Atlantis Studies in Uncertainty Modelling

In group decision making, the usage of linguistic information entails the requirement for computing with words, a methodology in which words from a natural language are the computational elements. Recently, a new approach based on a framework of granular computing has been applied to cope with linguistic...

When a group of individuals try to collectively make a decision, it is important that all of them accept the decision adopted. It means, to improve consensus, some adjustments could be inevitably performed to the initial assessments given by the individuals. To do it, several models have been recently...

With the rapid accumulation of rich media data on the Internet, this paper proposes a Multi-View Bayesian Personalized Ranking (MVBPR) recommendation model that combines visual and textual contents, along with uncertainty modeling in consumer preferences and in visual representation in forms of implicit...

Examining fuzzy preference relations together with the reciprocity condition, and a potential conceptual conflict arising between reciprocal fuzzy preferences and fuzzy preference structures, it is claimed that reciprocal preferences cannot be properly understood according to a weak nor a strict preference...

Four-valued logics were developed from three-valued logics aiming at creating tools dealing with missing values and indeterminable values at the same time in computer science. In this paper, we are motivated by the formation of such four-valued logics and construct a new set of operations able to work...

The increase in transactions on the Internet related to the purchase of products or services can provide facilities for the parties involved in these acquisitions, but they also generate uncertainties and possibilities of attacks that can originate from fraud. This work seeks to explore and extract knowledge...

The paper shows the possibility of applying the tool of non-additive measures and the belief functions theory to solving a number of problems of significance analysis and conflict of the political party positions. The study was performed on a database of online polls of parties in Germany before the...

Similarity-based reasoning systems consider the notion of similarity as crucial for their motivation and the whole design. However, similarity can be seen not only as a general notion but also as a particular family of binary fuzzy relations modeling a fuzzy equality. Moreover, these relations are tightly...

In real applications, sometimes it is necessary to evaluate inner or external conflict of pieces of evidence. However, these numerical values cannot give us explanations why this conflict occurs. Thus, we need deeper analysis of available information. In the paper, we propose the clusterization of a...

In this paper, we propose an interactive decision making method for multiobjectve bimatrix games with fuzzy payoffs. Using possibility measure and reference membership values, an equilibrium solution concept is introduced. To circumvent computational difficulties to obtain such a solution, equilibrium...

We prove the categorically equivalence between the quasi-implicative-Boolean algebras and the quasi-m Boolean algebras, a generalization of the categorically equivalence between the implicative-Boolean algebras and the Boolean algebras.

Methods of linear regression analysis are applied to fuzzy cognitive map construction according to history data from the standpoint of quantitative human sciences. When the linearized version of history data is also used, this construction may be reduced to ordinary linear regression analysis. This linearization...

This paper is a contribution to the study of two distinct kinds of modal logics for modeling uncertainty. Both approaches use logics with a two-layered syntax, but while one employs classical logic on both levels, the other involves a suitable system of fuzzy logic in the upper layer. We take two prominent...

The question of whether the use of crisp or fuzzy input information in the TOPSIS method produces a different ranking is explored. Using a basic representation of fuzziness through triangular fuzzy numbers, a set of randomly generated fuzzy and crisp multicriteria decision problems are solved. Then,...

The inhibition of new vessel creation, or anti-angiogenesis, has therapeutic interest. In this contribution, we introduce an automatic method to estimate objective indicators of new vessel creation. We use images of the chorioallantoic membrane of chicken embryos, some of which have been injected with...

Similarity-based reasoning is one of the well-established inference mechanisms which is widespread in the literature. An inference mechanism is required to have some properties to be an acceptable inference mechanism that can be used in an application. Interpolativity and continuity are two of the major...

Quadruple Conical Tank System (QCTS) is benchmark a laboratory setup for testing of various linear and nonlinear control algorithms for the multivariate control system. The multiple process conguration for multivariate input-output can be obtained from quadruple conical tank system. This article is concerned...

This paper presents a solution approach for multi-objective linear programming problem. We consider MOLP problem where optimization of multiple, conflicting objective functions subject to constraints is concerned. We give also comments how to deal with FMOLP problem, where the parameters are imprecisely...

In this article, we follow up on previous publications in which we studied generalized Peterson’s syllogisms. The main objective of this paper is to define a new intermediate quantifier “At least <Several, A few, A little>” and analyze new forms of valid syllogisms.

In this paper we show how `uncertainty of information' traditionally focuses mostly on `uncertainty' leaving `information' mostly as unravelled. We also try to explain why that is so, and we then provide suggestions on how to overcome this situation, in particular in work on applications involving information...

