INVITED LECTURES

BACZYŃSKI Michał

Title: New Horizons in Fuzzy Logic Connectives: Structural Theory and Recent Advances

This plenary lecture surveys selected developments from recent years in the theory of fuzzy logic connectives, with emphasis on conjunctions (t-norms), disjunctions (t-conorms), and fuzzy implication functions. The focus is on algebraic and order-theoretic properties, construction principles, representation issues, and comparative frameworks for different classes of connectives. Joint works of Baczyński-Dombi, Baczyński-Reformat, and Baczyński-Kaczmarek-Miś are discussed. Selected applications of fuzzy logic connectives in machine learning are also outlined. The talk concludes with an outlook on future research directions.

Javier Fernandez

Title: From Choquet-inspired to Choquet-functional integrals

In recent years, it is developing a growing interest on the use of fuzzy integrals for information fusion in different processes, ranging from deep learning to classification. This is due to the abaility of these techniques to represent relationships between data by means of an appropriate choice of the involved fuzzy measures. However, one of the main drawbacks of fuzzy integrals lays precisely on the difficulty and the computational cost of building the measures, as well as in the need to make a previous ordering of the inputs. For these reasons, some researchers, including my group, have been devloping new functions to fuse information which follow the spirit of Choquet integrals (as one of the main representatives of fuzzy integrals) but may provide a way to overcome this problems. In this talk, we are going to discuss the notion of Choquet-inspired function, as a function which mimics the structure of a discrete Choquet integral but replaces the measure by other functions, hence providing a more general framework to work. We will also show how these Choquet-inspired functions can be further extended to provide the so-called Choquet-functional integrals, which can be seen as a very general tool with many different applications. We will present all the relevant definitions, the main properties and the relation with usual fuzzy integrals. We will discuss some applications where these new approaches have shown themselves useful.

DE BAETS Bernard

Title: Law & Order: New Kids on the Block

Shortly after Lotfi Zadeh introduced fuzzy sets in the 1960s, Joe Goguen recognized that a lattice-theoretic framework — particularly that of complete residuated lattices — provides the most suitable foundation for developing fuzzy set theory. This challenge was taken up by numerous researchers, contributing not only to fuzzy set theory itself but also to the advancement of lattice theory. A similar observation applies to the fields of formal concept analysis and mathematical morphology. While the lattice-theoretic approach centers on the notion of an order relation (combining reflexivity, antisymmetry, and transitivity), an equally important role in fuzzy set theory is played by equivalence relations (combining reflexivity, symmetry, and transitivity) and by their transitive and non-transitive fuzzy generalizations. Notably, the transitive notions of order and equivalence converge in the context of pre-order relations. Given the close connection between fuzzy set theory and decision-making, even more general relational structures have been explored. Of particular importance are (fuzzy) preference structures consisting of a strict preference (generalizing strict order relations), an indifference (generalizing equivalence relations), and an incomparability component. The property of transitivity in this setting requires careful reflection and analysis. A notable example is that of pseudo-order relations, which may be non-transitive and can accommodate cycles. A characteristic feature of lattices is the existence of meet and join operations, binary operations that fulfill the laws of monotonicity and associativity. The concepts of lattices and pseudo-order relations jointly inspired Helen Skala in the 1970s to introduce trellises, a generalization of lattices that preserves the existence of meet and join operations while abandoning the transitivity of the underlying pseudo-order relation. Similarly, sponges represent a more recent generalization of complete lattices. Trellises have only recently attracted the attention of the fuzzy community. In this lecture, we provide a comprehensive overview of these structures, discussing both the motivations for and the caveats against their study in fuzzy set theory. In particular, we focus on alternatives to the monotonicity property, since in proper trellises the meet and join operations are no longer monotone (nor associative) and we explore the notion of triangular norms in this context.

FLAMINIO Tommaso

Title: Fuzzy Logic and Probability Theory are Cooperative (Rather than Complementary or Competitive)

Since its inception, fuzzy logic has been frequently compared with (and sometimes equated to) probability theory. Over the years, several attempts have been made to clarify the philosophical, mathematical, logical, and applicative differences between these two theories. Interestingly, two crucial papers addressing this topic were published in 1995: (1) “Probability Theory and Fuzzy Logic Are Complementary Rather Than Competitiv”, by Zadeh, and (2) “Probability and Fuzzy Logic”, by Hájek, Esteva, and Godo. The present talk aims to draw on recent literature that builds upon the paper by Hájek, Esteva, and Godo (2) in order to offer an additional perspective on the discussion initiated by Zadeh’s paper (1). Our goal, therefore, is not to further clarify the distinction between fuzzy logic and probability (or uncertainty in general). Rather, we aim to support the idea that these two theories often operate in a cooperative manner. We will support our general claim by showing how fuzzy logic aids probability theory in its generalization, and how probability theory can be (partially) reduced, interpreted, and represented within a formal fuzzy-logical framework.

RICO Agnès

Title: Integral Explanation

Today, decision support systems are widely used to help humans make decisions when selecting objects or alternatives. Qualitative representations and their use in reasoning processes have long been part of artificial intelligence (AI) since they are well aligned with human cognition and reasoning. One of their main advantages is their naturalness, as well as their ability to support reasoning with limited data. Although qualitative approaches are less expressive than quantitative ones, they can provide more robust results with much less effort. In this context it is natural to look for qualitative aggregation operators. Sugeno integrals are commonly used as aggregation functions in decision theory within a symbolic framework. They compute a global evaluation of alternatives or objects assessed on several criteria using an ordinal evaluation scale. They are based on set functions called capacities, or fuzzy measures. Generalized versions of Sugeno integrals extend the way the capacity value of each subset of criteria is combined with the utility values of the elements in the subset. This generalized notion of the Sugeno integral can be split into two functionals. In this talk, we focus on a particular case: Gödel integrals. Moreover both Sugeno integrals and Gödel integrals may be elicitated to represent and explain a dataset. In conclusion, Gödel integrals are applied in the field of explainable AI (XAI) to provide explanations that are better adapted to users, particularly in the case of counterfactual examples. An interactive incremental algorithm to elicit capacities for Gödel integrals, applied to the aggregation of two types of criteria present in counterfactual examples selection is presented.

VOMLEL Jiří

Title: Fuzzy Transforms Meet Bayesian Networks in Sociological Data Analysis

This talk explores the synergy between fuzzy set theory and Bayesian networks for modeling uncertainty in real-world applications. We demonstrate how the F-transform, a fundamental tool in fuzzy approximation theory, can be leveraged to achieve computational efficiency in probabilistic inference while maintaining interpretability–particularly when dealing with ordinal data from surveys and questionnaires.