Atlantis Studies in Uncertainty Modelling

Given a probability distribution of an output quantity of a model, it is generally not possible to infer a unique probability distribution of the uncertain input quantity. In this contribution, it is shown that by reverting back to the coarser framework of possibility theory this problem possesses a...

Labour force of all European countries is ageing and this natural demographic process has its own consequences on economic output and productivity. This issue has been widely discussed in Western countries for several years, but a deep economic and social discussion is still absent in the Czech Republic....

This paper aims to study the fuzzy partitioned discrete-event systems and its supervisory control theory under full observation. Specifically, we introduce the concept of a fuzzy partitioned automaton corresponding to a given automaton. Further, we introduce the model of a fuzzy partitioned discrete-event...

In many Artificial Intelligence problems an investigated object is considered as a set of its elements {ω1,...,ωt} and is characterized by properties of these elements and relations between them. These properties and relations may be set by predicates p1,..., pn. The problems appeared with...

In this paper, we follow up on the well-known interpretation of fuzzy relations as morphisms in Kleisli category defined in the category of sets using a suitable monad. This Kleisli category thus becomes a relational variant of the classical category of fuzzy sets. This interpretation and the associated...

The aim of this paper is to investigate the effect of structural changes in intermediate use on employment in the Czech economy. We combine the input-output analysis with the index theory. For the analysis, we use input-output and employment data for the period between the years 2005 and 2015. We focus...

The paper addresses a novel evolving functional fuzzy modeling algorithm using hyperboxes and min-max fuzzy granulation. Data space granulation is done as data are input, and adapted using expansion, reduction operations to encompass new information. A fuzzy rule is assigned to each hyperbox using Gaussian...

Fuzzy sets can help us with imprecision, however, there are situations we are not able to assign an accurate value. Interval-valued fuzzy sets are applied in decision-making to deal with imprecision. The convexity of interval-valued fuzzy sets establishes some interesting results about decision local...

The objective of national accounts is to present a model of the real economy in the most accurate way. It means that not only officially recorded data from business accounting are included, but also model computations are used (e.g. in estimating the size of the shadow economy or correcting a phenomenon...

Traditional group decision making methods work under the assumption that experts must provide their preferences to a computational system after carrying out a thorough debate. Nevertheless, this is not natural since the mean where experts express their ideas and preferences is inside the debate. In this...

We present basic properties of the operation of sup-T composition of partial fuzzy relations, i.e., fuzzy relations defined on arbitrary subsets of the Cartesian square of the referential set. We show that for partial fuzzy relations, these properties are fairly similar to those for totally defined fuzzy...

Evaluating each member's collaboration ability in an R\&D team is of vital importance for senior managers to improve the team performance for R&D activities. Due to the difference in knowledge and education background, each team member usually tends to use multi-granular hesitant fuzzy linguistic term...

Regional price levels attract attention of researchers as well as of general public due to the fact that regional price differences influence the interpretation of regional indicators. The current international approach reflects just price differences among countries, and regional disparities are excluded...

This paper firstly aims at investigating distinct properties of the Bandler-Kohout sub-product and superproduct of level fuzzy relations or level relations. We show that these triangular products preserve several desirable properties similar to those valid for the compositions of standard fuzzy relations....

Authors in this publication present the new approach to aircraft systems efficiency evaluation. The research station consists of two units: efficiency evaluation unit and flight simulation unit. The efficiency is evaluated with use of fuzzy inference systems designed in Matlab/Simulink Software. Simulations...

A Business Tendency Survey (BTS) is one of popular instruments used for providing rough forecasts of future conditions of the national economy. Economists, journalists and analysts are not the only ones interested in the future development of the economy; ordinary citizens are also attentive to such...

An extension of the notion of closure system is studied adapting the idea of meet-subsemilattice to a complete fuzzy lattice. Results relating closure operators and closure systems in the classical case are extended properly to this framework. This definition is proved to be equivalent to the most used...

