In this paper we consider the extensions of description logics that were proposed to represent uncertain or vague knowledge, focusing on the fuzzy and possibilistic formalisms. We compare these two approaches and comment on their differences concentrating on the consistency issue of knowledge bases represented in these extended frameworks. We present a classification of existing algorithms and ...

Possibilistic logic is a logic for reasoning with uncertain and partially inconsistent knowledge bases. Its standard version consists in ranking propositional formulas according to their certainty or priority level, by assigning them lower bounds of necessity values. We give a survey of automated deduction techniques for standard possibilistic logic, together with complexity results. We focus o...

An architecture for the implementation of possibilistic models in an object-oriented programming environment (C++ in particular) is described. Fundamental classes for special and general random sets, their associated fuzzy measures, special and general distributions and fuzzy sets, and possibilistic processes are speciied. Supplementary methods|including the fast MM obius transform, the maximum...

The design of closed-loop supply chain networks has attracted increasing attention in recent decades with environmental concerns and commercial factors. Due to the rapid growth of knowledge and technology, the complexity of the supply chain operations is increasing daily and organizations are faced with numerous challenges and risks in their management. Most organizations with limited resources...

Expert knowledge is an important source of input to risk analysis. In practice, experts might be reluctant to characterize their knowledge and the related (epistemic) uncertainty using precise probabilities. The theory of possibility allows for imprecision in probability assignments. The associated possibilistic representation of epistemic uncertainty can be combined with, and transformed into,...

The ability of an agent to make quick, rational decisions in an uncertain environment is paramount for its applicability in realistic settings. Markov Decision Processes (MDP) provide such a framework, but can only model uncertainty that can be expressed as probabilities. Possibilistic counterparts of MDPs allow to model imprecise beliefs, yet they cannot accurately represent probabilistic sour...

Carlsson and Fuller [C. Carlsson, R. Fuller, On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315–326] have introduced possibilisticmean, variance and covariance of fuzzy numbers and Fuller andMajlender [R. Fuller, P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003) 363–374] have introduced the...

Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former ranks the pieces of knowledge (expressed by logical formulas) according to their level of certainty, while the latter exhibits relationships between variables. The two types of representation are semantically equivalent when they lead to the same possibility distrib...

CP-nets (Conditional preference networks) are a well-known compact graphical representation of preferences in Artificial Intelligence, that can be viewed as a qualitative counterpart to Bayesian nets. In case of binary attributes it captures specific partial orderings over Boolean interpretations where strict preference statements are defined between interpretations which differ by a single fli...

Interval-based possibilistic logic is a flexible setting extending standard possibilistic logic such that each logical expression is associated with a sub-interval of [0, 1]. This paper focuses on the fundamental issue of conditioning in the interval-based possibilistic setting. The first part of the paper first proposes a set of natural properties that an interval-based conditioning operator s...