تصمیم گیری گروهی فازی برای قضاوت زبانی چند فرمت و چند ذره ذره بودن در گسترش کارکرد کیفیت

As a customer-driven tool, quality function deployment (QFD) is widely used in product planning or improvement to achieve higher product performance and customer satisfaction. QFD uses a matrix called the house of quality (HoQ) to translate customer requirements (CRs) into engineering characteristics (ECs). Constructing the HoQ, which includes determining the importance weights of CRs, the correlation matrix among ECs and the relationship matrix between CRs and ECs, is an important issue in the application of QFD. However, decision-makers (DMs) participating the construction of HoQ tend to give their individual judgments in multi-format or multi-granularity depending on their different knowledge, experience, culture and circumstance. Furthermore, these judgments are more difficult to assess with the precise quantitative forms due to the vagueness and uncertainty existed in the early stage of new product development. In this paper, a group decision-making approach incorporating with two optimization models (i.e. logarithmic least squares model and weighted least squares model) is proposed to aggregate these multi-format and multi-granularity linguistic judgments. Fuzzy set theory is utilized to address the uncertainty in the decision-making process. The proposed method is illustrated with a real-world case of horizontal directional drilling machine. The application indicates that the group decision-making method may be a promising tool for constructing the HoQ. Keywords

New product development is a crucial source of new sales and profits for enterprises under the environment of global competition. Shorter lead time, lower product cost, and higher customer satisfaction and market share which are the emphases of competition enable Quality Function Deployment (QFD) to be an important tool for new product development (Büyüközkan and Feyzioglu, 2004, Fung et al., 2002, Kwong and Bai, 2002 and Maffin and Braiden, 2001). QFD, as a well-known product planning approach, supports engineers to translate the “voice of customer”, i.e. customer requirement (CRs), into engineering characteristics (ECs), and subsequently into parts characteristics (PCs), process plans and production requirements through various stages in new product development (Hauser and Clausing, 1988 and Griffin and Hauser, 1993). Each translation can be represented graphically in a matrix configuration generally known as the house of quality (HoQ) (Karsak, 2004). The first translation, called HoQ of product planning, will be focused on analyzing in this paper since it can largely affect the target value setting of other translations in the later design stages. The crucial and essential activity in the application of QFD is to construct the HoQ accurately, which includes determining the importance weights of CRs, the relationship matrix between CRs and ECs, and the correlation matrix among ECs. As it is not the focus of this study, the authors do not discuss how to derive the importance weights of ECs which is another critical problem for the calculation of HoQ. Various methods have been developed to tackle with the construction of HoQ. The simplest method in prioritizing CRs is based on direct-rating scale, such as nine-point (Griffin & Hauser, 1993). Gustafsson and Gustafsson (1994) employed a conjoint analysis method in the form of pairwise comparisons to determine the relative importance of CRs. Analytic hierarchy process (AHP), a multi-criteria decision-making approach, was also used in weighting the importance of CRs under different circumstances (Akao, 1990; Armacost et al., 1994 and Lu et al., 1994). Considering the issue as a typical group decision-making problem, Lai, Ho, and Chang (1998) applied in the decision-making process combining voting and linear programming techniques to aggregate individual preference into group consensus. Ho, Lai, and Chang (1999) also proposed an integrated group decision-making method to aggregate team members’ opinions and minimize inconsistency over group and individual preferences for determining the importance weights of CRs. However, these aforementioned methods cannot effectively capture the inevitable vagueness and uncertainty in the decision-making process. Chan, Kao, Ng, and Wu (1999) combined fuzzy arithmetic and entropy method to calculate the importance weights based on converting the importance assessment from crisp values to fuzzy numbers. Büyüközkan, Feyzioglu, and Ruan (2007) and Kwong and Bai, 2002 and Kwong and Bai, 2003 employed group decision-making method and AHP incorporated with fuzzy set theory to determine the importance weights of CRs, respectively. By using fuzzy mathematical programming, Lai, Xie, Tan, and Yang (2008) rated CRs from three aspects, i.e. competition position, current performance and customers’ viewpoint. To reason about the implicit relationships between CRs and ECs and the correlations among ECs, Temponi, Yen, and Tiao (1999) developed a heuristic inference scheme based on a fuzzy logic-based extension to HoQ and a formal representation of requirements. Based on the quantified representation of ECs and customer perceptions, fuzzy regression approaches were developed to identify the relationship matrix between CRs and ECs (Kim et al., 2000 and Fung et al., 2006). As a typical group decision-making process, decision-makers (DMs), who may be product designers and managers, generally give their own judgments to construct the HoQ in many different ways, numerically or linguistically, depending on their individual culture, experience, knowledge and circumstance. However, determining consensus group decisions is not an easy task under so complex circumstances. Thus, Büyüközkan et al. (2007) proposed a fuzzy group decision-making approach to fuse multiple preference styles to respond CRs. Customers were assumed to give their importance values according to the following five formats, i.e. preference orderings, utility analysis, optimal subset method, linguistic preference relations and fuzzy pairwise comparisons. These five formats were unified by using corresponding transformation functions or LOWA operator (Chiclana et al., 1998 and Yager, 1996). Note that DMs participating the construction of HoQ should have good insights of CRs, ECs and other issues with regard to the developing product. Preference orderings and optimal subset method may be effective for customers to express their opinions but not for DMs because they can not provide adequate information to well express the opinions. For example, DMs can not compare the degrees of priorities among CRs through these two methods. Furthermore, for requiring the expected performance of each criteria to be represented with a quantitative form, utility analysis is also not appropriate to be used at the early design stage in which some design criteria are hard to be quantified precisely (Thurston and Carnahan, 1992 and Wang, 2001). From various studies mentioned in this paper, linguistic preference relations and fuzzy pairwise comparisons can be found as the familiar formats for DMs to give their assessments in constructing the HoQ. Considering their personal backgrounds and different understanding levels to the developing product, DMs may use different linguistic term sets to express their own judgment information (Herrera, Herrera-Viedma, & Martı´nez, 2000). To determine the relative weights in fuzzy comparison matrix, the general method was to solve crisp matrix obtained from the fuzzy matrix based on the indices of confidence and optimism provided by the participators (Kwong & Bai, 2002). For the purpose of handling the multi-granularity linguistic information in linguistic preference relations, most methods were generally adopted transformation functions to unify the information into a uniform representation base (Chiclana et al., 1998, Herrera et al., 2000). However, the two aspects mentioned above, i.e. determining the indices of confidence and optimism and unifying the multi-granularity linguistic information by using a transformation function, increase the DMs’ subjectivity distinctly and then lead to higher uncertainty in the decision-making process. To decrease the subjectivity and reach a better group consensus, a fuzzy group decision-making approach incorporated with two optimization models (logarithmic least squares model and weighted least squares model) is proposed to aggregate these assessments for constructing the HoQ. The rest of the paper is arranged as follows. Section 2 presents the problem for constructing the HoQ in linguistic preference relations and fuzzy pairwise comparisons with seven granularities. In Section 3, a new approach integrating the LLSM and WLSM is proposed to obtain the aggregated judgments. In Section 4, an application in a real-world product development of horizontal directional drilling (HDD) machine is used to illustrate the proposed method. Section 5 concludes the paper.

