Z-number-based conjoint analysis method for analyzing decision-makers' preference levels in attribute ratings

Fuzzy Conjoint Analysis Method (FCAM) is widely used in multi-attribute decision making areas particularly in analyzing decision makers' preferences towards attributes. Discrete fuzzy sets are commonly used to define the membership function of linguistic values. Nevertheless, the use of discrete fuzzy sets in representing human judgment and preference levels may not be sufficient in describing human preference defined on continuous scale. In FCAM, discrete fuzzy sets or fuzzy numbers are commonly used to represent the linguistic terms that merely describe ratings or levels of satisfaction on attributes based on decision makers' opinions or preferences. The certainty elements in terms of confidence level associated with decision makers' judgment and preferences are seldom considered in FCAM. Thus, in this study, Z-numbers which are composed of ratings with certainty components (in the form of confidence level) are integrated in the existing FCAM procedure. In the proposed procedure of Z-number based Conjoint Analysis Method (Z-CAM), preferences described in the form of ratings with confidence levels are expressed in the form Z-numbers. The existing FCAM procedure is slightly modified so as to cater the Z-number input data. Z-CAM has an additional feature in comparison to the existing FCAM whereby in addition to ranking the attributes, the former could also produce overall ratings supported with confidence levels.