Evaluation and Integration of Imprecise Information.
Abstract
Although fuzzy set theory has been rapidly gaining popularity as a rigorous framework for incorporating imprecision into quantitative reasoning, a survey of existing literature indicates the lack of any consistently applied operational definition for the fundamental concept of membership function. In the present case, the membership of an element x in a set S is defined as the degree of truth of the statement 'x is a member of S.' It then becomes necessary to develop an empirically valid scale of truth which allows not only the binary extremes of 'true' and 'false,' but also the continuum of intermediate values. In one experiment, subjects performed two tasks: pairwise comparison; and direct numerical scaling of the relative truth of simple sentences. Results indicated that (1) the high degree of transitivity in each subject's paired-comparison judgments leads us to reject the hypothesis of a two-valued true-false logic in favor of a continuum of values; (2) ability to discriminate, as judged by the consistency between direct ratings and paired-comparison judgments, seems to be uniform along the true-false continuum, again favoring the hypothesis of a continuum of truth values over that of a binary categorical judgment; and (3) the high correlation between an item's aggregate binary preference score for a given subject and that subject's direct rating for the item indicates that at least two different methods of inferring degree of truth are highly consistent.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1979
- Accession Number
- ADA077320
Entities
People
- Jonathan J. Weiss
- Michael L. Donnell
- Paul J. Sticha