An Approach to Determining Attribute Weights Based on Integrating Preference Information on Attributes with Decision Matrix.

Quan Zhang,Hongwei Xiu

doi:10.1155/2018/4864517

Abstract

The interval multiple attribute decision-making problems are studied in this paper, where the preference information on attributes is expressed with preference orderings, linguistic terms, interval numbers, and inequality constraints among partial attribute weights. An approach is proposed to determine the attribute weights based on the preference information on attributes and the interval decision matrix. Firstly, preference orderings, linguistic terms, and interval numbers are normalized and aggregated into the group opinions, based on which an optimization model is set up to calculate the subjective attribute weights by including inequality constraints among partial attribute weights in the model. Then, based on the interval decision matrix, the entropy method is adopted to calculate the objective attribute weights, which is integrated with the subjective weights so that both the subjective preference information and the objective information in the decision matrix are reflected. Finally, an example is used to illustrate the proposed approach.

Highlights

Multiple attribute decision making (MADM) refers to ranking or selecting the alternatives that are associated with noncommensurate and conflicting attributes [1,2,3]
While determining the attribute weights, commonly, there are two types of methods: the methods based on the subjective information [8, 9] and those based on the decision matrix
The attribute weights can be determined based on the decision matrix. e attribute values of alternatives in the decision matrix are considered as the objective information [3, 6]

Summary

Introduction

Multiple attribute decision making (MADM) refers to ranking or selecting the alternatives that are associated with noncommensurate and conflicting attributes [1,2,3]. It is desirable to deal with preference orderings, linguistic terms, interval numbers, and inequality constraints among the attribute weights in the MADM process since they are the common ways for experts to use when expressing their subjective preference on attributes and accurately. It is desirable to determine the attribute weights by integrating the interval decision matrix with experts’ preference information on attribute weights in the forms of preference orderings, linguistic terms, interval numbers, and inequality constraints among the attribute weights. E purpose of this paper is to propose an approach to determining attribute weights based on integrating interval decision matrix and the experts’ preference information on attributes in the formats of preference orderings, linguistic terms, interval numbers, and inequality constraints among them.

Problem Descriptions

The Proposed Approach

Determine Attribute Weights Based on the Experts’

Illustrations