On Implementing Usual Values

In many cases commonsense knowledge consists of knowledge of what is usual. In this paper we develop a system for reasoning with usual information. This system is based upon the fact that these pieces of commonsense information involve both a probabilistic aspect and a granular aspect. We implement this system with the aid of possibility-probability granules.

Nonmonotonic Reasoning via Possibility Theory

We introduce the operation of possibility qualification and show how. this modal-like operator can be used to represent "typical" or default knowledge in a theory of nonmonotonic reasoning. We investigate the representational power of this approach by looking at a number of prototypical problems from the nonmonotonic reasoning literature. In particular we look at the so called Yale shooting problem and its relation to priority in default reasoning.

Normalization and the Representation of Nonmonotonic Knowledge in the Theory of Evidence

We discuss the Dempster-Shafer theory of evidence. We introduce a concept of monotonicity which is related to the diminution of the range between belief and plausibility. We show that the accumulation of knowledge in this framework exhibits a nonmonotonic property. We show how the belief structure can be used to represent typical or commonsense knowledge.

Credibility Discounting in the Theory of Approximate Reasoning

We are concerned with the problem of introducing credibility type information into reasoning systems. The concept of credibility allows us to discount information provided by agents. An important characteristic of this kind of procedure is that a complete lack of credibility rather than resulting in the negation of the information provided results in the nullification of the information provided. We suggest a representational scheme for credibility qualification in the theory of approximate reasoning. We discuss the concept of relative credibility. By this idea we mean to indicate situations in which the credibility of a piece of evidence is determined by its compatibility with higher priority evidence. This situation leads to structures very much in the spirit of nonmonotonic reasoning.

A Non-Numeric Approach to Multi-Criteria/Multi-Expert Aggregation Based on Approximate Reasoning

We describe a technique that can be used for the fusion of multiple sources of information as well as for the evaluation and selection of alternatives under multi-criteria. Three important properties contribute to the uniqueness of the technique introduced. The first is the ability to do all necessary operations and aggregations with information that is of a nonnumeric linguistic nature. This facility greatly reduces the burden on the providers of information, the experts. A second characterizing feature is the ability assign, again linguistically, differing importance to the criteria or in the case of information fusion to the individual sources of information. A third significant feature of the approach is its ability to be used as method to find a consensus of the opinion of multiple experts on the issue of concern. The techniques used in this approach are base on ideas developed from the theory of approximate reasoning. We illustrate the approach with a problem of project selection.