Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment

Abstract

In this paper, we investigate a new method to handle multiple attribute group decision making (MAGDM) problems based on combined ranking value under interval type-2 fuzzy environment, in which all the attribute values provided by experts take the form of interval type-2 fuzzy sets (IT2FSs). We first introduce some basic concepts and related operational laws on IT2FSs. Then, we put forward three kinds of ranking value formulas to calculate the ranking value of IT2FSs based on arithmetic average (AA) operator, geometric average (GA) operator and harmonic average (HA) operator, respectively, and discuss some of its desirable properties. Based on these properties, we define the concept of combined ranking value and also further develop a new interval type-2 fuzzy entropy with trigonometric sine function to measure the uncertainty of the IT2FSs. By using the three types ranking value formulas and interval type-2 fuzzy entropy we proposed, a new approach based on the principle of combinatorial optimization with ranking-entropy and the least squares for determining attribute weight is given. Furthermore, a decision making procedure based on combined ranking value is given to select the best alternative(s). Finally, a simple practical example concerns that urban rail transit evaluation is provided to illustrate the practicality and effectiveness of the proposed method, and a comparative analysis is performed.