Belief rule-based methodology for mapping consumer preferences and setting product targets

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Abstract

Rapid and accurate identification of consumer demands and systematic assessment of product quality are essential to success for new product development, in particular for fast moving consumer goods such as food and drink products. This paper reports an investigation into a belief rule-based (BRB) methodology for quality assessment, target setting and consumer preference prediction in retro-fit design of food and drink products. The BRB methodology can be used to represent the relationships between consumer preferences and product attributes, which are complicated and nonlinear. A BRB system can initially be established using expert knowledge and then optimally trained and validated using data generated from consumer or expert panel assessments or from tests and experiments. The established BRBs can then be used to predict the consumer acceptance of new products or set product target values in retro-fit design. The proposed BRB methodology is applied to the design of a lemonade drink product using real data provided by a sensory product manufacturer in the UK. The results show that the BRB methodology can be used to predict consumer preferences with high accuracy and to set optimal target values for product quality improvement.

Introduction

Consumer preferences for a food and drink product are closely related to its sensory attributes, which are those such as appearance, aroma, flavor, and the like (Meilgaard, Civille, & Carr, 1999). It is very important to understand and establish such relationships for predicting consumer acceptance or liking in the design and testing of new food and drink product designs.

To investigate the impacts of sensory attributes of food and drink products on consumer preferences, models that can relate consumer preferences to sensory attributes need to be developed. Several methodologies have been suggested in the literature that can be used to model relationships between consumer preferences and sensory attributes. Multiple linear regression (MLR) analysis is perhaps the simplest methodology that could be used for this purpose, but it is proven to be not adequate in capturing consumer preferences from sensory attributes. This is largely because the relationships between consumer preferences and sensory attributes are complicated and highly nonlinear and hence cannot be adequately interpreted by linear models. Another reason is that the number of sensory attributes is often larger than the number of products, which makes MLR model parameters estimated from a small number of samples highly unstable, but in some cases, MLR can still provide some useful models.

External preference mapping (EPM) (Arditti, 1997, Faber et al., 2003, Geel et al., 2005, Guinard et al., 2001, Heyd and Danzart, 1998, Martínez et al., 2002, van Kleef et al., 2006) turns out to be the most extensively used methodology for sensory analysis. EPM models consumer preferences as a polynomial function of the first two principal components (PCs) that are extracted from the sensory data of food and drink products using the principal component analysis (PCA). The polynomial function could be quadratic, elliptical, circular, or vector models, as shown below (Faber et al., 2003):Vector:y=a+b1x1+b2x2+ε,Circular:y=a+b1x1+b2x2+cx12+x22+ε,Elliptical:y=a+b1x1+b2x2+c1x12+c2x22+ε,Quadratic:y=a+b1x1+b2x2+c1x12+c2x22+dx1x2+ε,where y is consumer preferences, x1 and x2 are the first two PCs, and ε is residual error.

A vector model is often used, but the choice for a more complex model is possible, depending upon a goodness-of-fit test. It is well documented that not all consumer preference data can be well fitted and accounted for by EPM (Faber et al., 2003). In particular, vector models are essentially linear, which makes their explanatory power very limited. Furthermore, the aggregation of all sensory attributes into two PCs without proper classification makes the PCs difficult to explain and understand.

Artificial neural networks (ANNs) (Boccorh and Paterson, 2002, Bomio, 1998, Krishnamurthy et al., 2007, Tan et al., 1999, Zhang and Chen, 1997) are another popular methodology for modeling the relationships between consumer preferences and sensory attributes, which model consumer preferences as a complicated nonlinear function of sensory attributes. The nonlinear function is defined by a multilayer network, including one or more hidden layers, with sensory attributes as inputs and consumer preferences as output. It is believed that a three-layer neural network with a sufficiently large number of hidden neurons can model any nonlinear relationships between inputs and outputs (Haykin, 1994). So, three-layer neural networks (NNs) are most widely used in practice. Although ANNs have very strong nonlinear modeling capabilities, they suffer from some drawbacks, two of which are black-box problem and over-fitting problem. The black-box problem means that ANNs are basically a black box simulator. The relationships between inputs and output are not explicit or transparent, so it is difficult to understand or predict its behaviors. The over-fitting problem means that ANNs may sometimes fit training data set perfectly well, whereas perform poorly on testing data set. In other words, ANNs may sometimes have a poor generalization capability. Another significant drawback of ANNs is their inability to be trained to set targets for sensory attributes.