By a T-relational variant of a category K we understand a Kleisli category K_T of a category K with respect to a monad T. Using explicit definitions we equivalently describe several T-relational examples of categories with fuzzy type objects, where T are apropriate monads in these categories.

Monotonicity is a major property of entropy measures. In this paper, we focus on entropy measures for intuitionistic fuzzy sets and interval-valued fuzzy sets. We consider their polar representation which provides an easy interpretation of monotonicity for several entropy measures introduced in the literature....

This study analyses the problem of ageing which is currently one of the biggest concerns for central authorities in the Czech Republic. The rapidly changing demographic structure has affected the fiscal policy framework. The focus here is on the economic impact of the ageing phenomenon with respect to...

We focus on the aggregation of partial T-indistinguishability operators. We provide a characterization of those functions that allow to merge a collection of partial T-indistinguishability operators into a new one in terms of (+, max)-tuples. Moreover, we see that this is equivalent to the characterization...

In this work, we provide a study on the representability of interval-valued fuzzy connectives considering partial and admissible orders. Our approach considers those orders based on injective aggregation functions which allowed the construction of interval-valued operators. An immediate result is the...

Supply chain management process includes many activities to transform raw materials into final products considering with customer satisfaction. Order fulfillment process is one of them and plays a critical role in ensuring customer satisfaction. This study proposes uncertain dynamic intuitionistic decision...

The paper evaluates the results of a survey regarding challenges connected to the Big Data phenomenon and the New Digital Divide. Following the authors’ previous research, these challenges consist of issues such as business advantage, privacy intrusion, or big brother effect. Perception of these challenges...

Conceptual Graphs (CGs) are a formalism to represent knowledge. The production of CG benchmarks is currently a crucial need in the community to validate algorithms. This paper proposes CG2A, an algorithm to build synthetic CGs exploiting most of their expressivity. CG2A takes as input constraints that...

Many practical problems necessitate faster and faster computations. Simple physical estimates show that eventually, to move beyond a limit caused by the speed of light restrictions on communication speed, we will need to use quantum -- or, more generally, reversible -- computing. Thus, we need to be...

Not completing the study by a large portion of students is a serious problem at universities worldwide. Regardless of the country, numbers are very similar: about one-half of students who enrolled for the bachelor study leave university before obtaining the degree. To deal with this problem, we create...

This paper addresses the use of data-driven evolving techniques applied to fault prognostics in Li-ion batteries. In such problems, accurate predictions of multiple steps ahead are essential for the Remaining Useful Life (RUL) estimation of a given asset. The fault prognostics’ solutions must be able...

In this paper, the concept of minimal intuitionistic dominating vertex subset of intuitionistic fuzzy graph was considered, and on its basis the notion of a domination set as an invariant of the intuitionistic fuzzy graph was introduced. A method and an algorithm for finding all minimal intuitionistic...

The three dimensional extensions of ordinary fuzzy sets such as intuitionistic fuzzy sets of type-2 (IFS2) or Pythagorean fuzzy sets (PFS), and neutrosophic sets (NS) aim at collecting experts’ judgments more informatively and explicitly. In the literature, generalized three-dimensional spherical fuzzy...

We present a method for incremental modeling and time-varying control of unknown nonlinear systems. The method combines elements of evolving intelligence, granular machine learning, and multi-variable control. We propose a State-Space Fuzzy-set-Based evolving Modeling (SS-FBeM) approach. The resulting...

The aim of the paper is to show some possible transformations of ordinal variables in cluster analysis and discuss their effect on hierarchical clustering results. Although several papers comparing different approaches to clustering objects characterized by ordinal variables have been published, the...

This study introduces a new method to the family of fuzzy k-nearest neighbor (FKNN) classifiers that is based on the use of power means in the calculation of multi-local means that are used in classification of samples. The proposed new classifier is called multi-local power means fuzzy k-nearest neighbor...

