Pre-Emptive-Weights Goal-Programming for a Multi-Attribute Decision-Making Problem with Positive Correlation among Finite Criteria

This paper analyzes the various properties of the positively correlated weights related to the subset of finite criteria in a multi-attribute decision-making problem. Given a finite number of criteria, the exact constraints of the positively correlated weights related to the subset of criteria are presented. Introducing the non-Archimedean number, the associated bounded polyhedral-set is shown. The number of the extreme points in the bounded polyhedral-set will increase as the number of criteria increase. Applying the proposed efficient extreme-point method, the pre-emptive-weights-goal-programming optimal solution is shown. These theoretical global-maximum values of the positively correlated weights related to the subset of finite criteria are useful for practical applications.

Automated summary

This paper analyzes the properties of positively correlated weights related to a subset of finite criteria in a multi-attribute decision-making problem. It presents the exact constraints of these weights and introduces the concept of non-Archimedean number and bounded polyhedral-set. The paper also shows the increase in the number of extreme points in the bounded polyhedral-set as the number of criteria increases. It applies an efficient extreme-point method to obtain the optimal solution for pre-emptive-weights-goal-programming.