Axiomatic foundations for Nonstandard Analysis

FOUNDATIONS OF NONSTANDARD ANALYSIS A Gentle Introduction to Nonstandard Extensions

Nonstandard analysis and differentiable manifolds - Foundations

We approach the study of differentiable manifolds modeled on Banach spaces by means of Nonstandard Analysis. We stay inside the category of classical manifolds and using nonstandard analysis techniques, we present some new nonstandard characterizations for the tangent bundle, differentiable function, differential of a function, directional derivatives, etc. We establish some relations between o...

Axiomatic Foundations for Compromise Theory†

We provide a characterization of the symmetric and weighted versions of the Euclidean compromise solution for multiobjective optimization problems first proposed by P.L.Yu. These solutions minimize a measure of the distance between a feasible set and the utopia point of that set, and are closely related to solutions that have been proposed in the bargaining with claims literature. We provide ne...

Axiomatic Foundations for Ranking Systems

Reasoning about agent preferences on a set of alternatives, and the aggregation of such preferences into some social ranking is a fundamental issue in reasoning about multi-agent systems. When the set of agents and the set of alternatives coincide, we get the ranking systems setting. A famous type of ranking systems are page ranking systems in the context of search engines. In this paper we pre...

Axiomatic Foundations for Satisficing Behavior∗

A theory of decision making is proposed that supplies an axiomatic basis for the concept of “satisficing” postulated by Herbert Simon. After a detailed review of classical results that characterize several varieties of preference-maximizing choice behavior, the axiomatization proceeds by weakening the inter-menu contraction consistency condition involved in these characterizations. This exercis...