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 p...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-12-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/12/1/20 |
| _version_ | 1797446169845039104 |
|---|---|
| author | Juin-Han Chen Hui-Chin Tang |
| author_facet | Juin-Han Chen Hui-Chin Tang |
| author_sort | Juin-Han Chen |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T13:37:26Z |
| format | Article |
| id | doaj.art-bd7ec9c9b9694475be6d108ad1216f2c |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:37:26Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-bd7ec9c9b9694475be6d108ad1216f2c2023-11-30T21:11:11ZengMDPI AGAxioms2075-16802022-12-011212010.3390/axioms12010020Pre-Emptive-Weights Goal-Programming for a Multi-Attribute Decision-Making Problem with Positive Correlation among Finite CriteriaJuin-Han Chen0Hui-Chin Tang1Department of Industrial Engineering and Management, Cheng Shiu University, Kaohsiung City 83347, TaiwanDepartment of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung City 80778, TaiwanThis 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.https://www.mdpi.com/2075-1680/12/1/20multi-attribute decision-makingcorrelationextreme pointsgoal-programming |
| spellingShingle | Juin-Han Chen Hui-Chin Tang Pre-Emptive-Weights Goal-Programming for a Multi-Attribute Decision-Making Problem with Positive Correlation among Finite Criteria Axioms multi-attribute decision-making correlation extreme points goal-programming |
| title | Pre-Emptive-Weights Goal-Programming for a Multi-Attribute Decision-Making Problem with Positive Correlation among Finite Criteria |
| title_full | Pre-Emptive-Weights Goal-Programming for a Multi-Attribute Decision-Making Problem with Positive Correlation among Finite Criteria |
| title_fullStr | Pre-Emptive-Weights Goal-Programming for a Multi-Attribute Decision-Making Problem with Positive Correlation among Finite Criteria |
| title_full_unstemmed | Pre-Emptive-Weights Goal-Programming for a Multi-Attribute Decision-Making Problem with Positive Correlation among Finite Criteria |
| title_short | Pre-Emptive-Weights Goal-Programming for a Multi-Attribute Decision-Making Problem with Positive Correlation among Finite Criteria |
| title_sort | pre emptive weights goal programming for a multi attribute decision making problem with positive correlation among finite criteria |
| topic | multi-attribute decision-making correlation extreme points goal-programming |
| url | https://www.mdpi.com/2075-1680/12/1/20 |
| work_keys_str_mv | AT juinhanchen preemptiveweightsgoalprogrammingforamultiattributedecisionmakingproblemwithpositivecorrelationamongfinitecriteria AT huichintang preemptiveweightsgoalprogrammingforamultiattributedecisionmakingproblemwithpositivecorrelationamongfinitecriteria |