This article aims to continue the analysis of generalized Peterson’s syllogisms with more premises. Namely, we use the theory of intermediate quantifiers, which provides the mathematical interpretation of natural language expressions indicating the amount or quantity of objects, such as “Almost all”,...

Most edge detection algorithms deal only with grayscale images, and the way of adapting them to use with RGB images is an open problem. In this work, we explore different ways of aggregating the color information of a RGB image for edges extraction, and this is made by means of well-known edge detection...

The main objective of this paper is to continue the study of generalized Peterson’s syllogisms and to formally define Peterson’s rules of distributivity, quantity and quality. While past results were based on mathematical definitions of generalized quantifiers the idea of this article is to take advantage...

This work describes the development of a type 2 Fuzzy Inference System by using Genetic Programming for applications in time series forecasting. The resulting model, called GPFIS-Forecast+ is based on the GPFIS-Forecast created previously, which made use of Multigene Genetic Programming an provided good...

The paper is focused on an overview of graded structures of opposition with generalized intermediate quantifiers. This article focuses mainly on achieving two goals. Firstly, classical structures of opposition (square, hexagon, cube) are introduced. Then, graded extensions of mentioned structures are...

Generalize fuzzy operators for the framework of lattices is the main objective of many recent researches. Here we present a study about how to define lattice-valued (U,N)-implications i.e. the class of implications generated from a uninorm U and a fuzzy negation N. Moreover, we discuss about its extension...

In this paper, we show how computational perceptions can be employed as labeled datasets to train agents in computer games. The idea is to automatically create a correspondence between perceptions and movements by using computational perception networks, next this knowledge is learned by the agents by...

Personalized linguistic summaries are developed with the use of protoforms in the sense of Yager and Kacprzyk. We discuss the construction and usefulness of such patient-dependent and disease-state-dependent linguistic summaries that may be examplified as `Most outgoing calls in mania state (disease...

This paper concentrates on investigating the preservation of the axioms and essential properties of residuated lattices in partial fuzzy set theory. We consider seven most-known partial algebras dealing with undefined values such as the Bochvar, Bochvar external, Sobociński, McCarthy, Nelson, Kleene,...

We present a new method for attribute selection for models with attribute values expressed via Atanassov's intuitionistic fuzzy sets (IFSs, for short). The three term representation of the IFSs makes it possible to construct a transparent and justified function that enables to select attributes...

We continue analyzing the properties of f - inclusion and f -contradiction, and provide an alternative interpretation of the square of opposition.

Combined Compromise Solution (COCOSO) method is a combination of different aggregation strategies that aim to find final scores of the alternatives with respect to determined criteria based on decision makers’ judgements. This method is extension of simple additive weighting and exponentially weighted...

The aim of this paper is to present categorical equivalences involving Nelson algebras with a consistency operator. These algebraic structures are the algebraic semantics of a paraconsistent logic, actually a logic of formal inconsistency, based on Nelson logic, also known as constructive logic with...

In this paper we investigate two generalizations, in fuzzy logic, of classical scheme of reduction to absurdity. We compare them with two possible generalizations of classical hypothetical syllogism (in fuzzy logic) and we show that generalized hypothetical syllogism is more general. We present new results...

Noticing certain limitations of concept lattices in the fuzzy context, especially in view of their practical applications, in this paper we propose a more general approach based on what we call graded fuzzy preconcept lattices. We believe that this approach is more adequate for dealing with fuzzy information...

Cut-based strong fuzzy partitions (SFP) are characterized by cuts, i.e. points in the universe of discourse where the non-zero membership degrees of the fuzzy sets in the partition is 0.5. Cuts are useful to identify the most representative regions for the fuzzy sets involved in a SFP but pose loose...

Since matching accuracy determines the performance of the overall algorithm, studies using image features require sophisticated classification technique for matching. However, there is a critical problem that the factors used to classify true or false matches are extremely limited. To solve this problem,...

This work studies typical hesitant fuzzy sets (THFS) which can be used in group decision making (GDM) due to the possibility of more flexible values for expressions given by a group of decision makers, instead of using only one value resulting from aggregation expressing their preferences. Besides,...

Surveillance systems are increasingly exploiting multimodal information for improved effectiveness. This paper presents an audio event detection method for road traffic surveillance, combining generative deep autoencoders and fuzzy modelling to perform anomaly detection. Baseline deep autoencoders are...

The performance of law offices can be comparatively measured by multicriteria decision making methods. Linguistic assessments can be used in this process rather than exact numerical evaluations. The performance evaluation is generally realized in a vague and imprecise environment. Fuzzy set theory is...

