Robert Fullér

7402383099

Publications - 27

Wasserstein distance for OWA operators

Lucian Coroianu István Harmati Robert Fullér

Publication Name: Fuzzy Sets and Systems

Publication Date: 2024-05-15

Volume: 484

Issue: Unknown

Page Range: Unknown

Description:

We suggest a distance measure for OWA operators. First we associate an OWA operator with a unique regular increasing monotone quantifier and then define the distance between two OWA operators as the Wasserstein-1 distance between their associated quantifiers.

Open Access: Yes

DOI: 10.1016/j.fss.2024.108931

The median under orness

Lucian Coroianu István Harmati Robert Fullér

Publication Name: Fuzzy Sets and Systems

Publication Date: 2024-04-01

Volume: 481

Issue: Unknown

Page Range: Unknown

Description:

Besides the mean, the median is the most widely used single-valued descriptor of data sets. It is well-known that the orness level of the median operator is 1/2. In this paper we provide approximations of the median operator under a given level of orness. We find the exact optimal weighting vector for the 1-norm approximation problem in all conceivable cases and for 2-norm approximation up to nine aggregates. The analytical results show that if the orness level is not 1/2, then not only the middle, but the extreme values also matter.

Open Access: Yes

DOI: 10.1016/j.fss.2024.108901

Best approximation of OWA Olympic weights under predefined level of orness

Lucian Coroianu István Harmati Robert Fullér

Publication Name: Fuzzy Sets and Systems

Publication Date: 2022-11-05

Volume: 448

Issue: Unknown

Page Range: 127-144

Description:

An ideal type of OWA aggregation operator is the one constructed on the so-called Olympic weights. The orness of this operator is 1/2. Therefore, sometimes we need a trade-off between the desire of having an OWA aggregation operator with weights as close as possible to the Olympic ones and the desire of having a predefined level of orness. In this paper, we choose these optimal weights by minimizing the Euclidean distance to the Olympic weights vector under the constraint of preserving a given level of orness. First, in the case n=4, we propose an iterative algorithm where the optimal solution is given for all possible values of the orness, values that are grouped along a partition of the unit interval. This iterative algorithm will inspire us to deduce the optimal weights in the general case. Consequently, we will obtain the analytical solution of the optimal weights as a function depending on the orness level.

Open Access: Yes

DOI: 10.1016/j.fss.2022.07.009

On stability of maximal entropy OWA operator weights

István Harmati I. Felde Robert Fullér

Publication Name: Fuzzy Sets and Systems

Publication Date: 2022-11-05

Volume: 448

Issue: Unknown

Page Range: 145-156

Description:

The maximal entropy OWA operator (MEOWA) weights can be obtained by solving a nonlinear programming problem with a linear constraint for the level of orness. Since the exact MEOWA weights are not known for the general case we can only find approximate solutions. We will prove that the nonlinear programming problem for obtaining MEOWA weights is well-posed: it has a unique solution and each MEOWA weight changes continuously with the initial level of orness. Using the implicit function theorem we will show that MEOWA weights are Lipschitz-continuous functions of the orness level. The stability property of the MEOWA weights under small changes of the orness level guarantees that small rounding errors of digital computation and small errors of measurement of the orness level can cause only a small deviation in MEOWA weights, i.e. every successive approximation method can be applied to the computation of the approximation of the exact MEOWA weights.

Open Access: Yes

DOI: 10.1016/j.fss.2022.01.003

An Iterative Approach for the Solution of the Constrained OWA Aggregation Problem with Two Comonotone Constraints

Lucian Coroianu Robert Fullér

Publication Name: Information Switzerland

Publication Date: 2022-10-01

Volume: 13

Issue: 10

Page Range: Unknown

Description:

In this paper, first, we extend the analytical expression of the optimal solution of the constrained OWA aggregation problem with two comonotone constraints by also including the case when the OWA weights are arbitrary non-negative numbers. Then, we indicate an iterative algorithm that precisely indicates whether a constraint in an auxiliary problem is either biding or strictly redundant. Actually, the biding constraint (or two biding constraints, as this case also may occur) are essential in expressing the solution of the initial constrained OWA aggregation problem.

