A Common Framework for Colloquil Quanti ers and Probability Terms

Publisher Summary This chapter examines common framework for colloquial quantifiers and probability terms. Colloquial quantifiers and uncertainty expressions can be interpreted as fuzzy numbers in the interval [0, 1]. Empirical procedures are suggested for the determination of these fuzzy numbers. The empirical results reveal that for propositions on a defined level of abstraction colloquial quantifiers and probability terms can not only be expressed as fuzzy numbers but furthermore can be used in according to the rules for fuzzy combination numbers. The operations with fuzzy numbers correspond to the standard operations in arithmetics. Any two fuzzy numbers can be concatenated by (1) calculating the resulting core by means of standard arithmetics, (ii) averaging the respective upper and lower boundaries, and by (iii) determining the resulting boundaries from the averaged boundaries in relation to the resulting core. Quantifiers expressed as fuzzy numbers in the interval [0, 1] and uncertainty expressions represented as fuzzy probabilities are comparable. The common framework for quantifiers and uncertainty expressions as established by the assignation of fuzzy numbers in [0, 1] has to be complemented by a comparison of the algorithms of inference.