شبکه های Choquet جدایی ناپذیر مبتنی بر سلسله مراتبی برای ارزیابی ادراکات خدمات مشتری در فروشگاه های فست فود

It is known that a hierarchical decision structure consisting of multiple criteria can be modeled by a Choquet integral-based hierarchical network. With a given input–output dataset, the degree of importance of each criterion can be directly obtained from the corresponding connection weight after the network has been trained from samples. Since each output value or the synthetic evaluation of an alternative derived from uncertain assessments has its upper and lower bounds, the degree of importance of each criterion should not be unique and can be distributed in a range. In this paper, the range of the degree of importance of each criterion is obtained by three Choquet integral-based hierarchical networks with the pre-specified hierarchical structure: one is a common network constructed by merely minimizing the least squared error, and the others are employed to determine a nonlinear interval regression model. The above three networks are trained with a given input–output dataset using the proposed genetic algorithm-based learning algorithm. Empirical results of evaluating customer service perceptions on fast food stores demonstrate that the proposed method can identify key factors that have stronger effect on service quality perceptions by employing three Choquet integral-based hierarchical networks with the hierarchical structure to determine possible ranges of the degree of importance of respective aspects and attributes.

A decision problem can be evaluated by a hierarchical structure consisting of diverse criteria. The hierarchy decomposes from the general goal to more specific attributes until a level of manageable decision criteria is met (Meade & Presley, 2002). As depicted in Fig. 1, the given hierarchical structure is usually composed of three decision levels including the objective, the aspects, and the attributes. To obtain the synthetic evaluation of an alternative, the weighted average method (WAM) with the additivity assumption is usually taken into account. In practice, the additive WAM is performed on the objective and each aspect assuming that there is no interaction among the attributes towards the objective attribute (Murofushi and Sugeno, 1989, Murofushi and Sugeno, 1991, Murofushi and Sugeno, 1993, Sugeno et al., 1998 and Tseng and Yu, 2005). Many well-known scoring methods with additive property, such as the Analytical Hierarchy Process (AHP) (Saaty, 1994), the Delphi method, the eigenvector method, the weighted least square method, the entropy method, SMARTS, SMARTER (Edwards & Barron, 1994), a weight-assessing method with habitual domains (Tzeng, Chen, & Wang, 1998), as well as the linear programming techniques for multi-dimensions of analysis preference (LINMAP), can be employed to find the degree of importance of respective criteria. For the above methods, the sum of degree of importance of respective criteria is assumed to be just one. Full-size image (6 K) Fig. 1. A hierarchical structure for a decision problem. Figure options Unfortunately, the additivity assumption is not warranted in many real-world problems (Wang et al., 2005 and Wang et al., 1998). Instead, the fuzzy measure can be employed to describe the interaction among the attributes in a set. Once a nonadditive fuzzy measure is employed to express the importance of relevant attributes towards the objective attribute, the synthetic evaluations of individual alternatives can be obtained by a nonadditive data mining technique, the Choquet integral (Murofushi and Sugeno, 1989, Murofushi and Sugeno, 1991, Murofushi and Sugeno, 1993 and Sugeno et al., 1998), rather than the additive techniques such as WAM (Wang et al., 2005). In view of the nonadditive property, the Choquet integral has been widely applied to multiple-criteria decision-making (MCDM) (Chen, 2001, Chen et al., 2000, Chiou and Tzeng, 2002, Jeng et al., 2003, Kwak and Pedrycz, 2004, Tsai and Lu, 2006, Tseng and Yu, 2005, Tzeng et al., 2005 and Wang et al., 2005). In particular, Chiang (1999) introduced the structure of the Choquet integral-based hierarchical network, which can be regarded as a fuzzy neural network, and demonstrated the effectiveness of the network for nonlinear mappings. The advantage of the Choquet integral-based hierarchical network is that, when the synthetic evaluation (i.e., output) of each alternative and its performance values (i.e., input) on individual attributes are acquired by the questionnaire, the fuzzy measure values or the degree of importance of each criterion including aspects and attributes can be identified from the corresponding connection weight after the Choquet integral-based hierarchical network has been trained with the input–output dataset. Similar to the back-propagation algorithm for a multi-layer perceptron (Jang, Sun, & Mizutani, 1997), the training performance of the common Choquet integral-based network is merely the least squared error. In particular, the Choquet Integral-based hierarchical Network with the Hierarchical Structure (CINHS) depicted in Fig. 1 is taken into account. In many practical applications, since available information is often derived from uncertain assessments, real intervals can be employed to represent uncertain and imprecise observations (Hwang, Hong, & Seok, 2006). The interval regression analysis, which provides interval estimation of individual dependent variables, is an important tool for dealing with the uncertain data (Huang et al., 1998, Hwang et al., 2006 and Jeng et al., 2003). The interval parameters of a linear interval model can be determined by solving a basic linear programming problem of interval regression analysis (Ishibuchi, 1990, Ishibuchi and Nii, 2001 and Ishibuchi and Tanaka, 1992). In view of the high capability of multi-layer neural networks as an approximator of nonlinear mappings, Ishibuchi and Tanaka (1992) employed two multi-layer perceptrons (MLPs), and Jeng et al. (2003) proposed using support vector interval regression networks to identify the upper and lower bounds of data interval. This motivates us to employ two CINHSs to determine a nonlinear interval regression model. In addition, since each output value or the synthetic evaluation of an alternative derived in an uncertain circumstance has its upper and lower bounds, the degree of importance of each criterion should not be unique and can be distributed in a range. In other words, the relative weights should be estimated as intervals because of a decision-maker’s uncertainty of judgments involved in real-world decision problems (Entani and Tanaka, 2007, Sugihara et al., 2004 and Wang et al., 2005). In recent years, many approaches have been proposed to determine interval weights in the analytic hierarchy process (AHP) (e.g., see Entani and Tanaka, 2007, Sugihara et al., 2004, Wang and Elhag, 2007 and Wang et al., 2005). There is no doubt that the identification of interval weights is a very important area of research. This also motivates us to identify interval weights in CINHSs. This paper aims to determine interval weights or possible ranges of the degree of importance of both aspects and attributes on the basis of three CINHSs with pre-specified hierarchical structure: one is a common network constructed merely by the least squared error, and the other two networks identify the upper and lower bounds of data interval. That is, each aspect or attribute has three relative weights. Furthermore, the key criteria can be further identified by inspecting the above ranges of the degree of importance. Learning algorithms of different CINHSs involving a general-purpose optimization technique, genetic algorithm (GA) (Goldberg, 1989), are proposed to automatically determine unknown connection weights from the input–output data. The rest of this paper is organized as follows. The Choquet integral and the fuzzy measure for hierarchical decisions are presented in Section 2. Section 3 introduces interval regression model. Section 4 describes the proposed GA-based learning algorithms of CINHSs for nonlinear interval model in detail. In Section 5, in order to demonstrate the effectiveness of the proposed method, the above-mentioned three CINHSs are evaluated by a practical decision problem about customer service perceptions on fast food stores in Taiwan. A simple but effective ranking method proposed by Wang et al. (2005) is further employed to compare the interval weights of criteria to identify key factors. The discussion and conclusions are presented in Section 6.

