Uncertain Linguistic Power Geometric Operators and Their Use in Multiattribute Group Decision Making

Huimin Zhang

doi:10.1155/2015/948380

Abstract

Based on the extended triangular norm, several new operational laws for linguistic variables and uncertain linguistic variables (ULVs) are defined. To avoid the limitations of existing linguistic aggregation operators, a series of extended uncertain linguistic (UL) geometric aggregation operators are proposed on the basis of the extended triangular norm. In addition, a multiattribute group decision making (MAGDM) method dealing with UL information is developed based on the extended UL geometric aggregation operators. Finally, an example is presented to show the efficiency of the developed approach in solving MAGDM problems.

Highlights

Due to the increasing complexity of the decision problem and our limited ability, in the multiattribute group decision making (MAGDM) process, decision makers sometimes have difficulty in providing their opinions with crisp numbers
Xu [13] proposed the concept of uncertain linguistic variables (ULVs) which can be regarded as one linguistic interval and is convenient for decision makers to better express their opinions
To overcome such issues, motivated by Lan et al [18], we introduce the extended triangular norm and propose several uncertain linguistic power geometric (PG) operators based on the extended triangular norm

Summary

Introduction

Due to the increasing complexity of the decision problem and our limited ability, in the multiattribute group decision making (MAGDM) process, decision makers sometimes have difficulty in providing their opinions with crisp numbers. Yager [21] introduced the power-average (PA) operator and the power OWA (POWA) operator which allow arguments to support each other in the aggregation process. On this basis, Xu and Yager [22] developed the power geometric (PG) operator, weighted PG operator, and POWG operator. Up to now, there is no PG operator developed for dealing with UL decision making problems To overcome such issues, motivated by Lan et al [18], we introduce the extended triangular norm and propose several uncertain linguistic PG operators based on the extended triangular norm.

Preliminaries

MAGDM Method Based on the Extended Uncertain Linguistic Aggregation Operators

Application Example

Conclusions