Summation of linguistic numbers

A new field of Computing with Words (CWW) intends to “compute” with phrases that involve linguistic numbers and relations between them such as “about five applies” and “close to six PM”. CWW includes answering arithmetic question such as: What is the number of apples that John obtained if he bought about 5 apples two times today? The common sense answer is “about 10 apples”. However the numeric values of “about 10” are not clear and different people give different intervals and confidence values for numbers in these intervals. The goal of this paper is to analyze existing approaches and to propose a new one based on the rigorous methodology of task formulation that involves convolution.