Possibility theory is applied to introduce and reason about the fundamental notion of a key for uncertain data. Uncertainty is modeled qualitatively by assigning to tuples of data a degree of possibility with which they occur in a relation, and assigning to keys a degree of certainty which says to which tuples the key applies. The associated implication problem is characterized axiomatically an...

Compared with the conventional probabilistic mean-variance methodology, fuzzy number can better describe an uncertain environment with vagueness and ambiguity. Based on this fact, possibilistic mean-variance utilities to portfolio selection for bounded assets are discussed in this paper. The possibilistic mean value of the expected return is termed measure of investment return and the possibili...

Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) accor?i�g to their level of certainty, while the latter exhibits relationships between variables. The two types of representations are semantically equivalent when they lead to the same possibility d...

Conditioning is an important task for designing intelligent systems in artificial intelligence. This paper addresses an issue related to the possibilistic counterparts of Jeffrey’s rule of conditioning. More precisely, it addresses the existence and unicity of solutions computed using the possibilistic counterparts of the socalled kinematics properties underlying Jeffrey’s rule of conditioning....

We extend hybrid possibilistic conditioning to deal with inputs consisting of a set of triplets composed of propositional formulas, the level at which the formulas should be accepted, and the way in which their models should be revised. We characterize such conditioning using elementary operations on possibility distributions. We then solve a difficult issue that concerns the syntactic computat...

Possibilistic logic and quasi-classical logic are two logics that were developed in artificial intelligence for coping with inconsistency in different ways, yet preserving the main features of classical logic. This paper presents a new logic, called quasi-possibilistic logic, that encompasses possibilistic logic and quasi-classical logic, and preserves the merits of both logics. Indeed, it can ...

Possibilistic logic provides an efficient tool for handling uncertain and nonmonotonic reasoning on the one hand, and for hypothetical reasoning on the other hand. In the first situation, logic formulas are simply weighted by lower bounds of a necessity measure. Thus, formulas in a knowledge base are rank-ordered according to their levels of certainty. In the case of hypothetical reasoning, the...

Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be es­ timated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possi­ bility degree or a necessity degree that ex­ presses to what extent the formula is pos­ sibly or necessarily true. Possibilistic reso­ lution yields a calculus for pos...

Possibilistic networks are important and efficient tools for reasoning under uncertainty. This paper proposes a new graphical model for decision making under uncertainty based on possibilistic networks. In possibilistic decision problems under uncertainty, available knowledge is expressed by means of possibility distribution and preferences are encoded by means another possibility distribution ...