Fuzzy Sets Theory and Applications pp 79-97 | Cite as

# Outline of a Theory of Usuality Based on Fuzzy Logic

## Abstract

The concept of *usuality* relates to propositions which are usually true or, more precisely, to events which have a high probability of occurrence. For example, *usually* *Cait is very cheerful, usually a TV set weighs about fifty pounds*, etc. Such propositions are said to be *usuality-qualified.* A usuality-qualified proposition may be expressed in the form *usually (X is F)*, in which *X* is a variable taking values in a universe of discourse *U* and *F* is a fuzzy subset of *U* which may be interpreted as a *usual value* of *X.* In general, a usual value of variable, *X*, is not unique, and any fuzzy subset of *U* qualifies to a degree to be a usual value of *X.* A usuality qualified proposition in which *usually* is implicit rather than explicit is said to be a *disposition.* Simple examples of dispositions are *snow is white, a cup of coffee costs* *about fifty cents* and *Swedes are taller than Italians.*

In this paper, we outline a theory of usuality in which the point of departure is a method of representing the meaning of usuality-qualified propositions. Based on this method, a system of inference for usuality-qualified propositions may be developed. As examples, a dispositional version of the Aristotelian Barbara syllogism as well as a dispositional version of the *modus ponens* are described. Such dispositional rules of inference are of direct relevance to commonsense reasoning and, in particular, to commonsense decision analysis. A potentially important application area for the theory of usuality is the management of uncertainty in expert systems.

## Keywords

Membership Function Fuzzy Logic Fuzzy Number Fuzzy Subset USUALITY Base## Preview

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