A general type-2 fuzzy model for computing with words

As a methodology, computing with words (CW) allows the use of words, instead of numbers or symbols, in the process of computing and reasoning and thus conforms more to humans' inference when it is used to describe real-world problems. In the line of developing a computational theory for CW, in this paper we develop a formal general type-2 fuzzy model of CW by exploiting general type-2 fuzzy sets (GT2 FSs) since GT2 FSs bear greater potential to model the linguistic uncertainty. On the one hand, we generalize the interval type-2 fuzzy sets (IT2 FSs)-based formal model of CW into general type-2 fuzzy environments. Concretely, we present two kinds of general type-2 fuzzy automata (i.e., general type-2 fuzzy finite automata and general type-2 fuzzy pushdown automata) as computational models of CW. On the other hand, we also give a somewhat universally general type-2 fuzzy model of computing with (some special) words and establish a retraction principle from computing with words to computing with values for handling crisp inputs in general type-2 fuzzy setting and a generalized extension principle from computing with words to computing with all words for handling general type-2 fuzzy inputs.