In this paper, using a fuzzy mathematical model, we analyze multiple stocks and produce a description for their interrelation. Our analysis is based on theories of F-transform and fuzzy natural logic. The suggested method consists of two main steps; first, we smooth out time series using F-transform....

In this work symmetric positive definite matrices with non-negative entries will be characterized by using the Yager's family of t-norms. It can always be assumed that such an n X n matrix corresponds to a reflexive and symmetric fuzzy relation A on a set of cardinality n and then A is positive definite...

Almost all businesses and organizations use the World Wide Web in the form of corporate websites. In today’s highly innovative and competitive environment, the level of corporate internet presentations is one of the key success factors. Approaches to corporate website evaluation are very variable. To...

As the number of online financial transactions increases, the problem of credit card fraud detection has become quite urgent. Machine learning methods, including supervised and unsupervised approaches, have been proven to be effective to detect fraudulent activities. In our previous work presented at...

We generalize the concept of moderate deviation functions D : [0,1]2 → R into (k + 1)- dimensional moderate deviation function D(k) : [0,1]k X [0,1] → R and propose a D(k)-based method for constructing idempotent aggregation functions. More, to enable to introduce weights of groups of criteria...

In the paper, a four-dimensional nonlinear macroeconomic model of a small open economy describing the development of net real national income, real physical capital stock, nominal interest rate and nominal money stock is analysed. The functions of investment, savings, real income tax, liquidity preference...

The academic community cannot ignore the growing opportunities offered by artificial intelligence. Especially relevant are developments in this ares against the background of growing challenges and threats arising from the use of the digital environment by actors of psychological warfare – by strategists...

Non-negative matrix factorization (NMF) is a basic method for analyzing the intrinsic structure of non-negative matrices but cannot work well when datasets include some subsets drawn from different generative schemes. This paper proposes a novel switching NMF algorithm, which simultaneously estimates...

Functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theory. The cross-migrative equation is a weaker form of the classical commuting equation. This paper is devoted to exploring cross-migrative commutative aggregation functions with respect to Archimedean...

Edit rules are simple tuple-level constraints that concisely model which tuples are not permitted in a consistent relation. Previously, developed algorithms mostly assumed nominal data. This implies that ordinal data either had to be discarded or discretized according to expert knowledge. We can omit...

This study aims to increase the reliability of activity detection by using fuzzy logic extended Semantic Web technologies to Wireless Multimedia Sensor Networks (WMSNs). The proposed approach consists of three layers: the sensor layer, the data layer, and the Semantic Web layer. The sensor layer comprises...

Increasing the pension age above the usual threshold of 65 years is very often recommended to ensure financial sustainability of old-age pension systems, especially of those based on the PAYG principle. At the same time, a closer and clearer relation between the pension age threshold and the level of...

The development of information and communication technology has motivated multi-source data to become more common and publicly available. Compared to traditional data that describe objects from a single-source, multi-source data is semantically richer, more useful, however many-feature, more uncertain,...

Expressive speech modeling is a new trend in speech processing, including emotional speech synthesis and recognition. So far, emotion recognition from speech signal has been mainly achieved using supervised classifiers. However, clustering techniques seem well fitted to resolve such a problem, especially...

The at-risk-of-poverty rate indicates the proportion of people with disposable income under the poverty threshold. The aim of the present study is to examine the development of the poverty rate indicator in the Czech Republic, Slovakia and Poland over the period 2005 – 2017 in the group of people with...

In modern data analysis, multi-source data appears more and more in real applications. Different data sources provide information about different data. Therefore, multi-source data linking is important to improve the processing performance. However, in practice multi-source data is often heterogeneous,...

The paper presents the hybrid model of gene expression profiles reducing based on complex use of fuzzy inference system and clustering quality criteria. The average of absolute values, the variance and Shannon entropy of the gene expression profiles were used as the input parameters of fuzzy inference...