The expression of a general opinion on a product or service may sometimes be broken down into different sub-opinions on the different aspects which characterise such a product or service. Sometimes, the general opinion about a product does not have to be the average of the other sub-opinions, but other...

Two-dimensional image reconstruction from projections is a well known research field with different applications and using different sources, e.g., varying from medical imaging to a synchrotron laboratory. In the mathematical sense, we are looking for a two dimensional piecewise function with compact...

The rising volume of data and its high complexity has brought the need of developing increasingly efficient knowledge extraction techniques, which demands efficiency both in computational cost and in accuracy. Most of problems that are handled by these techniques has complex information to be identified....

This manuscript proposes a framework to design an artifact that combines traffic data of different sources, addresses their low-penetration rate and imprecision, and enables their analysis. The implemented artifact uses probe data of en-route operations of delivery vehicles and Traffic Message Channel-based...

Due to the lack of quantum hardware, quantum simulation (QS) is the most common method to study quantum computing. Even so, simulators and simulations should be properly built to use the maxim computational power possible. This work focuses on the main problem related to the memory accesses, representing...

In this contribution we describe a novel procedure to represent uncertainty in rating scales in terms of fuzzy numbers. Following the rationale of fuzzy conversion scale, we adopted a two-step procedure based on a psychometric model (i.e., Item Response Theory-based tree) to represent the process of...

R-implications are studied on Ln(U) considering the conditions under which main properties are preserved, and their representability from U to Ln(U) are also presented. Some results in the class of n-dimensional R-implications obtained from t-representable norms on Ln(U) are discussed.

A recent book provides examples that a new class of probability distributions and membership functions – called kappa-regression distributions and membership functions – leads, in many practical applications, to better data processing results than using previously known classes. In this paper, we provide...

Fuzzy Rule Based Classification Systems (FRBCSs) are widely used tools in classification problems. An important aspect in the design of a FRBCS is the number of fuzzy labels per variable (granularity level), which significantly influences the performance of the fuzzy system. Another relevant issue to...

Counting data in presence of uncertainty leads to granular counts that can be represented in terms of possibility distributions. The formula of granular count is derived on the basis of two weak assumptions that can be applied in a wide variety of problems involving uncertain data. The formulation is...

A new resampling approach for simulating bootstrapped samples of fuzzy numbers is proposed. The secondary samples consist of fuzzy numbers which preserve the canonical representation (i.e., the value and ambiguity) of fuzzy numbers belonging to the primary sample, although may differ from the initial...

A random variable is said to stochastically dominate another random variable if the cumulative distribution function of the former is smaller than or equal to the cumulative distribution function of the latter. In this paper, we present a graded version of stochastic dominance by measuring the part of...

In this paper we investigate the problem of possibilistic-probabilistic optimization with constraints on possiblity/probability. Fuzzy parameters of the problem are considered to be related by the weakest t-norm, random parameters are normally distributed. For solving the problem an equivalent stochastic...

Capacities are monotonically increasing set functions that generalize probability and possibility measures. They are qualitative when they range on a finite linearly ordered scale. This paper pursues a parallel between qualitative capacities and the quantitative setting of belief functions. The qualitative...

Hidden conflict of belief functions in the case where the sum of all multiples of conflicting belief masses being equal to zero was observed. Degrees of hidden conflict and of non-conflictness are defined and analyzed including full non-conflictness. The hidden conflict between two belief functions...

Gaussian Markov Random Fields over graphs have been widely used in the context of both theoretical and applied Statistics. In this paper, we study the influence of the graph on the continuous entropy of the distribution. In particular, since the continuous entropy is highly dependant on the correlations...

A concept of uncertainty-aware similarity measure for interval--valued fuzzy sets is being defined and discussed. The aim of the paper is to support the opinion that both definition and construction of such measure should take into account the epistemic nature of compared incomplete (uncertain) information....

The aim of this contribution is to define a conditional probability for interval valued events. We show the connection between the conditional probability for interval valued events and the conditional probability for intuitionistic fuzzy events too. We formulate the properties of conditional probability...

Discovering new trends and co-occurrences in massive data is a key step when analysing social media, data coming from sensors, etc. Although, nowadays Data Mining is very useful and widely used for the industry, business and government, the main problem of application of machine learning or data mining...

A simplified calculus for aggregation of random variables is derived. The calculus provides a fast and simple estimation of a given quantile. It can be applied for testing of desired reliability of a production plan.

In the article we first review some known results on fuzzy versions of the dominance-based rough set approach (DRSA) where we expand the theory considering additional properties. Also, we apply Ordinal Weighted Average (OWA) operators in fuzzy DRSA. OWA operators have shown a lot of potential in handling...

