Susanne Saminger-Platz

Johannes Kepler University of Linz | JKU · Department of Knowledge-Based Mathematical Systems

Comprehensive families of copulas including the three basic copulas (at least as limit cases) are useful tools to model countermonotonicity, independence, and comonotonicity of pairs of random variables on the same probability space. In this contribution, we study how the transition from a (basic) copula to a copula modeling a different dependence...

One of the key problems in learning theory is to compute a function $f$ that closely approximates the relationship between some input $x$ and corresponding output $y$, such that $y\approx f(x)$. This approximation is based on sample points $(x_t,y_t)_{t=1}^{m}$, where the function $f$ can be approximated within reproducing kernel Hilbert spaces usi...

The Seventeenth International Conference on Fuzzy Set Theory and Applications Liptovský Ján, Slovak Republic January 28 - February 2, 2024

We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, 1-increasing functions with value $1$ at $(1,1,\ldots, 1)$. We characterize the existence of a $k$-increasing $n$-variate function $C$ fulfilling $A\leq C\leq B$ for standardized $n$-variate functions $A,B$ and discuss the method...

Copulas are functions that link an n-dimensional distribution function with its one-dimensional margins. In this contribution we show how n-variate copulas with given values at two arbitrary points can be constructed. Thereby, we also answer a so far open question whether lower and upper bounds for n-variate copulas with given value at a single arb...

Following a historical overview of the development of ordinal sums, a presentation of the most relevant results for ordinal sums of triangular norms and copulas is given (including gluing of copulas, orthogonal grid constructions and patchwork operators). The ordinal sums of copulas considered here are constructed not only by means of the comonoton...

A prominent example of a perturbation of the bivariate product copula (which characterizes stochastic independence) is the parametric family of Eyraud-Farlie-Gumbel-Morgenstern copulas which allows small dependencies to be modeled. We introduce and discuss several perturbations, some of them perturbing the product copula, while others perturb gener...

We demonstrate the establishment of data‐driven prediction and explanation models for three essential process variables in ironmaking blast furnace processes, namely hot metal temperature, silicon concentration and cooling capacity. Aside a reliable prediction quality of the models with sufficient prediction horizon, an additional main goal has bee...

Bivariate polynomial copulas of degree 5 (containing the family of Eyraud-Farlie-Gumbel-Morgenstern copulas) are in a one-to-one correspondence to certain real parameter triplets (a, b, c), i.e., to some set of polynomials in two variables of degree 1: p(x, y) = ax + by + c. The set of the parameters yielding a copula is characterized and visualize...

Domain adaptation algorithms are designed to minimize the misclassification risk of a discriminative model for a target domain with little training data by adapting a model from a source domain with a large amount of training data. Standard approaches measure the adaptation discrepancy based on distance measures between the empirical probability di...

We consider the problem of unsupervised domain adaptation (DA) in regression under the assumption of linear hypotheses (e.g. Beer–Lambert’s law) – a task recurrently encountered in analytical chemistry. Following the ideas from the non-linear iterative partial least squares (NIPALS) method, we propose a novel algorithm that identifies a low-dimensi...

Several extensions of the family of (bivariate) Eyraud-Farlie-Gumbel-Morgenstern copulas (EFGM copulas) are considered. Some of them are well-known from the literature, others have recently been suggested (copulas based on quadratic constructions, based on some forms of convexity, and polynomial copulas). For each of these extensions we analyze whi...

We start with some binary (“outer”) copula, apply it to an arbitrary binary (“inner”) copula and its dual (the latter being transformed by some real function) and ask under which conditions the result is again a binary copula. Sufficient convexity conditions for the transformation function and for the “outer” copula (ultramodularity and Schur conca...

We describe initial attempts to model the dynamic thermal behavior of electrical machines by evaluating the ability of linear and non-linear (regression) modeling techniques to replicate the performance of simulations carried out using a lumped parameter thermal network (LPTN) and two different test scenarios. Our focus falls on creating highly acc...

This paper describes a new transfer learning method for modeling sensor time series following multiple different distributions, e.g. originating from multiple different tool settings. The method aims at removing distribution specific information before the modeling of the individual time series takes place. This is done by mapping the data to a new...

Domain adaptation algorithms are designed to minimize the misclassification risk of a discriminative model for a target domain with little training data by adapting a model from a source domain with a large amount of training data. Standard approaches measure the adaptation discrepancy based on distance measures between the empirical probability di...

