From both a theoretical and a practical point of view, the study of the concept of independence has great importance in any formalism that manages uncertainty. In Independence Concepts in Possibility Theory: Part I (de Campos and Huete, Fuzzy Sets and Systems 103 (1999) 127-152) several independence relationships were proposed, using different comparison criteria between conditional possibility...

Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and modal logics. We present two modal logics that can be used to represent and reason with qualitative statements of possibility and necessity. These logics hav...

An important issue faced by risk analysts is how to deal with uncertainties associated with accident scenarios. In industry, one often uses single values derived from historical data or literature to estimate events probability or their frequency. However, both dynamic environments of systems and the need to consider rare component failures may make unrealistic this kind of data. In this paper,...

A counterpart to von Neumann and Morgenstern' expected utility theory is proposed in the framework of possibility theory. The existence of a utility function, representing a preference ordering among possibility distributions (on the consequences of decision-maker's actions) that satisfies a series of axioms pertaining to decision-maker's behavior, is established. The obtained utility is a gene...

This study explores the interconnections between interval analysis, fuzzy interval analysis, and interval, fuzzy, and possibility optimization. The key ideas considered are: (1) Fuzzy and possibility optimization are important methods in applied optimization problems, (2) Fuzzy sets and possibility distributions are distinct which in the context of optimization lead to ‡exible optimization on o...

A central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. In this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. The main stages of the modeling process are represented as fuzz...

The present paper proposes the first definition of a mixed equilibrium in an ordinal game. This definition naturally extends possibilistic (single agent) decision theory. Our first contribution is to show that ordinal games always admit a possibilistic mixed equilibrium, which can be seen as a qualitative counterpart to mixed (probabilistic) equilibrium. Then, we show that a possibilistic mixed...

My thesis is that backwards time travel can occur without causal loops. Specifically, I shall show that assuming that backwards time travel (‘time travel’ for short) is logically possible, it is logically possible to have a world where time travel occurs and yet no causal loops occur. To formulate this thesis more precisely, I need to distinguish two types of causal loops, closed and open causa...

A DataSpace Support Platform (DSSP) is a self-sustained and self-managed system which needs to support uncertainty among its mediated schemas and its schema mappings. Some approaches for managing such uncertainty by assigning probabilities and reliability degrees to schema mappings have been proposed. Unfortunately, the number of mappings self-generated by a DSSP is usually too large and among ...

The new …eld of judgment aggregation aims to …nd collective judgments on logically interconnected propositions. Recent impossibility results establish limitations on the possibility to vote independently on the propositions. I show that, fortunately, the impossibility results do not apply to a wide class of realistic agendas once propositions like “if a then b” are adequately modelled, namely a...