Models of linguistic connectives

It is known that the linguistic connectives such as AND, OR, IF...THEN, etc., have a vague, non-crisp meaning within the human use of natural languages, and yet all these connectives are presented by crisp connectives known as t-norms and t-conorms. It is proposed that the combination of point-valued fuzzy sets with linguistic connectives should be represented with interval-valued fuzzy sets in order that the meaning of linguistic connectives can be captured as an approximation to their vague use in human communications. It is found that the proposed interval-valued representations of linguistic combinations with linguistic AND and OR contain their crisp representations at one of their boundaries as well as containing the “Compensatory AND” combinations within its boundaries. It is also found that the proposed interval-valued representations of linguistic IF...THEN combinations also contain most of the well-known crisp representations of implication