Perceptual Reasoning: A New Computing with Words Engine

Zadeh proposed the paradigm of computing with words (CWW). We have proposed a CWW architecture for making subjective judgments, called a Perceptual Computer (Per- C). Because words mean different things to different people, the Per-C uses interval type-2 fuzzy sets (IT2 FSs). The encoder of the Per-C transforms words, in an application-dependent word- codebook, into IT2 FSs. The central element of the Per-C is the CWW engine, which maps IT2 FSs to IT2 FSs. Several CWW engines have appeared in the literature, e.g., fuzzy IF- THEN rules to perform inference and/or reasoning based on Mamdani or TSK models, linguistic weighted averages (LWAs) to aggregate linguistic data, and linguistic summarization to perform human friendly data mining. In this paper a new CWW engine-Perceptual Reasoning (PR)-is proposed. It also uses fuzzy IF-THEN rules; however, unlike a traditional Mamdani or TSK model, in which fired rules are combined using the union, or addition, or during the defuzzification process, in PR a LWA is used to combine the fired rules. We prove that the output IT2 FSs of PR can only look like the IT2 FSs in the application codebook. This is very important for CWW, because the last component of the Per-C is a decoder which converts the CWW output IT2 FS back into a word, e.g. a word whose IT2 FS is most similar to it.