Related papers: Fuzzy Arrovian Theorems when preferences are compl…
In this article, working in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions, we go deeper into the study of some type of decompositions defined by t-norms and t-conorms. This allows us to…
We interpret a fuzzy set as a random availability function and provide sufficient conditions under which a preference relation over the set of all random availability functions can be represented by a utility function.
Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review…
The classical property of associativity is very often considered in aggregation function theory and fuzzy logic. In this paper we provide axiomatizations of various classes of preassociative functions, where preassociativity is a…
The transitivity of fuzzy relations plays an important role in fuzzy set theory, artificial intelligence, clustering and decision-making. However, it is often difficult for fuzzy relations to satisfy the transitivity property in many…
Fuzzy implication functions have been widely investigated, both in theoretical and practical fields. The aim of this work is to continue previous works related to fuzzy implications constructed by means of non necessarily associative…
We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the…
Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple…
In the subjective Bayesian approach uncertainty is described by a prior distribution chosen by the statistician. Fuzzy set theory is another way of representing uncertainty. Here we give a decision theoretic approach which allows a Bayesian…
In this work we propose a formal system for fuzzy algebraic reasoning. The sequent calculus we define is based on two kinds of propositions, capturing equality and existence of terms as members of a fuzzy set. We provide a sound semantics…
Within the framework proposed in this paper, we address the issue of extending the certain networks to a fuzzy certain networks in order to cope with a vagueness and limitations of existing models for decision under imprecise and uncertain…
Prediction sets offer a binary inclusion/exclusion for each element at the same fixed confidence level. We generalize to fuzzy prediction sets, which exclude elements at their own data-driven confidence level. Our key insight is that a…
This paper shows that the fuzzy temporal logic can model figures of thought to describe decision-making behaviors. In order to exemplify, some economic behaviors observed experimentally were modeled from problems of choice containing time,…
The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well…
In real-life temporal scenarios, uncertainty and preferences are often essential and coexisting aspects. We present a formalism where quantitative temporal constraints with both preferences and uncertainty can be defined. We show how three…
We present generalization of the Bloom variety theorem of ordered algebras in fuzzy setting. We introduce algebras with fuzzy orders which consist of sets of functions which are compatible with particular binary fuzzy relations called fuzzy…
We consider the problem where a set of individuals has to classify $m$ objects into $p$ categories and does so by aggregating the individual classifications. We show that if $m\geq 3$, $m\geq p\geq 2$, and classifications are fuzzy, that…
In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category…
In fuzzy group theory many versions of the well-known Lagrange's theorem have been studied. The aim of this article is to investigate the converse of one of those results. This leads to an interesting characterization of finite cyclic…
Completeness and transitivity are standard rationality conditions in economics. However, under ambiguity, decision makers sometimes violate these requirements because of the difficulty of forming accurate predictions about ambiguous events.…