Constructing the HoQ of product planning is a fundamental problem in the application of QFD because it can largely affect the target value setting of ECs and also other translations in the following design stages. Due to the high degree of subjectivity and uncertainty in the decision-making process in constructing the HoQ, the application of fuzzy set theory provides an efficient to handle the subjective assessments. Participators tend to provide their opinions in many different ways with multi-granularity due to their personal backgrounds. To allow DMs to express their opinions more adequately, linguistic preference relations and fuzzy pairwise comparisons with seven granularities are provided to construct the HoQ. To decrease the subjectivity in deriving aggregated assessments, a new approach incorporated with LLSM and WLSM is proposed to handle these multi-format and multi-granularity assessments for constructing the HoQ which are given by the focus group. The LLSM and two normalized formulae are employed to solve the fuzzy comparison matrices and normalize the assessments in the form of linguistic preference relations. Then, the WLSM is developed to aggregate the final normalized multi-granularity assessments, respectively. Furthermore, an application of HDD machine is provided to illustrate the effectiveness of the proposed method. Further work would consider other familiar expressions with different granularities to incorporate into the proposed model for constructing the HoQ. In view of a real-world application, the correlations among CRs should be considered to construct the HoQ. Furthermore, the proposed method would be extended to the construction of subsequent HoQs for implementing the QFD application.