Open Access: Yes

DOI: 10.3390/info13100443

Constrained ordered weighted averaging aggregation with multiple comonotone constraints

Lucian Coroianu Marek Gagolewski Robert Fullér Simon James

Publication Name: Fuzzy Sets and Systems

Publication Date: 2020-09-15

Volume: 395

Issue: Unknown

Page Range: 21-39

Description:

The constrained ordered weighted averaging (OWA) aggregation problem arises when we aim to maximize or minimize a convex combination of order statistics under linear inequality constraints that act on the variables with respect to their original sources. The standalone approach to optimizing the OWA under constraints is to consider all permutations of the inputs, which becomes quickly infeasible when there are more than a few variables, however in certain cases we can take advantage of the relationships amongst the constraints and the corresponding solution structures. For example, we can consider a land-use allocation satisfaction problem with an auxiliary aim of balancing land-types, whereby the response curves for each species are non-decreasing with respect to the land-types. This results in comonotone constraints, which allow us to drastically reduce the complexity of the problem. In this paper, we show that if we have an arbitrary number of constraints that are comonotone (i.e., they share the same ordering permutation of the coefficients), then the optimal solution occurs for decreasing components of the solution. After investigating the form of the solution in some special cases and providing theoretical results that shed light on the form of the solution, we detail practical approaches to solving and give real-world examples.

Open Access: Yes

DOI: 10.1016/j.fss.2019.09.006

Fuzzy control of self-balancing robots: A control laboratory project

Péter Odry Akos Odry I. J. Rudas Robert Fullér

Publication Name: Computer Applications in Engineering Education

Publication Date: 2020-05-01

Volume: 28

Issue: 3

Page Range: 512-535

Description:

This paper presents a novel control laboratory project that provides hands-on experience in feedback control concepts (embedded control systems) through dedicated assignments, with a particular focus on the design and implementation of fuzzy control. The project is structured around an inexpensive, portable self-balancing robot (SBR), whose embedded system is realized using commercially available breakout boards as the first assignment. For the stabilization of the plant, students are guided to execute the essential stages of control system design, from system modeling and parameter optimization, over basic or advanced control strategy design in the MATLAB/Simulink environment, to both implementation and validation of the closed loop on the real robot. To demonstrate and foster the application of fuzzy logic, the second part of the paper introduces a simple control strategy based on fuzzy logic controllers. Then, a lookup table-based implementation technique is described for the demonstration of manual interfacing and embedded coding of fuzzy control strategies. The proposed methods are clear and straightforward; they highly foster the understanding of feedback control techniques and allow students to gain vast knowledge in the practical implementations of control systems.

Open Access: Yes

DOI: 10.1002/cae.22219

On the lower limit for possibilistic correlation coefficient with identical marginal possibility distributions

István Harmati Robert Fullér

Publication Name: Studies in Computational Intelligence

Publication Date: 2019-01-01

Volume: 794

Issue: Unknown

Page Range: 99-113

Description:

In 2011 Fullér et al. [An improved index of interactivity for fuzzy numbers, Fuzzy Sets and Systems, 165 (2011), pp. 50–60] introduced a new measure of interactivity between fuzzy numbers (interpreted as possibility distributions), called the weighted possibilistic correlation coefficient, which can be determined from their joint possibility distribution. They also left two questions open regarding the lower limit of the weighted possibilistic correlation coefficient of marginal possibility distribution with the same membership function. In this paper we will answer these questions not only in the case of fuzzy numbers, but also for quasi fuzzy numbers.

Open Access: Yes

DOI: 10.1007/978-3-030-01632-6_7

On possibilistic version of distance covariance and correlation

István Harmati Robert Fullér

Publication Name: Studies in Computational Intelligence

Publication Date: 2019-01-01

Volume: 796

Issue: Unknown

Page Range: 175-181

Description:

Distance correlation is a relatively new measure of dependence in probability theory and statistics, which has the great advantage that it gives zero if and only if the variables are independent. In this paper we define its possibilistic version. Namely, we equip each γ -level set of the joint possibility distribution with a uniform probability distribution, then we determine the probabilistic distance covariance and correlation between the marginal distributions. Finally, the possibilistic distance covariance and correlation is computed as the weighted average of these probabilistic measures of dependence.

