, congestion and...

Fuzzy Clustering is one of the mining techniques that have been used to extract information from Data Streams. In our previous research we have developed an algorithm called d-FuzzStream, a fuzzy version of the Online-Offline Framework, which consists of two steps: an online step, where a summary structure...

In this paper, we give the first steps towards a formal definition of fuzzy relational Galois connection between fuzzy sets with arbitrary fuzzy transitive relations (fuzzy T-digraphs), where the two components of the connection are fuzzy relations. To this end we consider, on the one hand, our definition...

This paper describes a set of Prolog modules with predicates to access the information stored in the lexical data base WordNet. The aim is to use the dened predicates for empowering (fuzzy) logic programming systems for approximate reasoning tasks. To achieve this goal it is necessary to have means to...

The aim of this contribution is to connect two techniques: the F-transform on a space with a fuzzy partition and dimensionality reduction. We show how a space with a fuzzy partition can be characterized in terms of the graph Laplacian. After making the spectral analysis of the corresponding Laplacian...