Atlantis Studies in Uncertainty Modelling

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226 articles
Proceedings Article

Aggregation of Operators of Fuzzy Relational Mathematical Morphology: Erosion and Dilation

Alexander Šostak, Ingrīda Uļjane
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...
Proceedings Article

Type-2 Fuzzy Logic Approach for Overloaded Hosts in Consolidation of Virtual Machines in Cloud Computing

Bruno Moura, Guilherme Schneider, Adenauer Yamin, Mauricio Pilla, Renata Reiser
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...
Proceedings Article

Order Based on Non-Associative Operations

Kavit Nanavati, Balasubramaniam Jayaram
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...
Proceedings Article

Interpolative Boolean Algebra for Generalizations of Intuitionistic Fuzzy Sets

Pavle Milošević, Bratislav Petrović
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...
Proceedings Article

A debate model for cooperative agents to achieve common objectives

Abdelhak Imoussaten, Jacky Montmain
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...
Proceedings Article

Inf- and Sup-preserving Aggregation Functions

Marta Cardin
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...
Proceedings Article

On the Preservation of Some Additional Properties via the Quadratic Polynomial Construction Method of Fuzzy Implication Functions

Isabel Aguiló, Sebastia Massanet, J. Vicente Riera
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...
Proceedings Article

An Approach Towards Image Edge Detection Based on Interval-Valued Fuzzy Mathematical Morphology and Admissible Orders

Peter Sussner, Lisbeth Corbacho Carazas
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...
Proceedings Article

Scalarization for Approximate Multiobjective Multiclass Support Vector Machine Using the Large-k Norm

Yoshifumi Kusunoki, Keiji Tatsumi
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...
Proceedings Article

2-Tuple Linguistic Integrated Group Decision Making Methodology for E-Commerce Strategy Selection

Gulcin Buyukozkan, Deniz Uztürk
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...
Proceedings Article

Pattern Classification on Complex System Using Modified Gustafson- Kessel Algorithm

Miguel Khatounian Filho, Leo Koki, Renato Aguiar
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...
Proceedings Article

Modelling competing theories

Willem Conradie, Andrew Craig, Alessandra Palmigiano, Nachoem Wijnberg
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...
Proceedings Article

Modified multivariate F-transform based on B-splines

Martins Kokainis, Svetlana Asmuss
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...
Proceedings Article

Incremental Learning of Fuzzy Decision Trees for Streaming Data Classification

Riccardo Pecori, Pietro Ducange, Francesco Marcelloni
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...
Proceedings Article

Stability of Fuzzy Cognitive Maps with Interval Weights

Istvan Harmati, Laszlo T. Koczy
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...
Proceedings Article

On the relationship between L-fuzzifying approximation spaces and L-fuzzifying pretopological spaces

Anand Pratap Singh, Irina Perfilieva
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.
Proceedings Article

Transitivity properties of ternary fuzzy relations

Lemnaouar Zedam, Bernard De Baets
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...
Proceedings Article

Some remarks on topological structures in the context of fuzzy relational mathematical morphology

Alexander Sostak, Ingrida Uljane
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)...
Proceedings Article

Content Determination for Natural Language Descriptions of Predictive Bayesian Networks

Martín Pereira-Fariña, Alberto Bugarín
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...
Proceedings Article

Convex preferences as aggregation of orderings

Marta Cardin
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.
Proceedings Article

Formal Equivalence Analysis

Francisco José Valverde Albacete, Carmen Peláez-Moreno, Pablo Cordero, Manuel Ojeda-Aciego
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...
Proceedings Article

Prioritizing the Strategies to Enhance Smart City Logistics by Intuitionistic Fuzzy CODAS

Gulcin Buyukozkan, Fethullah Göçer
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...
Proceedings Article

Merging Clusters in Summary Structures for Data Stream Mining based on Fuzzy Similarity Measures

Leonardo Schick, Priscilla Lopes, Heloisa Camargo
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...
Proceedings Article

Towards fuzzy relational Galois connections between fuzzy T-digraphs

Inma P. Cabrera, Pablo Cordero, Emilio Muñoz-Velasco, Manuel Ojeda-Aciego
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...
Proceedings Article

WordNet and Prolog: why not?

Pascual Julian-Iranzo, Fernando Saenz-Perez
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...
Proceedings Article

Dimensionality Reduction and Its F-Transform Representation

Jiří Janeček, Irina Perfilieva
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...