A Multiple Attribute Decision Making Method Based on Uncertain Linguistic Heronian Mean

Xiaodi Liu,Guodong Liu,Jianjun Zhu,Jingjing Hao

doi:10.1155/2013/597671

Abstract

The Heronian mean is a useful aggregation operator which can capture the interrelationship of the input arguments. In this paper, we develop some Heronian means based on uncertain linguistic variables, such as the generalized uncertain linguistic Heronian mean (GULHM) and uncertain linguistic geometric Heronian mean (ULGHM), and some of their desirable properties are also investigated. Considering the different importance of the input arguments, we define the generalized uncertain linguistic weighted Heronian mean (GULWHM) and uncertain linguistic weighted geometric Heronian mean (ULWGHM). Then, a method of multiple attribute decision making under uncertain linguistic environment is presented based on the GULWHM or the ULWGHM. In the end, an example is given to demonstrate the effectiveness and feasibility of the proposed method.

Highlights

Multiple attribute decision making exists here and there, and a multiple attribute decision making problem is to find the most desirable candidate from some feasible alternatives
We develop some Heronian means based on uncertain linguistic variables, such as the generalized uncertain linguistic Heronian mean (GULHM) and uncertain linguistic geometric Heronian mean (ULGHM), and some of their desirable properties are investigated
Decision-makers often provide their preferences on alternatives using linguistic term sets instead of numerical values owing to the fuzziness of human thinking process, and multiple attribute decision making under linguistic environment is a focus in recent years [1,2,3,4,5,6,7,8,9,10,11,12]

Summary

Introduction

Multiple attribute decision making exists here and there, and a multiple attribute decision making problem is to find the most desirable candidate from some feasible alternatives. In the process of decision making, the input arguments need to be aggregated by some proper approaches so that the decision makers can select the most desirable alternative. Among these approaches, the operators are widely used. Yager [13] introduced the ordered weighted averaging (OWA) operator, which has only been used in situations in which the input arguments are the exact numerical values. The ULWA operator only weights the uncertain linguistic arguments while the ULOWA operator only weights the ordered positions of the uncertain linguistic arguments. The ULHA operator combines the advantages of the ULWA and the ULOWA operator and weights the given arguments and their ordered positions. In order to solve the drawbacks of the ULWGM and the ULOWG operator, Wei [21] developed

Methods

Discussion

Conclusion