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The parameter h in a fuzzy linear regression model is vital since it influences the degree of the fitting of the estimated fuzzy linear relationship to the given data directly. However, it is usually subjectively pre-selected by a decision-maker as an input to the model in practice. In Liu and Chen (2013) , a new concept of system credibility was introduced by combining the system fuzziness with the system membership degree, and a systematic approach was proposed to optimize the h value for fuzzy linear regression analysis using the minimum fuzziness criterion with symmetric triangular fuzzy coefficients. As an extension, in this paper, their approach is extended to asymmetric cases, and the procedure to find the optimal h value to maximize the system credibility of the fuzzy linear regression model with asymmetric triangular fuzzy coefficients is described. Some illustrative examples are given to show the detailed procedure of this approach, and comparative studies are also conducted via the testing data sets. [ABSTRACT FROM AUTHOR]

In recent years, the fuzzy linear regression (FLR) approach is widely applied in the quality function deployment (QFD) to identify the vague and inexact functional relationships between the customer requirements and the engineering characteristics on account of its advantages of objectiveness and reality. However, the h value, which is a vital parameter in the proceeding of the FLR model, is usually set by the design team subjectively. In this paper, we propose a systematic approach using the FLR models attached with optimized h values to identify the functional relationships in QFD, where the coefficients are assumed as symmetric triangular fuzzy numbers. The h values in the FLR models are determined according to the criterion of maximizing the system credibilities of the FLR models. Furthermore, an illustrative example is provided to demonstrate the performance of the proposed approach. Results of the numerical example show that the fuzzy coefficients obtained through the FLR models with optimized h values are more effective than those obtained through the FLR models with arbitrary h values selected by the design team. [ABSTRACT FROM AUTHOR]

Abstract: Product planning is one of four important processes in new product development (NPD) using quality function deployment (QFD), which is a widely used customer-driven approach. In our opinion, the first problem to be solved is how to incorporate both qualitative and quantitative information regarding relationships between customer requirements (CRs) and engineering characteristics (ECs) as well as those among ECs into the problem formulation. Owing to the typical vagueness or imprecision of functional relationships in a product, product planning is becoming more difficult, particularly in a fuzzy environment. In this paper, an asymmetric fuzzy linear regression approach is proposed to estimate the functional relationships for product planning based on QFD. Firstly, by integrating the least-squares regression into fuzzy linear regression, a pair of hybrid linear programming models with asymmetric triangular fuzzy coefficients are developed to estimate the functional relationships for product planning under uncertainties. Secondly, using the basic concept of fuzzy regression, asymmetric triangular fuzzy coefficients are extended to asymmetric trapezoidal fuzzy coefficients, and another pair of hybrid linear programming models with asymmetric trapezoidal fuzzy coefficients is proposed. The main advantage of these hybrid-programming models is to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression. Next, the illustrated example shows that trapezoidal fuzzy number coefficients have more flexibility to handle a wider variety of systematic uncertainties and ambiguities that cannot be modeled efficiently using triangular number fuzzy coefficients. Both asymmetric triangular and trapezoidal fuzzy number coefficients can be applicable to a much wider variety of design problems where uncertain, qualitative, and fuzzy relationships are involved than when symmetric triangular fuzzy numbers are used. Finally, future research direction is also discussed. [Copyright &y& Elsevier]