We consider the problem of unsupervised domain adaptation (DA) in regression under the assumption of linear hypotheses (e.g. Beer-Lambert's law) – a task recurrently encountered in analytical chemistry. Following the ideas from the non-linear iterative partial least squares (NIPALS) method, we propose a novel algorithm that identifies a low-dimensi...

Purpose The paper aims to raise awareness in the industry of design automation tools, especially in early design phases, by demonstrating along a case study the seamless integration of a prototypically implemented optimization, supporting design space exploration in the early design phase and an in operational use product configurator, supporting t...

A novel approach for unsupervised domain adaptation for neural networks is proposed that relies on a metric-based regularization of the learning process. The metric-based regularization aims at domain-invariant latent feature representations by means of maximizing the similarity between domain-specific activation distributions. The proposed metric...

We describe an effective optimization strategy that is capable of discovering innovative cost-optimal designs of complete ascent assembly structures. Our approach relies on a continuous 2D model abstraction, an application-inspired multi-objective formulation of the optimal design task and an efficient coevolutionary solver. The obtained results pr...

We describe two enhancements that significantly improve the rapid convergence behavior of DECMO2-a previously proposed robust coevolutionary algorithm that integrates three different multi-objective space exploration paradigms: differential evolution, two-tier Pareto-based selection for survival and decomposition-based evolutionary guidance. The fi...

Multivariate calibration models often fail to extrapolate beyond the calibration samples due to changes associated with the instrumental response, environmental condition or sample matrix. Most of the current methods used to adapt a source calibration model to a target domain exclusively apply to calibration transfer between similar analytical devi...

Tribological systems are mechanical systems that rely on friction to transmit forces. The design and dimensioning of such systems requires prediction of various characteristic, such as the coefficient of friction. The core contribution of this paper is the analysis of two data-based modeling techniques which can be used to produce accurate and at t...

We describe initial results obtained when applying different multi-objective evolutionary algorithms (MOEAs) to direct topology optimization (DTO) scenarios that are relevant in the field of electrical machine design. Our analysis is particularly concerned with investigating if the use of discrete or real-value encodings combined with a preference...

We present an effective optimization strategy that is capable of discovering high-quality cost-optimal solution for 2D path network layouts (i.e., groups of obstacle-avoiding Euclidean Steiner trees) that, among other applications, can serve as templates for complete ascent assembly structures. The main innovative aspect of our approach is that ou...

In this paper we study the smallest and the greatest M-Lipschitz continuous n-ary aggregation functions with a given diagonal section. We show that several properties that were studied for the smallest and the greatest 1-Lipschitz continuous binary aggregation functions with a given diagonal section extend naturally to higher dimensions while consi...

We discuss several types of ordinal sums for conjunctive operations for an infinite set of truth values (modeled by the real unit interval). In some cases, they can be seen as both a construction method and a representation (for example, when considering copulas), this is no more true for the product-based ordinal sums when considering quasi-copula...

In this paper, we propose a new strategy for retrospective identification of feed phases from online sensor-data enriched feed profiles of an Escherichia Coli (E. coli) fed-batch fermentation process. In contrast to conventional (static), data-driven multi-class machine learning (ML), we exploit process knowledge in order to constrain our classific...

The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the domain-specific latent feature representations directly in the hidden activation space. Although some standard distribution matching approaches exist that can be interpret...

Based on a general construction method by means of bivariate ultramodular copulas we construct, for particular settings, special bivariate conic, extreme value, and Archimax copulas. We also show that the sets of copulas obtained in this way are dense in the sets of all conic, extreme value, and Archimax copulas, respectively.

We study a generalized Frank functional equation in the broader framework of associative aggregation functions and show that, up to the two projections, we obtain exactly the same set of solutions as in the original paper by M. J. Frank (Aequationes Mathematicae 19, 1979).

We discuss and stress the role of ultramodularity and Schur concavity in special types of constructions of copulas. After recalling some known ultamodularity-based results, we focus on the so-called D-product of a copula and its dual. We show that for each copula D which is ultramodular and Schur concave on the left upper triangle of the unit squar...

Six different functions measuring the defect of a quasi-copula, i. e., how far away it is from a copula, are discussed. This is done by means of extremal non-positive volumes of specific rectangles (in a way that a zero defect characterizes copulas). Based on these defect functions, six transformations of quasi-copulas are investigated which give r...

