A Gaussian-Shaped Fuzzy Inference System for Multi-Source Fuzzy Data

Abstract

Fuzzy control theory has been extensively used in the construction of complex fuzzy inference systems. However, we argue that existing fuzzy control technologies focus mainly on the single-source fuzzy information system, disregarding the complementary nature of multi-source data. In this paper, we develop a novel Gaussian-shaped Fuzzy Inference System (GFIS) driven by multi-source fuzzy data. To this end, we first propose an interval-value normalization method to address the heterogeneity of multi-source fuzzy data. The contribution of our interval-value normalization method involves mapping heterogeneous fuzzy data to a unified distribution space by adjusting the mean and variance of data from each information source. As a result of combining the normalized descriptions from various sources for an object, we can obtain a fused representation of that object. We then derive an adaptive Gaussian-shaped membership function based on the addition law of the Gaussian distribution. GFIS uses it to dynamically granulate fusion inputs and to design inference rules. This proposed membership function has the advantage of being able to adapt to changing information sources. Finally, we integrate the normalization method and adaptive membership function to the Takagi–Sugeno (T–S) model and present a modified fuzzy inference framework. Applying our methodology to four datasets, we confirm that the data do lend support to the theory implying the improved performance and effectiveness.