Atlantis Studies in Uncertainty Modelling

Revising the definitions of fuzzy relational erosion and dilation introduced by N. Madrid et al. (L-fuzzy relational mathematical morphology based on adjoint triples. Inf. Sci. 474, 75–89, 2019), we define the structured versions of these operators and study their basic properties. Our principal interest...

Dynamic consolidation of virtual machines (VMs) is an effective way to improve resource utilization and power efficiency in cloud computing. Determining when it is best to relocate VMs from an overloaded host is one aspect of dynamic VM consolidation that directly influences the resource utilization...

Recently there have been many works studying orders obtained from fuzzy logic connectives, using the relation proposed in [12]. However, almost all of these works have dealt only with associative operations. In this work, we investigate the conditions under which the above relation leads to a partial...

The idea of this paper is to investigate intuitionistic fuzzy set (IFS) generalizations and make one step further into that direction by introducing interpolative Boolean algebra (IBA) to Liu’s generalized IFS. First, we aim to give an overview of the existing attempts to generalize or alter the definition...

We consider the situation where a group of agents are involved in the achievement of a common goal. Each agent owns a set of actions that are partial solutions for the problem to be solved. Moreover, different agents may have the same actions. In order to decide which action to select from different...

We introduce inf-lattices, sup-lattices and convexity algebras and we define closure or interior operators and congruences in these algebraic structures. We prove that any inf-lattice can be represented as a quotient of a power set lattice with respect to a congruence. Moreover we consider closure operators...

Following the extensively studied line of research of proposing new construction methods of fuzzy implication functions, recently a construction method based on a quadratic polynomial function and a given fuzzy implication function was proposed. The importance of this method relies on the fact that some...

Edge detection is an important step for pre-processing digital images before more advanced methods of image analysis such as segmentation can be applied. There are an infite number of edge detectors that can be derived from pairs of fuzzy dilation and erosion operators. Usually, an edge detector is based...

We study a multiclass extension of support vector machine (SVM) based on geometric margin maximization. Since there are different margins for different class-pairs, the maximum-margin SVM can be formulated as a multiobjective optimization problem. This multiobjective multiclass SVM (MMSVM) is difficult...

2-Tuple linguistic model, which is a fuzzy logic based linguistic decision-making tool, enables the use of multi-granulated linguistic variables in decision making. This property facilitates the decision-making process for decision makers (DMs) and provides a comfortable decision-making environment for...

This work has been focused in the application of Gustafson- Kessel Algorithm in a complex system through a methodology proposed. The complex system here considered will be the financial market. So, the main objective of this paper is to classify objects in two patterns: winner and loser. The methodology...

We introduce a many-valued semantics for basic normal lattice-based modal logic. This semantics is based on reflexive many-valued graphs. We discuss an interpretation and possible applications of this logical framework in the context of the formal analysis of the interaction between (competing) scientific...

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...