Open Access: Yes

DOI: 10.1007/978-3-030-00485-9_20

Minimum of Constrained OWA Aggregation Problem with a Single Constraint

Lucian Coroianu Robert Fullér

Publication Name: Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics

Publication Date: 2019-01-01

Volume: 11291 LNAI

Issue: Unknown

Page Range: 183-192

Description:

In a recent paper we found an analytical formula for the constrained ordered weighted aggregation problem (OWA) when we need to maximize the objective function. In this note we prove that the method works in the case when we need to minimize the objective function. If in the case of the maximization problem we need to rearrange the coefficients in the constrained in nondecreasing order, for the nontrivial minimization problem, it suffice to rearrange them in nonincreasing order.

Open Access: Yes

DOI: 10.1007/978-3-030-12544-8_15

Kalman filter for mobile-robot attitude estimation: Novel optimized and adaptive solutions

Péter Odry Akos Odry I. J. Rudas Robert Fullér

Publication Name: Mechanical Systems and Signal Processing

Publication Date: 2018-09-15

Volume: 110

Issue: Unknown

Page Range: 569-589

Description:

This paper proposes two novel approaches to estimate accurately mobile robot attitudes based on the fusion of low-cost accelerometers and gyroscopes. The first part of the paper demonstrates the use of a special test bench that both enables simulations of various dynamic behaviors of wheeled robots and measures their real attitude angles along with the raw sensor data. These measurements are applied in a simulation environment and we outline an offline optimization of Kalman filter parameters. The second part of the paper introduces a novel adaptive Kalman filter structure that modifies the noise covariance values according to the system dynamics. The instantaneous dynamics are characterized regarding the magnitudes of both the instantaneous vibration and the external acceleration. The proposed adaptive solution measures these magnitudes and utilizes fuzzy-logic to modify the filter parameters in real time. The results show that the adaptive filter improves the overall filter convergence by a remarkable 10.9% over using the optimized Kalman filter, thereby demonstrating its efficacy as an accurate and robust attitude filter. The proposed filter performances are also benchmarked against other common methods indicating that the flexibility of the developed adaptive filter allowed it to compete and even outperform the benchmark filters.

Open Access: Yes

DOI: 10.1016/j.ymssp.2018.03.053

Comparison of optimized PID and fuzzy control strategies on a mobile pendulum robot

Akos Odry Robert Fullér

Publication Name: Saci 2018 IEEE 12th International Symposium on Applied Computational Intelligence and Informatics Proceedings

Publication Date: 2018-08-20

Volume: Unknown

Issue: Unknown

Page Range: 207-212

Description:

S-This paper investigates the optimized control performances of fuzzy and proportional-integral-derivative (PID) control schemes developed for the stabilization of an under-actuated mobile robot. The fuzzy control strategy had been designed in an earlier paper, its equivalent PID controller-based scheme is established first. Then a complex cost function is defined that evaluates the reference tracking performance, the efficiency of system oscillations suppression and the average current consumption in the motor drive system. The particle swarm optimization (PSO) is applied to tune both control schemes under the same circumstances by minimizing the formulated cost function. Results demonstrate that the optimized fuzzy control strategy provides the same reference tracking quality with significantly better suppression of system oscillations and current peaks compared to the optimized PID control.

Open Access: Yes

DOI: 10.1109/SACI.2018.8440947

Nguyen type theorem for extension principle based on a joint possibility distribution

Lucian Coroianu Robert Fullér

Publication Name: International Journal of Approximate Reasoning

Publication Date: 2018-04-01

Volume: 95

Issue: Unknown

Page Range: 22-35

Description:

In this paper, first we prove that making abstraction of the output obtained from the interactive extension principle based on a joint possibility distribution, in the case of unimodal fuzzy numbers and when the function that generates the operation is continuous and strictly increasing in each argument restricted to the support of each fuzzy number used in the process, then we can use joint possibility distributions with the property that the left/right side of the output is obtained from the convolution of the values in the left/right side of these fuzzy numbers. Then, considering joint possibility distributions with the aforementioned property, we find an Nguyen type characterization of the level sets of the output based on interactive extension principle, in terms of the level sets of the fuzzy numbers used in the process. These two key results complete well-known results obtained in the case of Zadeh's extension principle and also in the case of triangular norm-based extension principle. As an interesting corollary, in the special case of unimodal fuzzy numbers, the Nguyen theorem can be used to present a new proof concerning necessary and sufficient conditions on the equality of the outputs based on joint possibility distributions, respectively based on Zadeh's extension principle.