The aim of the paper is to analyse the socio-economic development of selected European countries represented by various social policies, and to verify the hypothesis of different speeds of development within the groups into which these countries divide. The following groups are considered in the analysis:...

Artificial Intelligence (AI) is part of our everyday life and has become one of the most outstanding and strategic technologies of the 21st century. Explainable AI (XAI in short) is expected to endow AI systems with explanation ability when interacting with humans. This paper describes how to provide...

This paper presents a study on the advection equation with an uncertain condition given by a fuzzy-number-valued function. A fuzzy solution to the problem is presented. This solution is obtained from the sup-J extension principle, which is a generalization of the Zadeh’s extension principle. In this...

Income inequality represents one of the central issues that are widely discussed by present-day economists. In Slovakia, significant income inequality linked to disparities between regions persists. The central aim of our paper is to offer an alternative insight into the issue of income inequality measurement...

This paper presents many expert fuzzy extensions of the Black-Litterman portfolio selection model. Black and Litterman identified two sources of information regarding the expected returns, and they combined these two sources of information in one expected return formula. The first source of information...

In this contribution, we focus on extending the Laplacian processing used in data-driven dimensionality reduction based on weighted graphs by incorporating the concept of singular value decomposition. We indicate a novel point of view on generalized eigenvalue problem by pointing out geometric meaning...

Differential operators definitely play an important role in image processing tasks. One of the most frequently used operator for this purpose is the Laplace operator, usually defined as the divergence of a gradient of a function. Since images are considered as discrete objects, many applications require...

The paper deals with unpaid work in Slovak households whilst focusing upon unpaid work performed by younger members of the household. Studies of unpaid work of people up to 26 years are still not well documented in literature. The aim of this paper is twofold: First, it seeks to answer the question whether...

We propose a fuzzy confidence interval estimation based on the likelihood ratio. This ratio, often used in hypotheses testing seems to be an efficient tool for calculating confidence intervals since it is known to be general, and thus can be applied on any parameter. The strength of the defended procedure...

We analyze various multi-scale representations of a one-dimensional signal in spaces with a closeness relation determined by a symmetric and positive semi-definite kernel. We discuss other kernels than the predominant Gaussian kernel in a scale space representation of a one-dimensional signal. We show...

An augmented appraisal degree (AAD) has been conceived as a mathematical representation of the connotative meaning in an experience-based evaluation, which depends on a particular experience or knowledge. Aiming to improve the interpretability of computer predictions, we explore the use of AADs to represent...

The aim of this paper is to examine the probability distribution of wealth of the richest persons in the world based on estimates from the CEOWORLD magazine’s rich list for March 2019. Since one can safely assume that there are a tiny number of people out of the whole world’s population in this list,...

The goal of this study is to solve fuzzy Fredholm integral equations of the second kind. In order to solve these equations with respect to fuzzy valued functions, we propose a very powerful and relatively simple technique called fuzzy transform. This approach allows the transformation of a fuzzy Fred-holm...

The objective of this paper is to characterize the quotient structures of fuzzy multiset finite automata. We introduce different congruence relation on multiset associated with fuzzy multiset finite automata and show that each congruence relation associates a semigroup with the fuzzy multiset finite...

One of the fundamental problems of modern physics is the problem of divergence: e.g., when we try to compute the overall energy of the electric field generated by a charged elementary particle, we get a physically meaningless infinite value. In this paper, we show that one way to avoid these infinities...

Nowadays, society often faces decision problems under uncertainty that hardly can manage by a single expert or a few of them because of their complexity. Under these conditions, large-scale group decision making (LS-GDM) problems are becoming more and more common. The decisions made on these types of...

Efficiency in using resources to achieve desired results at the lowest possible cost is not important only for profit-making subjects, but also for non-profit subjects. Economic efficiency of public administration is a permanent topic in Slovakia. Local self-government, represented by municipalities,...