Statistics with interval-valued data are getting less interest from practitioners than it really deserves. This is partly because the solutions it offers are often too conservative and hence do not fully meet the expectations of potential users. Thus it is necessary to develop methods which, despite...

Developing agents for automated game playing is a demanding task in the general game production cycle. Especially the involvement of frequent balance changes after the release, e.g. as they often occur in collectible card games, require constant updates of the developed agent. The game's developers need...

Fuzzy data applied for modeling imprecise observations cause many problems in statistical reasoning and data analysis. To handle better such observations a new bootstrap technique designed for epistemic fuzzy data is proposed. Our new method is conceptually simple and is not hard computationally. Some...

In this paper we study Lotka-Volterra model of oscillating chemical reactions via fuzzy differential equations, where the initial conditions are given by interactive fuzzy numbers. The concept of interactivity is associated with the notion of joint possibility distribution. The fuzzy solution is given...

This paper introduces a novel procedure for statistical monitoring of acoustic data streams supported by possibilistic aggregation and multi-label learning. The primary goal is to learn improved control limits for the residual control charts due to the objective removal of measurements from the non-healthy...

Digitisation, digitalisation and digital transformation represent one of the primary incentives of today’s development. To successfully implement these changes, countries need to create smart digital policies which are evidence- and data-based. The study presented in this paper uses the logical clustering...

The concept of aggregation has been usually associated with that of aggregation functions, assuming that any aggregation process can be represented by a function. Recently, computable aggregations have been introduced considering that the core of the aggregation processes is the program that enables...

This case study evaluates to what extent personal preferences can be automatically derived from user event data in an mHealth setting. Based on a theoretical framework, user preferences are described using six classes. Based on this framework, a structure of six Takagi-Sugeno fuzzy inference systems...

The need of establishing a consensus ranking from the preferences expressed by different voters arises in several contexts. The method proposed by Kemeny to this purpose is famously known due to its numerous fulfilled properties and intuitive interpretation, as it minimizes the number of pairwise comparisons...

Logs of arrhythmia episodes in patients with pacemakers are used to estimate the temporal progression of atrial arrhythmia. In order to attain an early detection, a stream of dates and episode lengths are fed to an array of detectors, each of which is responsive to a narrow range of arrhythmias. The...

In this contribution, we analyse in details the recently introduced definition of migrative t-conorms [see Fuzzy implications: alpha migrativity and generalised laws of importation, M. Baczyński, B. Jayaram, R. Mesiar, 2020]. We also focus on some general functional equations, which might be obtained...

Fuzzy Cognitive Maps (FCM) and other Dynamic Cognitive Maps (DCM) were originally developed as mechanisms to simulate the evolution of complex qualitative dynamic systems. In this paper we present a case study where we show that Evolving DCM (specifically Evolving Rule Based Fuzzy Cognitive Maps, Ev-RBFCM)...

In this paper, we revisit the definition of a convolution of aggregation functions and we will examine the convolution of collection integrals defined on a finite space. Also, we introduce the concept of a convolution and of a lower convolution for monotone measures and examine properties of these convolutions...

In this paper we introduce an NP-hard optimization problem and examine preferences of decision-maker towards imprecise alternatives (modes) in a fuzzy temporal graph structure model. Fuzzy Z-number preference matrix is introduced and types of generalized precedence relations in fuzzy multimode resource-constrained...

Positive homogeneity of aggregation functions is one of important properties reflecting the ratio scales in decision making. We recall, introduce and discuss some generalizations of this property, including k-homogeneity, quasi-homogeneity and endpoint linearity.

Inspired by the basic fuzzy connectives min (t-norm TM) and max (t-conorm SM), we introduce and study outliers-based extended aggregation functions. Simply said, A is an (a, b)-outliers-based extended aggregation function if for each arity n ≥ a + b, its output values depend on the number a minimal and...

Fuzzy relation equations have recently been extended to a more general framework in which the unknown variables appear together with their logical negation connectives, giving rise to the called bipolar fuzzy relation equations. This paper shows an abductive procedure for a special kind of normal residuated...

Discrete OWA operators introduced by Yager (1988) have been widely used and their theoretical as well as application aspects have been studied since their introduction. Some generalizations to continuous case have already been proposed. In this contribution we extend the approach by Jin et al. (2020).

In Hlinena et al. (2014) the authors, inspired by Karacal and Kesicioglu (2011), introduced a pre-order induced by uninorms. This contribution is devoted to a classification of families of uninorms by means of types of pre-orders (and orders) they induce. Philosophically, the paper follows the original...

