Based on existing fuzzy simulation algorithms, this paper presents two innovative techniques for approximating the expected values of fuzzy numbers' monotone functions, which is of utmost importance in fuzzy optimization literature. In this regard, the stochastic discretization algorithm of is enhanced by updating the discretization procedure for the simulation of the membership function and the calculation formula for the expected values. This is achieved through initiating a novel uniform sampling process and employing a formula for discrete fuzzy numbers, respectively, as the generated membership function in the stochastic discretization algorithm would adversely affect its accuracy to some extent. What is more, considering that the bisection procedure involved in the numerical integration algorithm of Li ( 2015) is time-consuming and also not necessary for the specified types of fuzzy numbers, a special numerical integration algorithm is proposed, which can simplify the simulation procedure by adopting the analytical expressions of α-optimistic values. Subsequently, concerning the extensive applications of regular fuzzy intervals, several theorems are introduced and proved as an extended effort to apply the improved stochastic discretization algorithm and the special numerical integration algorithm to the issues of fuzzy intervals. Throughout the article, a series of numerical experiments are conducted from which the superiority of both the two novel techniques over others are conspicuously displayed in aspects of accuracy, stability, and efficiency.
Due to customers’ growing concern about logistics performances related to products, logistics service increasingly contributes to the core competence of an enterprise or product, which calls an appropriate tool to develop effective strategic actions to improve logistics performances and gain customer satisfaction. Therefore, an uncertain quality function deployment (QFD) approach for selecting the most effective strategic actions in terms of efficiency to meet the customer requirements is developed in this paper, which integrates uncertainty theory into the traditional QFD methodology in order to rationally deal with imprecise information inherently involved in the QFD process. The framework and systematic procedures of the approach are presented in the context of logistics services. Specifically, the calculations for the prioritization of strategic actions are discussed in detail, in which uncertain variables are used to capture the linguistic judgements given by customers and experts. Applications of the proposed approach are presented as well for illustration.
Quality function deployment (QFD) is a new product development tool remarked with interpreting customer requirements into engineering characteristics of the design process. On account of the inherent imprecise and uncertain elements in the weights of customer requirements, the relationships between customer requirements and engineering characteristics, and the correlations among engineering characteristics, uncertain variables are preferred to be applied in this paper. By taking advantage of expected value modelling to determine the target values of engineering characteristics in handling different practical design scenarios, two uncertain programming models are proposed for optimizing the QFD process in an uncertain environment. Subsequently, the proposed uncertain models are implemented in a motor car design for quality development.
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