An Analysis of Shopping Choice behavior Using Fuzzy Multiattribute Attitude Model

There have been a number of investigations of the impact of the location of a town, city, or trading area as a determinant of store patronage. For example, it was found that the large majority living in small towns shopped beyond the town boundalies (Engel et al., 1986; Nakanishi, 1983). However, it is suggested that the consumer's attitude (or mental image) related to store or shopping area is more important in explaining shopping behavior and preferences than is actual location.Attitude is a central concept in consumer psychology, and defined as sum total of evaluation of the perceived attributes of alternatives. Traditional approaches to the measurement of attitude have involved method such as the semantic differential, the Likert scale, or the Thurstone scale. Althoguh insights into ambiguous nature of attitudes were identified early in the development of attitude measurement, the subsequent methods used failed to capture this ambiguity, no doubt because traditional mathematics was not well developed for dealing with ambiguity of judgment.We propose a fuzzy multiattribute attitude model (FMA model) for explaining shopping choice behavior. The FMA model is an extension of traditional multiattribute attitude model such as Fishbein model, and the application of the fuzzy set theory to the multiattribute attitude model.A fuzzy set A is defined as follows. Let X denote a universal set. Then, the membership function, μA by which a fuzzy set A is defined has the formWhere [0, 1] denotes the interval of real numbers from 0 to 1, inclusive. A convex and normalized fuzzy set whose membership function is piecewise continuous is called a fuzzy number. Fuzzy rating data we postulated in the FMA model can be approximated to fuzzy numbers.Symbolically, the FMA model can be expressed aswhere: A basic principle that allow the generalization of crisp mathematical concepts to the fuzzy framework is known as the extension principle proposed by Zadeh (1975). It provides the means for any function f that maps points x1, x2, /…, xn in the crisp set X to the crisp set Y to be generalized such that it maps fuzzy subsets of X to Y. According to the extension principle, the membership function for the FMA model can be expressed as follows.Where: In order to test the FMA model, we use the fuzzy rating method (Hesketh et al., 1988; Takemura, 1990, 1991). The fuzzy rating scale presents respondents with the option of indicating a preferred point and then asks them to extend the rating to the left or light if they wish. By making certain simplifying assumption, the fuzzy rating data can be viewed as fuzzy numbers, hence making possible the use of fuzzy set theoretic operations. For the purpose of explaining shopping choice behavior, a survey study has been undertaken in Kyoto city, Japan.