Open Access: Yes

DOI: 10.1016/j.ijar.2018.01.007

On the constrained OWA aggregation problem with single constraint

Lucian Coroianu Robert Fullér

Publication Name: Fuzzy Sets and Systems

Publication Date: 2018-02-01

Volume: 332

Issue: Unknown

Page Range: 37-43

Description:

In this note we present a simple proof for the constrained OWA aggregation problem with a single constraint but with variable coefficients.

Open Access: Yes

DOI: 10.1016/j.fss.2017.04.013

Necessary and sufficient conditions for the equality of interactive and non-interactive extensions of continuous functions

Lucian Coroianu Robert Fullér

Publication Name: Fuzzy Sets and Systems

Publication Date: 2018-01-15

Volume: 331

Issue: Unknown

Page Range: 116-130

Description:

In this contribution we find the class of n-dimensional joint possibility distributions with the property that the interactive extension principle coincides with the non-interactive extension principle as long as the interactive operations are determined by continuous functions strictly increasing in each argument. This result completes recent studies by the authors, where the particular case of interactive additions and multiplications versus non-interactive additions and multiplications were investigated. In addition, this time we propose results that also cover the cases when we know the fuzzy numbers only from their membership functions. It means that we eliminated the limitations that appear when we cannot pass from membership function representation to parametric representation of fuzzy numbers. As important new applications, we mention the study on the completely correlated fuzzy numbers. Also of note is that we propose two simple methods to extend bidimensional joint possibility distributions to n-dimensional joint possibility distributions. One method is based on an inductive construction while the other one is based on a pairwise construction.

Open Access: Yes

DOI: 10.1016/j.fss.2017.07.023

On measures of dependence between possibility distributions

István Harmati P. Várlaki Robert Fullér

Publication Name: Acta Polytechnica Hungarica

Publication Date: 2018-01-01

Volume: 15

Issue: 1

Page Range: 231-246

Description:

A measure of possibilistic correlation between marginal possibility distributions of a joint possibility distribution can be defined as (see Fullér, Mezei and Várlaki, An improved index of interactivity for fuzzy numbers, Fuzzy Sets and Systems, 165(2011), pp. 56-66) the weighted average of probabilistic correlations between marginal probability distributions whose joint probability distribution is defined to be uniform on the level sets of their joint possibility distribution. Using the averaging technique we shall discuss three quantities (correlation coefficient, correlation ratio and informational coefficient of correlation) which are used to measure the strength of dependence between two possibility distributions. We discuss the inverse problem, as we introduce a method to construct a joint possibility distribution for a given value of possibilistic correlation coefficient. We also discuss a special case when the joint possibility distribution is defined by the so-called weak t-norm and based on these results, we make a conjecture as an open problem for the range of the possibilistic correlation coefficient of any t-norm based joint distribution.

Open Access: Yes

DOI: 10.12700/APH.15.1.2018.1.14

On possibilistic dependencies: A short survey of recent developments

István Harmati Robert Fullér

Publication Name: Studies in Fuzziness and Soft Computing

Publication Date: 2018-01-01

Volume: 360

Issue: Unknown

Page Range: 261-273

Description:

Carlsson and Fullér introduced the notions of possibilistic mean value and variance of fuzzy numbers. Fullér and Majlender introduced a measure of possibilistic covariance between marginal distributions of a joint possibility distribution as the average value of the interactivity relation between the level sets of its marginal distributions. Fullér et al. introduced the possibilistic correlation ratio, the possibilistic correlation coefficient and the possibilistic informational coefficient of correlation. In this paper we give a short survey of some later works which extend and develop these notions.

