| Abstract: | Among the problems raised by admitting statements which are neither true nor false is the problem of how we are to cope with
vague concepts. One method of dealing with such concepts has been suggested by Rosser/Turquette (1952), i.e. the employment
of a many valued set theory. It is our intention in this paper to discuss the use of many valued logics, especially the set
theoretical proposals of Zadeh and Brown, in dealing with this problem. Towards this end, we shall pay close attention to
the development of the concepts of fuzzy sets and fuzzy systems. In this regard, it will be argued that Zadeh had in mind
a many valued logic where the connectives are interpreted according to Lukasiewicz and Tarski, whereas Brown's version may
be based upon a Boolean-valued logic. Furthermore, we shall have occasion to distinguish between two sources of imprecision
in specifying the membership of classes, i.e. conceptual vagueness and imprecision due to inexact measurement. Due to Suppes'
work in this field, the latter sort of imprecision may be exemplified by providing a theory of the inexact measurement of
subjective probability. Finally, we shall discuss some ways in which these two types of imprecision are intertwined. |