This paper introduces the notion of a bidimensional fuzzy initial value problem for a special class of fuzzy functions. These functions, also called A-linearly correlated fuzzy processes, are a particular case of the so-called S-linearly correlated fuzzy processes, whose range is embedded in Banach spaces...

The aggregation of compositional data vectors arises naturally in many fields of application. In particular, the weighted centroid is inherently linked to the process of mixing two or more compounds. However, as natural and simple as this process may be, the weighted centroid does not fit the standard...

Interactivity naturally occurs in many real-world problems. The main goal of this paper is to propose a first approach toward characterizing the interactivity that is inherently present in the derivative of an unknown interval or fuzzy number valued function that is subject to certain restrictions. A...

This paper is dedicated to the 100th anniversary of establishing the State Statistical Office (an ancestor of today’s Czech and Slovak statistical offices) in 1919. The paper first describes troubles with organization of the statistical service in Austria-Hungary where the Austrian and Hungarian parts...

Since their introduction in 1976, edit rules have been a standard tool in statistical analysis. Basically, edit rules are a compact representation of non-permitted combinations of values in a dataset. In this paper, we propose a technique to automatically find edit rules by use of the concept of T-dependence....

Traffic accidents are one of the leading causes of death around the world. One well-established strategy to deal with this public health issue is the design and deployment of road safety systems, which are in charge of predicting traffic crashes to promote safer roads. Increasing data availability has...

We consider orthogonality spaces subjected to the condition that gradual transitions between any two elements are possible. More precisely, given elements e and f, we require a homomorphism from the unit circle to the automorphism group to exist such that one of these automorphisms maps e to f, and any...

Climate change is causing abrupt changes in temperature, which adds to earlier flowering of crops and possible crop failure due to negative temperatures at night. Anti-frost techniques exist to save crops but they require natural and human resources which increase costs. Therefore the application of...

The problem of credit card fraud detection is approached by a semi-supervised classification task on a data stream. The DISSFCM algorithm is applied, which is based on Dynamic Incremental Semi-Supervised Fuzzy C-Means that processes data grouped in small-size chunks. Experimental results on a real-world...

Several situations associated with the Sustainable Development Goals can be modeled as optimization problems that, under certain circumstances, can be solved with metaheuristics. In this paper we focus in the environmental impact (carbon footprint) that running such techniques produces. Through the...

The purpose of the present work is to use the concepts of reachability and obsrvability maps to provide a solution of a well-known characterization of fuzzy regular languages. In between, we associate two deterministic fuzzy automata with a given deterministic fuzzy automaton and show that the reachability...

The site selection process to optimize renewable facilities has become a relevant issue, mainly due to the variability of such resources. Among the different solutions, Geographic Information Systems in combination with fuzzy logic and Multi-Criteria Decision Making approaches provide a consistent tools...

This paper is towards the study of theory of fuzzy automata with fuzzy partitions. Specifically, we study the concept of the L-fuzzy partitioned automaton corresponding to a given L-fuzzy automaton. Further, we introduce the concept of a crisp-deterministic L-fuzzy automaton corresponding to the L-fuzzy...

The widespread and capability of Iot devices have made them a primary enabler for online fraud and fake authorship on social media. We present a novel approach, which uses sentiment analysis, to solve the problem of author verification in short text. We perform experimentation with our model on tweets,...

The goal of this contribution is to propose LM-valued F-transforms, which are essentially the many-valued generalizations of the notion of lattice-valued F-transforms. Further, we associate the concepts of LM-valued fuzzy rough sets with LM-valued F-transforms. Moreover, we show that the notion of F-transforms...

The paper aims at studying the solvability of fuzzy relational equations where the input fuzzy sets may have undefined values. The appropriate operations dealing undefined values are taken from the algebras built in partial fuzzy logic, in particular, the Bochvar operations, Sobocinski operations, Kleene...

The additional ability to span over multiple Knowledge Bases would further increase the usefulness and potentially comprehensiveness of the system’s responses. Multiple different Knowledge Bases, as much as they can complement each other regarding the lack of specific information, quite often contain...