Open Access: Yes

DOI: 10.1007/978-3-319-64286-4_16

Unsupervised clustering for deep learning: A tutorial survey

Péter Galambos Artúr István Károly Robert Fullér

Publication Name: Acta Polytechnica Hungarica

Publication Date: 2018-01-01

Volume: 15

Issue: 8

Page Range: 29-53

Description:

Unsupervised learning methods play an essential role in many deep learning approaches because the training of complex models with several parameters is an extremely data-hungry process. The execution of such a training process in a fully supervised manner requires numerous labeled examples. Since the labeling of the training samples is very time-consuming, learning approaches that require less or no labeled examples are sought. Unsupervised learning can be used to extract meaningful information on the structure and hierarchies in the data, relying only on the data samples without any ground truth provided. The extracted knowledge representation can be used as a basis for a deep model that requires less labeled examples, as it already has a good understanding of the hidden nature of the data and should be only fine-tuned for the specific task. The trend for deep learning applications most likely leads to substituting as much portion of supervised learning methods with unsupervised learning as possible. Regarding this consideration, our survey aims to give a brief description of the unsupervised clustering methods that can be leveraged in case of deep learning applications.

Open Access: Yes

DOI: 10.12700/APH.15.8.2018.8.2

Maximal entropy and minimal variability OWA operator weights: A short survey of recent developments

Christer Carlsson Robert Fullér

Publication Name: Studies in Fuzziness and Soft Computing

Publication Date: 2018-01-01

Volume: 357

Issue: Unknown

Page Range: 187-199

Description:

The determination of ordered weighted averaging (OWA) operator weights is a very important issue of applying the OWA operator for decision making. One of the first approaches, suggested by O’Hagan, determines a special class of OWA operators having maximal entropy of the OWA weights for a given level of orness; algorithmically it is based on the solution of a constrained optimization problem. In 2001, using the method of Lagrange multipliers, Fullér and Majlender solved this constrained optimization problem analytically and determined the optimal weighting vector. In 2003 Fullér and Majlender computed the exact minimal variability weighting vector for any level of orness using the Karush-Kuhn-Tucker second-order sufficiency conditions for optimality. The problem of maximizing an OWA aggregation of a group of variables that are interrelated and constrained by a collection of linear inequalities was first considered by Yager in 1996, where he showed how this problem can be modeled as a mixed integer linear programming problem. In 2003 Carlsson, Fullér and Majlender derived an algorithm for solving the constrained OWA aggregation problem under a simple linear constraint: the sum of the variables is less than or equal to one. In this paper we give a short survey of numerous later works which extend and develop these models.

Open Access: Yes

DOI: 10.1007/978-3-319-60207-3_12

Characterization of the level sets for interactive additions

Lucian Coroianu Robert Fullér

Publication Name: Cinti 2016 17th IEEE International Symposium on Computational Intelligence and Informatics Proceedings

Publication Date: 2017-02-07

Volume: Unknown

Issue: Unknown

Page Range: 35-40

Description:

In this paper, on the set of unimodal fuzzy numbers, first we prove that under some minimal assumptions, it suffices to consider only those joint possibility distributions that satisfy that the left/right side of the fuzzy number generated by the interactive addition based on the given joint possibility distribution, is obtained by evaluating only the left/right side of the summands. Then, we will obtain a representation theorem for the level sets of this interactive addition in terms of the level sets of the summands. These results generalize corresponding results for the special case of triangular-norm-based additions.

Open Access: Yes

DOI: 10.1109/CINTI.2016.7846376

On weighted possibilistic informational coefficient of correlation

István Harmati P. Várlaki I. J. Rudas Robert Fullér

Publication Name: International Journal of Mathematical Models and Methods in Applied Sciences

Publication Date: 2012-12-19

Volume: 6

Issue: 4

Page Range: 592-599

Description:

In their previous works Fullér et al. introduced the notions of weighted possibilistic correlation coefficient and correlation ratio as measures of dependence between possibility distributions (fuzzy numbers). In this paper we introduce a new measure of strength of dependence between marginal possibility distributions, which is based on the informational coefficient of correlation. We will show some examples that demonstrate some good properties of the proposed measure.

Open Access: Yes

DOI: DOI not available

Probabilistic correlation coefficients for possibility distributions

István Harmati P. Várlaki Robert Fullér

Publication Name: Ines 2011 15th International Conference on Intelligent Engineering Systems Proceedings

Publication Date: 2011-08-22

Volume: Unknown

Issue: Unknown

Page Range: 153-158

Description:

The goal of this paper to introduce two alternative definitions for the possibilistic correlation coefficient by equipping the level sets of a joint possibility distribution with nonuniform probability distributions which are directly derived from the shape function of the joint possibility distribution. We also show some examples for their exact calculation for joint possibility distributions defined by Mamdani, Łukasiewicz and Larsen triangular norms. © 2011 IEEE.

