Likelihood-based multivariate fuzzy model with linear inequality constraints

In this paper, we investigate the multivariate linear regression of fuzzy data when model parameters are constrained by a set of linear inequalities. It is motivated by the facts that the measurement results of device in real-life situations are always not precise numbers and that (model) structure involving linear inequalities is usually faced to in practice. With assuming fuzzy data are seen as a possibility distribution associated to a precise realization of a random variable, we first propose a restricted fuzzy expectation/conditional maximization (RFECM) algorithm for calculating restricted maximum likelihood estimates of parameters of interest from fuzz data. We then demonstrate the convergence of RFECM algorithm. Using RFECM finally establishes the so-called likelihood-based multivariate fuzzy linear regression model with crisp inputs and fuzzy outputs, constrained by linear inequalities. Some simulations are conducted to validate the performance of our proposed model.