We propose the use of a fuzzy system evaluating a feature space extracted from the daily power production profile of a photovoltaic solar plant. The fuzzy system proposed is able to detect inverter power limiting situations, as well as stages where the photovoltaic solar plant is showing steady state power production. The approach has been validate...

The book is a collection of contributions by leading experts, developed around traditional themes discussed at the annual Linz Seminars on Fuzzy Set Theory. The different chapters have been written by former PhD students, colleagues, co-authors and friends of Peter Klement, a leading researcher and the organizer of the Linz Seminars on Fuzzy Set Th...

Two new ways to construct involutive residuated semigroups are introduced in this paper, namely, connected and disconnected co-rotation-annihilations. Co-rotation-annihilations utilizes two particular kinds of residuated semigroups to construct a third one. The method is suitable for constructing a large class of examples of negative rank involutiv...

Graded properties of binary and unary fuzzy connectives (valued in MTL△MTL△-algebras) are studied, including graded monotony, a generalized Lipschitz property, commutativity, associativity, unit and null elements, and the dominance relation between fuzzy connectives. The apparatus of Fuzzy Class Theory (or higher-order fuzzy logic) is employed as a...

In Saminger-Platz and Sempi (Aequationes Math 76:201–240, 2008) we presented an overview of concepts, facts and results on triangle functions based on the notions of t-norm, copula, (generalized) convolution, semicopula, quasi-copula. Here, we continue our presentation. In particular, we treat the concept of duality and study a few important cases...

The dominance relationship between two members of the family of Sugeno Weber t-norms is proven by using a quantifer elimination algorithm. Further it is shown that dominance is a transitive, and therefore also an order relation, on this family of t-norms.

The paper studies graded properties of MTL_Delta-valued binary connectives, focusing on conjunctive connectives such as t-norms, uninorms, aggregation operators, or quasicopulas. The graded properties studied include monotony, a generalized Lipschitz property, unit and null elements, commutativity, associativity, and idempotence. Finally, a graded...

We present a method for constructing bivariate copulas by changing the values that a given copula assumes on some subrectangles of the unit square. Some applications of this method are discussed, especially in relation to the construction of copulas with different tail dependencies.

The dominance relation in several families of continuous Archimedean t-norms and copulas is investigated. On the one hand, the contribution provides a comprehensive overview on recent conditions and properties of dominance as well as known results for particular cases of families. On the other hand, it contains new results clarifying the dominance...

Dominance between triangular norms (t-norms) is a versatile relationship. For con- tinuous Archimedean t-norms, dominance can be verified by checking one of many sufficient conditions derived from a generalization of the Mulholland inequality. These conditions pertain to various convexity properties of compositions of additive generators and their...

As is well known, the Fréchet–Hoeffding bounds are the best possible for both copulas and quasi-copulas: for every (quasi-) copula Q, max{x+y−1,0}≤Q(x,y)≤min{x,y} for all x,y∈[0,1]. Sharper bounds hold when the (quasi-)copulas take prescribed values, e.g., along their diagonal or horizontal resp. vertical sections. Here we pursue two goals: first,...

In this paper, we provide two different representations of 2-increasing binary aggregation functions by means of their lower and upper margins and a suitable copula.

This primer aims at providing an overview of existing concepts and facts about triangle functions as they have been presented in [41]. Moreover, it contains new results on triangle functions and proofs for results not easily available. In this first part we present the most important classes of triangle functions, based on the recent notions of sem...

In recent years, there has been a raise of interest in the determination of copulas with given values at some fixed points, or with given horizontal, vertical, affine, diagonal, or sub-diagonal sections and combinations thereof. Closely related to these investigations are the determination and characterization of increasing and 2-increasing functio...

It is well known that dominance between strict t-norms is closely related to the Mulholland inequality, which can be seen as a generalization of the Minkowski inequality. However, strict t-norms constitute only one part of the class of continuous Archimedean t-norms, the basic elements from which all continuous t-norms are composed. In this paper,...

Smallest and largest possible extensions of triangular norms on bounded lattices are discussed. As such ordinal and horizontal sum like constructions for t-norms on bounded lattices are investigated. Necessary and sufficient conditions for the lattice guaranteeing that the extension is again a t-norm are revealed.

Graded properties of binary and unary fuzzy connectives (valued in MTL-algebras) are studied, including graded monotony, a generalized Lipschitz property, commutativity, associativity, unit and null elements, and the dominance relation between fuzzy connectives. The apparatus of Fuzzy Class Theory (or higher-order fuzzy logic) is employed as a tool...

