An interval type-2 fuzzy model of computing with words

As a methodology, computing with words 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. Motivated by Zadeh’s paradigm of computing with words, the literature has proposed a kind of type-1 fuzzy automata as a formal model of computing with words, which takes type-1 fuzzy subsets of symbols as input. However, type-1 fuzzy representation provides a limited platform for approximating the meaning of words since it is not able to capture linguistic uncertainty. In this paper, we develop a formal interval type-2 fuzzy model of computing with words by generalizing the existing type-1 fuzzy sets-based model to an interval type-2 fuzzy environment. Concretely, we take interval type-2 fuzzy automata (i.e., interval type-2 fuzzy finite automata and interval type-2 fuzzy pushdown automata), which combine interval type-2 fuzzy set theory and automaton theory, as a computational model of computing with words. Furthermore, we develop the extension principles to extend from computing with values to computing with words and show that computing with words can be implemented with computing with values in the interval type-2 fuzzy setting at an extra computational cost.