An Approach to Computing With Words Based on Canonical Characteristic Values of Linguistic Labels

Herrera and Martinez initiated a 2-tuple fuzzy linguistic representation model for computing with words (CW), which offers a computationally feasible method for aggregating linguistic information (that are represented by linguistic variables with equidistant labels) through counting "indexes" of the corresponding linguistic labels. Lawry introduced an alternative approach to CW based on mass assignment theory that takes into account the underlying definitions of the words. Recently, we provided a new (proportional) 2-tuple fuzzy linguistic representation model for CW that is an extension of Herrera and Martinez\´s model and takes into account the underlying definitions of linguistic labels of linguistic variables in the process of aggregating linguistic information by assigning canonical characteristic values (CCVs) of the corresponding linguistic labels. In this paper, we study further into CW based on CCVs of linguistic labels to provide a unifying link between Lawry\´s framework and Herrera and Martinez\´s 2-tuple framework as well as allowing for computationally feasible CW. Our approach is based on a formal definition of CCV functions of a linguistic variable (which is introduced under the context of its proportional 2-tuple linguistic representation model as continuation of our earlier works) and on a group voting model that is for the probabilistic interpretation of the (whole) semantics of the ordered linguistic terms set of an arbitrary linguistic variable. After the general framework developed in the former part of this paper, we focus on a particular linguistic variable - probability. We show that, for a linguistic probability description, the expectation of its posterior conditional probability is a canonical characteristic value of the linguistic probability description. Then, a calculus for reasoning with linguistic syllogisms and inference from linguistic information is introduced. It is investigated under the context that linguistic quantifiers in su- ch linguistic syllogisms can be arbitrary linguistic probability description and that the related linguistic information can be linguistic facts, overfacts, or underfacts. Intrinsically, our approach to this calculus is with computing with words based on canonical characteristic values of linguistic labels.