Purchase Preference Analaysis and Trend Forecast
Consumer Behaviors and Preference One consumer would in general have different*consumption behaviors or preferences*from another. He may spend money on computers and technical books, while the other may spend on clothing and food. Availability of this information on consumer preference will be of great value to a marketing company, a bank, or a credit card company that can use this information to target different groups of consumer for improved*response rate*or*profit*. By the same token, information on consumption preference of the residents in one specific region can help businesses in*planning*their operations in this region for improved profit. Therefore, it is very important to have a tool that can help analyze*consumers behaviors*and forecast the*changes in purhcase patterns*and*changes in purchase trend*.Fuzzy Consumption Utility Functions-based Utility Theory In studying advanced methodology for consumption behaviors, AI researchers at Zaptron Systems have developed the so called*fuzzy utility functions*that can model and describe the consumption behaviors of a target consumer group.Consumption Utility - it is a criterion (or index) used to evaluate the effectiveness of customers consumption. A low value of consumption utility, say 0.15, indicates that a customer is not satisfied with the consumption of a certain commodity; while high value, say 0.96, indicates that the customer is very satisfied. There are formal theories on utility, including ordinal utility, cardinal utility and marginal utility. Consumption utility function - The behavioral characteristics of human beings can be represented by the concept of *consumption utility*, and consumption utility function is the mathematical description of this concept. In addition, human consumption behaviors are determined by the following two types of factors:objective factors - the physical, chemical, biological and artistic properties of goods; subjective factors - consumer's interest, preference and psychological state.
Fuzzy Set Theoretical Approach -- In fact, consumption utility is a fuzzy concept. To model the above subjective factors, fuzzy set theory is used to describe different levels of consumers satisfaction with respect to various consumption plans (spending patterns), such as "not satisfied," "somehow satisfied," "very satisfied," and etc. Mathematically, the fuzzy utility function is a more accurate measure on the consumption utility. It can describe the relationships among spending, price, consumption composition (decomposition), preference and subjective measure on commodity or service values. Mathematical model of fuzzy consumption functions - to model the consumption of one commodity, a fuzzy function Ui must satisfy the following three conditions (Xi is the spending on i-th commodity):
Ui: Xi --> Ui Ui --> 1 if Xi is infinity, Ui --> 0 if Xi is 0 The first derivative of Ui w.r.t. Xi must be positive,and the second derivative negative.
Di - a parameter related to customer's subjective evaluation on consumption (depreciation) Qi = Di*Pi, appreciation (not "satisfaction"), consumer's *subjective measure on the value*of a consumptionPi - price of the i-th commodity or service Si - percentage of spending on i-th commodity, 0 < Si < 1 and Si = Ai + Bi/C Ai - *Limit spending**percentage*of the i-th commodity in total spending when average personal income level increases so greatly that one could afford to spend to "limit" (as much as he or she desires) with unlimited financial resources. We always have 0.0 < Ai < 1.0.Bi - The trend of change in Ai due to change in average personal income level. Note the relationship between Ai an Bi as follows: Bi > 0 if Ai decreases, and Bi < 0 if Ai increases.C - total spending amount, in dollars, on all *N*commodities or servicesWi - a weighting factor representing a consumer's preference to the i-th commodity (0<Wi<1) Computation of Parameters {Di, Qi, Si, Ai, Bi, Wi} - Based on the Maximum Utility Principle, they can be computed by solving a set of complex mathematical equations. Zaptron's DataX™ software suite has special modules that compute them.
Problem Background - The annual data of the average spending amount (in dollars) on 5 categories by customers in a remote rural area (with severe electric power shortage, indicated by the smaller spending amount in the "Energy" column of Table-1) are available (see Table-1 below). Table-2 shows the parameters computed using the Zaptron model.
Table-1 Annual average consumption data for 5 categories (unit: 100 US$):
Table-2 Parameters computed using fuzzy consumption function:
Explanation of the Result **-** By studying Table-1 and Table-2, we can make the following observations:
4.1 Forecast on Future Consumption Trend We used the data for the years from 1980 to 1984 given in Table-2 above to forecast the consumption trend using the Time Series Analysis Tool of DataX. In forecasting, it is assumed that the annual spending rate increases by 8% and population increases by 0.9%. The forecast results so obtained for the years 1985, 1990, 1995 and 2000 are listed in Table-3. The following observations can be made from Table-3 and are consistent with the Engles Principle in economics.
4.2 Forecast on Consumer's Satisfaction Level Utility functions discussed above present the consumer's satisfaction level on individual and combined consumption. They can be used to forecast the customer satisfaction levels on various consumption categories. Table-4 gives the results computed by using DataX.. The table shows that the satisfaction level for housing is lowest (U4 = 0.0788), therefore the demand on housing (living) will be high - more than double every 5 years from 1985 to 2000.
Table-4 Forecast on Consumption Utility (Consumer Satisfaction Level Ui)
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Last updated November 25, 2000,
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