This paper offers a new concept of {\it possibility} as an alternative to the now-a-days standard concept originally introduced by L.A. Zadeh in 1978. This new version was inspired by the original but, formally, has nothing in common with it other than that they both adopt the Łukasiewicz multivalent interpretation of the logical connectives. Moreover, rather than seeking to provide a general notion of possibility, this focuses specifically on the possibility of a real-world event. An event is viewed as having prerequisites that enable its occurrence and constraints that may impede its occurrence, and the possibility of the event is computed as a function of the probabilities that the prerequisites hold and the constraints do not. This version of possibility might appropriately be applied to problems of planning. When there are multiple plans available for achieving a goal, this theory can be used to determine which plan is most possible, i.e., easiest or most feasible to complete. It is speculated that this model of reasoning correctly captures normal human reasoning about plans. The theory is elaborated and an illustrative example for vehicle route planning is provided. There is also a suggestion of potential future applications.

Due to the fact that basic uncertain information provides a simple form for decision information with certainty degree, it has been developed to reflect the quality of observed or subjective assessments. In order to study the algebra structure and preference relation of basic uncertain information, we develop some algebra operations for basic uncertain information. The order relation of such type of information has also been considered. Finally, to apply the developed algebra operations and order relations, a generalized TODIM method for multi-attribute decision making with basic uncertain information is given. The numerical example shows that the developed decision procedure is valid.

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the available information concerning the value of a logical or numerical variable is represented by a possibility distribution which restricts its more or less possible values. We first discuss different kinds of queries asking for explanations before focusing on the two following types : i) how, a particular possibility distribution is obtained (emphasizing the main reasons only) ; ii) why in a computed possibility distribution, a particular value has received a possibility degree which is so high, so low or so contrary to the expectation. The approach is based on the exploitation of equations in max-min algebra. This formalism includes the limit case of certain and precise information.

Recently, it has been emphasized that the possibility theory framework allows us to distinguish between i) what is possible because it is not ruled out by the available knowledge, and ii) what is possible for sure. This distinction may be useful when representing knowledge, for modelling values which are not impossible because they are consistent with the available knowledge on the one hand, and values guaranteed to be possible because reported from observations on the other hand. It is also of interest when expressing preferences, to point out values which are positively desired among those which are not rejected. This distinction can be encoded by two types of constraints expressed in terms of necessity measures and in terms of guaranteed possibility functions, which induce a pair of possibility distributions at the semantic level. A consistency condition should ensure that what is claimed to be guaranteed as possible is indeed not impossible. The present paper investigates the representation of this bipolar view, including the case when it is stated by means of conditional measures, or by means of comparative context-dependent constraints. The interest of this bipolar framework, which has been recently stressed for expressing preferences, is also pointed out in the representation of diagnostic knowledge.

Possibilistic networks are useful tools for reasoning under uncertainty. Uncertain pieces of information can be described by different measures: possibility measures, necessity measures and more recently, guaranteed possibility measures, denoted by Delta. This paper first proposes the use of guaranteed possibility measures to define a so-called Delta-based possibilistic network. This graphical representation tries to express and to deal with the minimal (lower-bound) possibility degree guaranteed for each variable. We then establish relationships between graphical and logical-based representations of uncertain information encoded by guaranteed possibility measures. We show that possibilistic networks based on guaranteed possibility measures can be easily transformed, in a polynomial time, in Delta-based knowledge bases. Then we analyze propagation algorithms in Delta-based possibilistic networks. In fact, standard possibilistic propagation algorithms can be re-used since we show that a simple rewriting of the chain rule allows the transformation of the initial Delta-based possibilistic networks into standard min-based possibilistic networks.