Support vector machines (SVMs) as an Artificial Intelligence method have gained increasing popularity in recent years and also been used for learning consumer preferences from the analysis of sensory data by Bahamonde, Díez, Quevedo, Luaces, and del Coz (2007). SVM is a machine learning algorithm developed by Vapnik (1995) and has been shown to be very effective for both classification and regression analyses. In classification analysis, SVMs attempt to find an optimal hyperplane to separate two classes. For regression analysis, SVMs are aimed at estimating an unknown continuously-valued function based on a finite number of noisy samples. In SVMs for regression analysis, input data are mapped into a high dimensional feature space where a linear model is constructed and linear regression is performed by using ε-insensitive loss. Mathematically, SVM regression is formulated as a convex quadratic programming problem (QPP) with inequality constraints, which produces a global optimal solution. SVMs offer new possibilities to learn consumer preferences from sensory data with a high order polynomial kernel function or even a Gaussian radial basis function (RBF), but they need to pre-specify kernel functional forms and predetermine SVM parameters, which prove to be highly subjective and may have significant impact on the performances of SVM regression models. Since the true relationships between consumer preferences and sensory attributes are not known, it is not appropriate, if not entirely impossible, to specify the functional forms of the relationships in advance. Besides, why an unknown relationship could be described by a particularly chosen kernel function is also difficult to explain in theory.

Based on the above analyses, in this paper we propose a belief rule-based (BRB) methodology for quality assessment, target setting and consumer preference prediction in retro-fit design of food and drink products. The BRB methodology does not need to specify any functional form and characterizes the causal relationships between consumer preferences and product attributes using belief rule bases (BRBs). Each BRB is a collection of belief rules which are the generalization of traditional IF-THEN rules. So, a BRB system can represent functional relationships transparently, where expert knowledge can be explicitly embedded. Several types of parameters as well as the structure of a BRB system, such as belief degrees, rule weights and attribute weights, can be trained using collected data for food and drink products. The trained BRB system can then be used for predicting consumer preferences for new products or setting target values for product attributes to support product retro-design. In this paper, a practical retro-fit design case for a lemonade drink product is examined using the BRB methodology to show its potential in wide applications.

The rest of the paper is organized as follows. In Section 2, we investigate the BRB methodology and the models for learning and target setting. In Section 3, we examine a case study using the BRB methodology to illustrate its applications and potentials in sensory analysis and the retro design of food and drink products. The paper is concluded in Section 4.

Section snippets

BRB methodology

The BRB methodology for preference mapping and target setting of food and drink products includes preference mapping, inference, learning, prediction and target setting, which are elaborated in this section in detail.

Problem description and assessment data

A company designing and manufacturing sensory products in Northwest England wishes to design a lemonade drink product. Table 5, Table 6 show the sensory profiles of 27 lemonade drink products and consumer preferences for these products provided by the company, where the first 26 products are the popular products available in the market and the last one is the product of the company. The quality of the 27 lemonades is evaluated by a panel of nine experts using the 1–9 hedonic rating as shown in

Conclusions

Rapid and accurate identification of consumer demands and systematic assessment of product quality are very important to manufacturers. In this paper we investigated a novel belief rule-based (BRB) methodology for predicting consumer preferences in the retro-fit design of food and drink products. The BRB methodology links consumer preferences for food and drink products with their sensory attributes through a group of BRB models, which can be trained and validated using sensory data and

Acknowledgements

This project was supported by DEFRA under the Grant No. AFM222 and by EPSRC under the Grant No. EP/F024606/1. The work was also partially supported by the Natural Science Foundation of China (NSFC) under the Grant Nos. 60736026 and 70925004 and by City University of Hong Kong under the Grant No. 7002571.

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