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 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...

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...

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...

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....

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...

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....

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...

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...

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...

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...

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....

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...

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...

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...

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,...

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,...

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...

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...

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...

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...

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...

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...

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...

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...

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 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...

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 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...

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...

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...

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...

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...

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 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...

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...

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...

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...

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...

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 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...

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...

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,...

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...

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.

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”,...

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...

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...

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...

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

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...

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...

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,...

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...

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...

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...

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...

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...

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 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...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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...

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...

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...

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).

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....

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...

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...

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,...

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 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...

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...

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...

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...

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...

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...

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...