In this paper, we study relations between fuzzy implicators and some kinds of fuzzy conjunctors, in particular, quasi-copulas and copulas. We show that there is a duality be- tween the classes of all quasi-copulas and 1- Lipschitz fuzzy implicators. In addition, we introduce a construction method for...

Advanced control strategies can play an important role in improving the efficiency of solar plants. In particular, linear model predictive control strategies have been applied successfully when controlling solar trough plants. However, if the control algorithm uses a linear model associated only with...

The detection and analysis of sentiment in textual communication is a topic attracting attention in both academia and industry. In fact, thanks to the explosion of the Social Networks a wealth of information is produced every day. This huge amount of contents can be very helpful in assessing the general...

One of the main components of a Digital Twin is the modeling of the virtual entity, being this a high-fidelity digital model of the physical entity that represents the modeling of geometry, modeling of physical properties, modeling of behavior, and modeling of rules in the virtual world. This paper...

Unsolved roots of ``privacy paradox'' motivate researchers to extricate the underlying reasons of such phenomenon. In the field of privacy research, the majority of empirical studies lack the availability of the real data collected from the actual platform instead of data received from the experimental...

This paper focuses on the intelligent management of domestic hot water (DHW) systems in buildings. Thermal installations are studied in depth due to the high percentage they represent in energy consumption, moreover, they usually lack management systems. To address this problem, firstly a functional...

This paper deals with a novel Fault-Tolerant Control (FTC) strategy for non-linear systems without hardware redundancy in case of actuator and system component failures. These failures correspond to blocking or loss of effectiveness of an actuator, leakage of tank bottom and pipes which could lead to...

The robustness analysis investigates the optimality of a solution in a linear programming problem that contains uncertainties. Conventionally, researchers concentrated on the one with a fixed feasible set, while in this paper, we focus on an inexact one. Since an inexact feasible set usually makes a...

In former papers a decision and optimization algorithm based on interactions between goals was introduced and it was shown how it solves relevant real-world problems. However, the algorithm assumed preference information on the goals as initially given. In this paper we describe a learning algorithm...

In this paper, we propose a novel activation function, namely, Interval Type-2 Fuzzy (IT2) Rectifying Unit (FRU), to improve the performance of the Deep Neural Networks (DNNs). The IT2-FRU can generate linear or sophisticated activation functions by simply tuning the size of the footprint of uncertainty...

The objective of this paper is to establish the relationship between fuzzy approximation operators and fuzzy transformation systems. We show that for each upper/lower fuzzy transformation system there exits a fuzzy approximation space induced by a fuzzy reflexive relation and vice-versa.

This paper proposes a set of minimal conditions which should be fulfilled by any multi-criteria additive procedure set out to work under imprecision. The proposed conditions are defined in terms of binary preference relations, which are inferred from interval-valued alternatives, and are shown to be...

In this paper, we present a many-level version for the Pawlak - Dubois and Prade theory of rough approximation of fuzzy sets. Basing on the many-level upper and lower fuzzy rough approximation operators, we define the measure of rough approximation that in a certain sense characterizes the quality of...

In many practical situations, users describe their preferences in imprecise (fuzzy) terms. In such situations, fuzzy techniques are a natural way to describe these preferences in precise terms. Of course, this description is only an approximation to the ideal decision making – that a person would perform...

It is well-known that the semantics of a given fuzzy logic can be formally axiomatized by means of a residuated poset. Based on a notion of dualizing (cyclic) element we introduce the notion of a Frobenius (Girard) poset. With this paper we hope to contribute to the theory of Frobenius posets and Girard...

Classical Group Decision Making (GDM) problems require the use of aggregation functions to fuse the information elicited from the experts who participate in the decision process. One of the most widely adopted aggregation functions employed in GDM are the Ordered Weighting Averaging (OWA) operators which...