We present an environment for learning and teaching mathematics that aims at inspiring the creative potential of students by enabling the learners to perform various kinds of interactive experiments during their learning process. Computer interactions are both of visual and purely formal mathematical nature, where the computer-algebra system Mathem...

Commuting is an important property in any two-step information merging procedure where the results should not depend on the order in which the single steps are performed. We investigate the property of commuting for aggregation operators in connection with their relationship to bisymmetry. In case of bisymmetric aggregation operators we show a suff...

CreaComp provides an electronic environment for learning and teaching math- ematics that aims at inspiring the creative potential of students. During their learning process, students are encouraged to engage themselves in various kinds of interactive experiments, both of visual and purely formal mathematical na- ture. The computer-algebra system Ma...

Two different characterizations of self-dual aggregation operators are available in the literature: one based on C(x,y)=x/(x+1-y) and one based on the arithmetic mean. Both approaches construct a self-dual aggregation operator by combining an aggregation operator with its dual. In this paper, we fit these approaches into a more general framework an...

Dominance is a relation on operations which are defined on a common poset. We treat the dominance relation on the set of ordinal sum t-norms which involve either exclusively the Lukasiewicz t-norm or exclusively the product t-norm as summand operations. We show that in both cases, the question of dominance can be reduced to a simple property of the...

Ordinal sums have been introduced in many different contexts, e.g., for posets, semigroups, t-norms, copulas, aggregation operators, or quite recently for hoops. In this contribution, we focus on ordinal sums of t-norms acting on some bounded lattice which is not necessarily a chain or an ordinal sum of posets. Necessary and sufficient conditions a...

This contribution provides a comprehensive overview on the theoretical framework of aggregating fuzzy relations under the premise of preserving underlying transitivity conditions. As such it discusses the related property of dominance of aggregation operators. After a thorough introduction of all necessary and basic properties of aggregation operat...

This paper addresses the added value that is provided by using distance-based fuzzy relations in flexible query answering. To use distances and/or concepts of gradual similarity in that domain is not new. Within the last ten years, however, results in the theory of fuzzy relations have emerged that permit a smooth and pragmatic, yet ex- pressive an...

This paper addresses the relation of dominance on the class of continuous t-norms with a particular focus on continuous ordinal sum t-norms. Exactly, in this framework counter-examples to the conjecture that dominance is not only a reflexive and antisymmetric, but also a transitive relation could be found. We elaborate the details which have led to...

This contribution deals with the dominance relation on the class of conjunctors, containing as particular cases the subclasses of quasi-copulas, copulas and t-norms. The main results pertain to the summand-wise nature of the dominance relation, when applied to ordinal sum conjunctors, and to the relationship between the idempotent elements of two c...

The present contribution deals with domination in the framework of continuous t-norms. Ba- sic properties and recent results for continuous Archimedean and continuous ordinal sum t-norms are presented and discussed. The domination property within several families of t-norms is men- tioned.

Ordinal sums of t-norms on bounded lattices are discussed. It is shown that this construction leads always to a t-norm in the case of horizontal sums of chains. Moreover, we obtain a t-norm also if the underlying lattice is an ordinal sum (in the sense of Birkho) of the carriers of the summands.

Abstract Two difierent characterizations of self-dual aggre- gation operators are available in the literature: one based on CCC(x;y) = x=(x + 1 ¡ y) and one based on the arithmetic mean. In this contribu- tion, we flt the existing approaches into a more general framework and characterize N-invariant aggregation operators, with N an involutive nega-...

The fusion of transitive fuzzy relations preserving the transitivity is linked to the domination of the involved aggregation operator. The aim of this contribution is to investigate the domination of OWA operators over t-norms whereas the main emphasis is on the domination over the ukasiewicz t-norm. The domination of OWA operators and related oper...

We propose a concept of decomposable bi-capacities based on an analogous property of decomposable capacities, namely the valuation property. We will show that our approach extends the already existing concepts of decomposable bi-capacities. We briefly discuss additive and k-additive bi-capacities based on our definition of decomposability. Finally...

Aggregation processes are fundamental in any discipline where the fusion of information is of vital interest. For aggregating binary fuzzy relations such as equivalence relations or fuzzy orderings, the question arises which aggregation operators preserve specific properties of the underlying relations, e.g. T-transitivity. It will be shown that pr...