Power geometric operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making |
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| Affiliation: | 1. College of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China;2. School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China;3. Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China;1. Department of Accounting Information, Takming University of Science and Technology, Taipei 114, Taiwan, ROC;2. Department of Computer Science and Information Engineering, Chinese Culture University, Taipei 111, Taiwan, ROC;3. Department of Management Information Systems, National Chengchi University, Taipei 116, Taiwan, ROC;1. International Islamic University, Islamabad, Pakistan;2. Gwangju Institute of Science and Technology, South Korea;1. Samsung Electronics, Republic of Korea;2. Intelligent Systems and Emotional Engineering (ISEE) Laboratory, Department of Mechatronics Engineering, Chungnam National University, Republic of Korea;1. Department of Economics, Ca’ Foscari University of Venice, Italy;2. Department of Management, Ca’ Foscari University of Venice, Italy |
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| Abstract: | As a special intuitionistic fuzzy set on a real number set, trapezoidal intuitionistic fuzzy numbers (TrIFNs) have the better capability to model ill-known quantities. The purpose of this paper is to develop some power geometric operators of TrIFNs and apply to multi-attribute group decision making (MAGDM) with TrIFNs. First, the lower and upper weighted possibility means of TrIFNs are introduced as well as weighted possibility means. Hereby, a new lexicographic method is developed to rank TrIFNs. The Minkowski distance between TrIFNs is defined. Then, four kinds of power geometric operators of TrIFNs are investigated including the power geometric operator of TrIFNs, power weighted geometric operator of TrIFNs, power ordered weighted geometric operator of TrIFNs and power hybrid geometric operator of TrIFNs. Their desirable properties are discussed. Four methods for MAGDM with TrIFNs are respectively proposed for the four cases whether the weight vectors of attributes and DMs are known or unknown. In these methods, the individual overall attribute values of alternatives are generated by using the power geometric or power weighted geometric operator of TrIFNs. The collective overall attribute values of alternatives are determined through constructing the multi-objective optimization model, which is transformed into the goal programming model to solve. Thus, the ranking order of alternatives is obtained according to the collective overall attribute values of alternatives. Finally, the green supplier selection problem is illustrated to demonstrate the application and validation of the proposed method. |
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| Keywords: | Multi-attribute group decision making Trapezoidal intuitionistic fuzzy number Weighted possibility mean Power geometric operator |
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