Constructing T–S fuzzy model from imprecise and uncertain knowledge represented as fuzzy belief functions

Abstract

The classical Takagi–Sugeno (T–S) fuzzy model is an effective tool used to approximate the behaviors of nonlinear systems on the basis of precise and certain input and output observations. In many real-life situations, however, the knowledge of our interest, i.e., the output observations, can only be imprecise, uncertain, or both. This paper presents a method used to construct T–S fuzzy model when the output is imprecise and uncertain, represented as fuzzy belief function, and then proposes the so-called Evidential knowledge-based T–S regression model (ETS). The consequents of ETS are identified by using maximum likelihood estimate strategy, in which, a novel fuzzy evidential Expectation-Maximization (EM) algorithm is proposed to iteratively maximize the likelihood. The antecedents of ETS are automatically constructed by using a data-driven strategy, considering both the accuracy and complexity of the produced ETS. The performance of ETS was validated by using some unreliable sensor experiments and comparing with other similar methods in the literature. The numerical simulations suggest that the ETS can be used to approximate nonlinear systems with high accuracy when the outputs of systems are imprecisely and uncertainly observed. Correspondingly, the investigations on T–S fuzzy regression of fuzzy output and point-valued output, called Fuzzy knowledge-based T–S regression model (FTS) and classical data based T–S fuzzy regression model, respectively, are covered, when the output fuzzy belief functions degenerate to be fuzzy functions and point-valued data, respectively.