Discrete copulas are useful tools in statistics to represent the joint distribution of discrete random vectors. Furthermore, they are fascinating mathematical objects that admit a representation as a convex polytope. In this work, we analyze the set of extreme points of convex polytopes of discrete copulas....

Fuzzy tensors encode to what extent n-ary predicates are satisfied. The disjunctive box cluster model is a regression model where sub-tensors are explanatory variables for the values in the fuzzy tensor. In this article, the most informative patterns according to that model, with high areas times squared...

Classification relies on the rules expressed by domain experts, or on the labeled attribute explaining the output classes. However, such information is not always available. In this work, we explore classification according to aggregation functions of mixed behaviour by the variability in ordinal sums...

In this paper, we study an application of qualitative possibility theory to decision making under uncertainty. The word “qualitative” means that uncertainty is modeled using comparative possibility distributions on a universal set Ω. Such a possibility distribution defines how likely each elementary...

This paper introduces solution for numeric evaluation of money laundering risk containing several different risk factors. For this purpose we consider the options for aggregation of risk factors and obtaining consolidated risk level. The proposed models are constructed using maximum t-conorm and Łukasiewicz...

Neural network language models become the main tool to solve tasks in NLP field. These models already have shown state-of-the-art results in classification, translation, named entity recognition and so on. Pre-trained models are distributed freely in the internet, and could be reused with help of transfer...

Cluster analysis aims at grouping objects represented by some feature vectors and as such revealing insight into subset structures among the considered objects. However, in many cases, the observations are subject to experimental errors and/or uncertainty. In such a case, a popular way is to summarize...

Relative information about locations of places can be described using the cardinal direction calculus (CDC). Some extensions of the calculus allow to express vague information and others include nearness/closeness. The development of description logics for qualitative spatial calculi has also been done....

Fuzzy relations that are not T -transitive have not merited as much scrutiny as their T - transitive counterparts. Recently monometrics on a given betweenness set, or a B-set, has garnered a lot of attention, especially for their role in decision making and penalty based data aggregation. In this work,...

In this work, we use a Mamdani fuzzy controller based on fuzzy rules that represent position and velocity of a particle for a free mechanical vibration model. Here, we focus on three major cases: the harmonic oscillator, the damped vibration, and the negative damping case. This study combines classical...

Recently many works have proposed different ways of obtaining orders from associative fuzzy logic operations. While the order ⊑ investigated by Karaçal and Kesicioğlu [10] was modified in [6] to obtain orders on uninorms, this order relation was based on the sub-domains of the arguments. Recently in...

In this paper we propose a new approach for forecasting the cryptocurrency time series, which combines the fuzzy transform and the fuzzy inference system. We also test whether fuzzy transform yields better results forecasting results in comparison to Fourier transform. Finally, we will investigate whether...

In this paper, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for the clarity. Then, we investigate the relation between introduced methods and present methods given in Theorem...

Need for faster and faster computing necessitates going down to quantum level -- which means involving quantum computing. One of the important features of quantum computing is that it is reversible. Reversibility is also important as a way to decrease processor heating and thus, enable us to place more...

Recently, the notation of the order induced by uninorms (t-norms, nullnorms) has been studied widely. In this paper, we study on the direct product of uninorms on bounded lattices. Also, we define an order induced by uninorms which are a direct product of two uninorms on bounded lattices. Also, we investigate...

The study investigates the proposed approach for behavior modeling on the base of Bayesian belief networks that allows predicting behavior characteristics using small and incomplete data from surveys about behavior episodes. We explored the prediction quality of the models in case of rare behavior. The...

Customer segmentation has been one of most important decision in marketing. In general, demographics of customers, monetary value of customer transactions, types of product/service used are the sources of segmentation process. In recent years, new technology enabled new sources of data. On of these new...

Starting with three bivariate copulas and some auxiliary univariate functions, we determine a construction method of trivariate copulas, which generalizes a class of copulas previously introduced by M. Úbeda-Flores (2005). Specifically, we provide a characterization of this class of 3–copulas and we...

In papers \cite{BartkovaCunderlikova18, BartkovaCunderlikova18p} we proved the Fisher-Tippett-Gnedenko theorem and the Pickands-Balkema-de Haan theorem on family of intuitionistic fuzzy events. Since between the intuitionistic fuzzy events and the interval valued events exist a connection, so we try...

At present, in the field of aggregation of various input values, attention is focused on the construction of aggregation functions using other functions that can affect the resulting aggregated value. This resulting value should characterize the properties of the individual input values as accurately...