Open Access: Yes

DOI: 10.1109/INES.2011.5954737

On possibilistic correlation coefficient and ratio for fuzzy numbers

József Mezei István Harmati P. Várlaki Robert Fullér

Publication Name: Recent Researches in Artificial Intelligence Knowledge Engineering and Data Bases 10th Wseas International Conference on Artificial Intelligence Knowledge Engineering and Data Bases Aiked 11

Publication Date: 2011-06-17

Volume: Unknown

Issue: Unknown

Page Range: 263-268

Description:

In this paper we show some properties of possibilistic correlation coefficient and correlation ratio for marginal possibility distributions. We will show some examples for their computation from some joint possibility distributions.

Open Access: Yes

DOI: DOI not available

An improved index of interactivity for fuzzy numbers

József Mezei P. Várlaki Robert Fullér

Publication Name: Fuzzy Sets and Systems

Publication Date: 2011-02-16

Volume: 165

Issue: 1

Page Range: 50-60

Description:

In this paper we will introduce a new index of interactivity between marginal possibility distributions A and B of a joint possibility distribution C. The starting point of our approach is to equip each γ-level set of C with a uniform probability distribution, then the probabilistic correlation coefficient between its marginal probability distributions is interpreted as an index of interactivity between the γ-level sets of A and B. Then we define the index of interactivity between A and B as the weighted average of these indexes over the set of all membership grades. This new index of interactivity is meaningful for the whole family of joint possibility distributions. © 2010 Elsevier B.V. All rights reserved.

Open Access: Yes

DOI: 10.1016/j.fss.2010.06.001

On possibilistic correlation coefficient and ratio for triangular fuzzy numbers with multiplicative joint distribution

István Harmati P. Várlaki Robert Fullér

Publication Name: 11th IEEE International Symposium on Computational Intelligence and Informatics Cinti 2010 Proceedings

Publication Date: 2010-12-01

Volume: Unknown

Issue: Unknown

Page Range: 103-108

Description:

The goal of this paper is to provide calculation formulas for the possibilistic correlation coefficient and ratio for two marginal possibility distributions of triangular form when their joint possibility distribution is defined by the product t-norm. We will also introduce an alternative definition for the possibilistic correlation coefficient and ratio when their joint possibility distribution is defined by the product t-norm. ©2010 IEEE.

Open Access: Yes

DOI: 10.1109/CINTI.2010.5672266

Some examples of computing the possibilistic correlation coefficient from joint possibility distributions

József Mezei P. Várlaki Robert Fullér

Publication Name: Studies in Computational Intelligence

Publication Date: 2010-11-03

Volume: 313

Issue: Unknown

Page Range: 153-170

Description:

In this paper we will show some examples for computing the possibilistic correlation coefficient between marginal distributions of a joint possibility distribution. First we consider joint possibility distributions, (1-x-y), (1-x 2-y 2), and (1-x 2-y) on the set {(x,y)≡R2| x≥0,y≥0,x+y≤1}, then we will show (i) how the possibilistic correlation coefficient of two linear marginal possibility distributions changes from zero to -1/2, and from -1/2 to -3/5 by taking out bigger and bigger parts from the level sets of a their joint possibility distribution; (ii) how to compute the autocorrelation coefficient of fuzzy time series with linear fuzzy data. © 2010 Springer-Verlag Berlin Heidelberg.

Open Access: Yes

DOI: 10.1007/978-3-642-15220-7_13

A correlation ratio for possibility distributions

József Mezei P. Várlaki Robert Fullér

Publication Name: Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics

Publication Date: 2010-07-29

Volume: 6178 LNAI

Issue: Unknown

Page Range: 178-187

Description:

Generalizing the probabilistic correlation ratio we will introduce a correlation ratio for marginal possibility distributions of joint possibility distributions. © 2010 Springer-Verlag Berlin Heidelberg.

Open Access: Yes

DOI: 10.1007/978-3-642-14049-5_19