Perceptual reasoning using interval type-2 fuzzy sets: Properties

Perceptual reasoning (PR) is an approximate reasoning mechanism that can be used as a computing with words (CWW) Engine, i.e., given input words, PR can infer the output from a rulebase. When the input words and the words in the rulebase are modeled by interval type-2 fuzzy sets (IT2 FSs), the output of PR, Ytilde_PR, is also an IT2 FS, and it will be mapped to a word in a codebook. For accurate mapping, we need to ensure that Ytilde_PR resembles the IT2 FSs in the codebook. The concept of PR using IT2 FSs was originally proposed in [10]. In this paper, the procedures to compute PR are introduced, and the properties of PR are studied in more detail. More specifically, we show under what conditions Ytilde_PR can be a shoulder or interior footprint of uncertainty.