# Unconstrained Estimation of Multitype Car Rental Demand
## 2 Unconstrained Estimation
### Improved Multitype Spill Model
#### 2.3.1 SP/RP Survey  
The basic data of customer selection preference were obtained by stated preference (SP) and revealed preference (RP) surveys. The SP survey preresearches the subjective preferences of customers when renting a car before the rental occurs. The RP survey analyzes the actual selection behavior of customers in the context of what has happened. SP data were more flexible, while RP data were more reliable. The SP survey can obtain multiple data from a single interviewee, with the advantages of small sample and low survey cost. The basic principle of the SP survey is to predetermine the various attribute factors and their influence levels and then invite interviewees to score the plan in the set situation. The respondents' choices may be different from their actual actions, but they can still find the main factors that can be calculated and have a large impact on the overall mean. Then, the secondary factors that are difficult to measure will be removed. The data obtained from the RP survey are the actual occurrence data, since the data records behaviors that have been taken by the respondent or the actual selection behavior observed. The basic principle of the RP survey is to describe the occurrence or existence of the situation with different attribute factors and influence levels and to invite the respondents to score the content. Before the SP survey plan is designed, condition attributes, decision attributes, and corresponding level values should be determined. The survey content includes the importance of the brand effect, the satisfaction of car rental type, the sensitivity of the rental price, returning location, satisfaction of the vehicle status, and the satisfaction with a special offer, service attitude, procedure convenience, and accident handling. The RP survey is aimed at customers who have made choices, and the influencing factors are rated as very satisfied, satisfied, general, not satisfied, and very dissatisfied. The survey includes the type of rental vehicle and satisfaction with the rental price, return location restrictions, vehicle status, service attitude, procedure convenience, and accident handling when the preferred rental vehicle is rejected. See Appendices A and B for the SP/RP questionnaire of the case study. Customers are affected by many attributes when selecting multiple models. In order to determine the degree of influence of each attribute, AHP is usually used. AHP (analytic hierarchy process) is an easy way to quantitatively and qualitatively deal with some fuzzy and complex subjective problems. The most critical step is to obtain a judgment matrix by pairwise comparison to calculate the weight of each factor. The specific calculation process is not given. However, due to the uncertainty of expert experience, the subjective constructed judgment matrix may not meet the conditions of complete consistency. In order to reduce the inconsistency of subjective judgment, the VPRS (variable precision rough set) can be used to simplify the factors affecting the customer's choice behavior, and similar factors are described by several factors to construct the judgment matrix. VPRS expands the Pawlak rough set by introducing a confidence level \(\eta(0.5<\eta\leq 1)\), so that admissible classification error is allowed to a certain extent. It can improve the flexibility of decision rules and, at the same time, reflect the correlation in data analysis, which is beneficial to the discovery of relevant data from unrelated data, that is, the implicit patterns in the data can be more clearly expressed [37]. Let \(S=(U,A,V,f)\) be an information system, where \(U=\left\{u_{1},u_{2},\cdots,u_{|U|}\right\}\) is a finite nonempty set called the domain object space. \(A=\left\{a_{1},a_{2},\cdots,a_{|A|}\right\}\) is a finite nonempty subset of attributes.