Related papers: Preassociative aggregation functions
We give a new heuristic for all of the main terms in the quotient of products of L-functions averaged over a family. These conjectures generalize the recent conjectures for mean values of L-functions. Comparison is made to the analogous…
This paper is devoted to proving the general {\L}ojasiewicz inequality, in both the definable and subanalytic cases, under the most relaxed assumptions. It means that we drop the usual continuity and compactness assumptions. In the second…
Categorization axioms have been proposed to axiomatizing clustering results, which offers a hint of bridging the difference between human recognition system and machine learning through an intuitive observation: an object should be assigned…
This paper proposes a new category theoretic account of equationally axiomatizable classes of algebras. Our approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered…
Since categories are graphs with additional "structure", one should start from fuzzy graphs in order to define a theory of fuzzy categories. Thus is makes sense to introduce categories whose morphisms are associated with a plausibility…
We introduce some classical concepts in the representation theory of compact groups, in order to use them for a new generalization of the Peter-Weyl Theorem. We mostly deal with functions on locally compact groups possessing large…
The paper investigates the properties of a fuzzy logic of typicality. The extension of fuzzy logic with a typicality operator was proposed in recent work to define a fuzzy multipreference semantics for Multilayer Perceptrons, by regarding…
In this note we give some sufficient conditions for an analytic function $f(z)$ normalized by $f'(0)=1$ to belong to certain subfamilies of the class of Bazilevic functions. In earlier works, the closure property of many classes of…
We describe how properties of metric groups and of unitary representations of metric groups can be presented in continuous logic. In particular we find $L_{\omega_1 \omega}$-axiomatization of amenability. We also show that in the case of…
Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; but some systems are much deeper, such as the axioms of…
The paper considers asymptotics of summation functions of additive and multiplicative arithmetic functions. We also study asymptotics of summation functions of natural and prime arguments. Several assertions on this subject are proved and…
We prove that any optimal, independent, and zero unanimous fuzzy classification aggregation function of a continuum of individual classifications of $m\ge 3$ objects into $2\le p\le m$ types must be a weighted arithmetic mean. We also…
Admissible orders play a key role in ranking subintervals of the unit interval. In 2013, Bustince et al. proposed constructing such relations by means of admissible pairs of aggregation functions. The only significant example in the…
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…
This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on…
A formalized and quantifiable responsibility score is a crucial component in many aspects of the development and application of multi-agent systems and autonomous agents. We can employ it to inform decision making processes based on ethical…
Relational presheaves generalize traditional presheaves by going to the category of sets and relations (as opposed to sets and functions) and by allowing functors which are lax. This added generality is useful because it intuitively allows…
The aim of this paper is to classify order-preserving functions according to their arity gap. Noteworthy examples of order-preserving functions are so-called aggregation functions. We first explicitly classify the Lov\'asz extensions of…
We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function…
The theory of two binary relations has the strong amalgamation property when the first relation is assumed to be coarser than the second relation, and each relation satisfies a chosen set of properties from the following list: transitivity,…