A short survey on the usage of choquet integral and its associated fuzzy measure in multiple attribute analysis

Choquet integral operator is currently making inroads into many real multiple attribute analysis due to its ability on modeling the usual interactions held by the attributes during the aggregation process.Unfortunately, the process of identifying 2n values of fuzzy measure prior to employing Choquet integral normally turns into a very complex one with the increasing number of attributes, n.On that note, this paper mainly reviews on some of the methods that have been proposed in reducing the complexity of identifying fuzzy measure values together with their pros and cons. The paper begins with a discussion on the aggregation process in multiple attribute analysis which then focuses on the usage of Choquet integral and its associated fuzzy measure before investigating some of the fuzzy measure identification methods A simple numerical example to demonstrate the merit of using Choquet integral and the indications for future research are provided as well.The paper to some extent would be helpful in stimulating new ideas for developing simpler or enhanced versions of fuzzy measure identification methods

A multi-attribute decision making procedure using fuzzy numbers and hybrid aggregators

The classical Analytical Hierarchy Process (AHP) has two limitations. Firstly, it disregards the aspect of uncertainty that usually embedded in the data or information expressed by human. Secondly, it ignores the aspect of interdependencies among attributes during aggregation. The application of fuzzy numbers aids in confronting the former issue whereas, the usage of Choquet Integral operator helps in dealing with the later issue. However, the application of fuzzy numbers into multi-attribute decision making (MADM) demands some additional steps and inputs from decision maker(s). Similarly, identification of monotone measure weights prior to employing Choquet Integral requires huge number of computational steps and amount of inputs from decision makers, especially with the increasing number of attributes. Therefore, this research proposed a MADM procedure which able to reduce the number of computational steps and amount of information required from the decision makers when dealing with these two aspects simultaneously. To attain primary goal of this research, five phases were executed. First, the concept of fuzzy set theory and its application in AHP were investigated. Second, an analysis on the aggregation operators was conducted. Third, the investigation was narrowed on Choquet Integral and its associate monotone measure. Subsequently, the proposed procedure was developed with the convergence of five major components namely Factor Analysis, Fuzzy-Linguistic Estimator, Choquet Integral, Mikhailov‘s Fuzzy AHP, and Simple Weighted Average. Finally, the feasibility of the proposed procedure was verified by solving a real MADM problem where the image of three stores located in Sabak Bernam, Selangor, Malaysia was analysed from the homemakers‘ perspective. This research has a potential in motivating more decision makers to simultaneously include uncertainties in human‘s data and interdependencies among attributes when solving any MADM problems