A fuzzy set approach to modifiers and vagueness in natural language.

Abstract

SUMMARYRecent developments in semantic theory, such as the work of Labov (1973) and Lakoff (1973), have brought into question the assumption that meanings are precise. It has been proposed that the meanings of all terms are to a lesser or greater degree vague, such that, the boundary of the application of a term is never a point but a region where the term gradually moves from being applicable to nonapplicable.Developments in fuzzy set theory have made it possible to offer a formal treatment of vagueness of natural language concepts. In this article, the proposition that natural language concepts are represented as fuzzy sets of meaning components and that language operators-adverbs, negative markers, and adjectivescan be considered as operators on fuzzy sets was assessed empirically. In a series of experiments, we explored the application of fuzzy set theory to the meaning of phrases such as very small, sort of large, and so on.In Experiment 1, subjects judged the applicability of the set of phrases to a set of squares of varying size. The results indicated that the group interpretation of the phrases can be characterized within the framework of fuzzy set theory. Similar results were obtained in Experiment 2, where each subject's responses were analyzed individually. Although the responses of the subjects, in general, could be interpreted in terms of fuzzy logical operations, one subject responded in a more idiomatic style.Experiments 3 and 4 were attempts to influence the logical-idiomatic distinction in interpretation by (a) varying the presentation mode of the phrases and by (b) giving subjects only a single phrase to judge.Overall, the results were consistent with the hypothesis that natural language concepts and operators can be described more completely and more precisely using the framework of fuzzy set theory.Picture a conversation between a mother mother's statement. If the son had been and her S-year-old son. The son asks the asked directly how many constitute a few, mother if he might have some jelly beans he probably would have hesitated for a from the bowl on the table. The mother moment and then responded "three" (or replies that he may take a few, and he does "four," or "five," and so on). Pose the just that. It is a perfectly normal conversa-same question to the mother, and the odds tion until one stops and considers how are that she would have responded with many a few are. The mother obviously not too different a number. The number of knows what is meant by the term a few. beans taken might have differed from what The information was understood by her either person might have replied, but the son because he responded correctly to the actual number was probably an acceptable 254

Wiener's conjecture about transformation groups helps predict which fuzzy techniques work better

“…This list of reasonable operations includes the original operations of fuzzy logic, algebraic (probabilistic) operations, bold operations, Hamacher operations, operations of MYCIN for positive certainty factors (for negative factors MYCIN uses non-monotonic operations, so our results are not applicable). These results are also in good accordance with the experimental results that show that among associative operations min, max, and algebraic sum and product are the best fit for human reasoning [3].…”

“…In particular, for k = 0, we get the operation f ¬ (x) = 1−x which was originally proposed by Zadeh [14] and experimentally confirmed in [3]. The above more general negation operations was originally proposed by Sugeno [11], [12]; these operations are also sometimes a good fit for human reasoning [12].…”

The language of possibility and probability: Effects of negation on meaning

“…Instead, the orders are approximately the same. Hersh and Caramazza (1976) have examined the effect of negation on combinations of "very" with the adjectives "large" and "small." Subjects judged the applicability of each constructed phrase (e.g., "not very small") to the same series of squares of varying sizes.…”

How Much Is “About”? Fuzzy Interpretation of Approximate Numerical Expressions

“…As supported by empirical evidence [6], fuzzy logic is therefore a relevant formalisation of the vagueness inherent to natural language: any term can be modeled by a membership function.…”