A least-squares framework for developing interval type-2 fuzzy semantics

The developing of IT2 fuzzy semantics is critical for computing with words (CWW), but exiting approaches lack flexibility and fail to adapt user’s diversified demands. The study proposes a least-squares framework for designing CWW encoders that construct interval type-2 fuzzy sets (IT2 FSs) to represent the semantic meanings of linguistic words. In the least-squares framework, an CWW encoder is characterized by two elements: an intra-uncertain semantic mapping and an inter-uncertain semantic family. The intra-uncertain semantic mapping transforms data intervals into type-1 fuzzy sets (T1 FSs), then an optimal IT2 FS is derived from the inter-uncertain semantic family using the least-squares method. Furthermore, several intra-uncertain semantic mappings are introduced, and a compatibility measure is defined to facilitate model selection. The least-squares framework benefits from the flexible selection of intra-uncertain semantic mappings and least-squares optimization-based construction of IT2 FSs. In experiments, the least-squares framework is applied to handle real-world online survey data and the large-scale online review data set of a Chinese life service review site, Dianping.com. Compared to the enhanced interval approach and the Hao-Mendel approach, the least-squares framework shows its favorable efficiency in experiments and statistical tests, and adapts to user-defined intra- and inter-uncertain semantic families.