Towards a general type-2 fuzzy logic approach for Computing With Words using linear adjectives

Abstract

The concept of Computing With Words (CWW) was coined by Zadeh to be a methodology in which words are used instead of numbers for computing and reasoning. Since then, there have been various angles to interpret CWW. However, there is a need to tackle the problem of modeling a ‘word’ by fuzzy sets, which is one of the building blocks of the CWW concept. In this paper, we investigate the ‘word’ from the perspective of the parts of speech in English language. We point out that there exists a hierarchical analogy between the parts of speech and a linguistic variable in a fuzzy system. In other words, the linguistic variable in a fuzzy system can be interpreted to be a noun whereas the corresponding linguistic labels quantifying the linguistic variable can be classified as being ‘qualifiers + adjectives’. We propose to model the linguistic uncertainty conveyed by qualifiers as second-order word uncertainty using a general type-2 fuzzy set based approach where the qualifiers can be exploited in linear terms. In particular, we suggest a linear representation of the third dimension of a general type-2 fuzzy set where we consider only left and right shoulder membership functions. We show that the interpretation of the paradigm using linear adjectives simplifies the comprehension of the third dimension as well as offering a way to avoid the shortcomings of type-1 and interval type-2 fuzzy sets in modeling a word for CWW. For illustration, we present examples comparing the interval type-2 fuzzy labels (which are greater in number) and the linear general type-2 (LGT2) fuzzy labels which provide an efficient management of the linguistic variable by revealing a potential to reduce complexity.