In this article, we present a first-order logic programming language for fuzzy reasoning under possibilistic uncertainty and poorly known information. Formulas are represented by a pair (φ, α), in which φ is a first-order Horn clause or a query with fuzzy constants and regular predicates, and α ∈ [0, 1] is a lower bound on the belief on φ in terms of necessity measures. Since fuzzy constants can occur in the logic component of formulas, the truth value of formulas is many-valued instead of Boolean. Moreover, since we have to reason about the possibilistic uncertainty of formulas with fuzzy constants, belief states are modeled by normalized possibility distributions on a set of many-valued interpretations. In this framework, (1) we define a syntax and a semantics of the underlying logic; (2) we give a sound modus ponens-style calculus by derivation based on a semantic unification pattern of fuzzy constants; (3) we develop a directional fuzzy unification algorithm based on the distinction between general and specific object constants; and (4) we describe a backward first-order proof procedure oriented to queries that is based on the calculus of the language and the computation of the unification degree between fuzzy constants in terms of a necessity measure for fuzzy events. © 2002 Wiley Periodicals, Inc.

This paper is an attempt at providing a fuzzy set formalization of case-based reasoning and decision. Learning aspects are not considered here. The proposed approach assumes a principle stating that “the more similar are the problem description attributes, the more similar are the outcome attributes.” A weaker form of this principle concluding only on the graded possibility of the similarity of the outcome attributes, is also considered. These two forms of the case-based reasoning principle are modelled in terms of fuzzy rules. Then an approximate reasoning machinery taking advantage of this principle enables us to apply the information stored in the memory of previous cases to the current problem. A particular instance of case-based reasoning, named case-based decision, is especially investigated. A logical formalization of the basic case-based reasoning inference is also proposed. Extensions of the proposed approach in order to handle imprecise or fuzzy descriptions or to manage more general forms of the principle underlying case-based reasoning are briefly discussed in the conclusion. © 1998 John Wiley & Sons, Inc.

The objective of this article is to describe the MILORD Shell and particularly its architecture and its management of uncertainty. MILORD is an expert systems building tool consisting of two inference engines and an explanation module. the system allows one to perform different calculi of uncertainty on an expert defined set of linguistic terms expressing uncertainty. Each calculus corresponds to specific conjunction, disjunction, and implication operators. the internal representation of each linguistic uncertainty value is a fuzzy subset of the interval [0,1]. the different calculi of uncertainty applied to the set of linguistic terms give, as a result, a fuzzy subset that is approximated, by means of a linguistic approximation process, to a linguistic certainty value belonging to the set of linguistic terms. This linguistic approximation keeps the calculus of uncertainty closed. This has the advantage that, once the linguistic certainty values have been defined, the system computes, off-line, the conjunction, disjunction, and implication operations for all the pairs of linguistic uncertainty values in the term set and stores the results in matrices. Therefore, when MILORD is run, the propagation and combination of uncertainty is performed by simply accessing these precomputed matrices. MILORD also deals with nonmonotonic reasoning in the same framework of uncertainty management. Finally, an application to the diagnosis and treatment of pneumoniae is presented.