Since available information is often derived from uncertain assessments according to decision-makers’ intuition, it is reasonable to use interval evaluations to deal with the MCDM with uncertain information. Real intervals can suitably represent imprecise observations. There is no doubt that bounds of data interval and interval weights of respective criteria are important representations for dealing with uncertain information. This means that except for the traditional regression function determined by merely minimizing the least squared error, a nonlinear interval regression model consisting of the upper and lower bounds of data interval should be taken into account. The main contribution of this paper is that it employs three novel fuzzy neural networks with a pre-specified hierarchical structure, namely CINHSs, to determine respective regression functions using the proposed GA-based learning algorithm. A CINHS using multiple Choquet integral-based neurons can be used as the aggregation tool in information fusion. Furthermore, interval weights or possible ranges of the degree of importance of both aspect and attribute can be further identified from connection weights of the three trained CINHSs. The empirical results further demonstrate interesting and prominent findings obtained by the proposed method. From the empirical results with respect to customer service perceptions on fast food stores in Taiwan, it can be seen that the valence of the outcome can affect customer satisfaction. Thus, the improvement of customer satisfaction may not be only dependent on both interaction and physical environment for fast food stores. Although merely five fast food stores of foreign enterprises in Taiwan are taken into account, the findings suggest that the fast food stores or other service industries should seriously draw attention to valence. Even the outcome valence could not be easily controlled through the managing process, in order to improve customer perceptions and increase the probability of positive valence, managers still make more effort on achieving the desired outcome of customers, and creating affecting experience of consumption. It would be interesting to investigate that whether the valence has a stronger effect on satisfaction than both interaction and physical environment for fast food industries. As mentioned above, many approaches have been proposed to determine interval weights in the analytic hierarchy process (AHP) from the viewpoint of uncertain assessments of decision-makers. For instance, Sugihara et al. (2004) proposed using an interval approach to obtain interval weights from an interval comparison matrix by the interval regression analysis. Wang et al. (2005) developed a nonlinear programming approach to generating interval weights in the AHP. Wang and Elhag (2007) further proposed a goal programming (GP) method for obtaining interval weights for both crisp and interval comparison matrices. In Wang and Elhag (2007), the GP method showed some advantages over the interval regression analysis for some cases. The common concern among the proposed method and the above approaches is that available information is derived from uncertain assessments according to decision-makers’ intuition. Nevertheless, interval weights in the AHP are acquired from pairwise comparison matrices, whereas those in CINHSs are acquired by available input–output samples. In other words, this paper deals with the inverse problem of information fusion by optimally identifying fuzzy densities used in the fuzzy integral. Additionally, this paper assumes that the given training data are not contaminated by outliers for simplicity. However, it is possible that the training data could be spoiled by outliers. It is known that, since the interval model determined by the neural network approaches introduced by Ishibuchi and Tanaka (1992) could include all training data, such neural approaches are sensitive to outliers (Huang et al., 1998). In order to overcome the problem of contamination by outliers for the nonlinear interval regression analysis, many robust algorithms have been introduced (e.g., see Huang et al., 1998, Hwang et al., 2006 and Jeng et al., 2003). Although the robustness of the proposed GA-based learning algorithms is not the focus of this paper, it merits further exploration in future studies.