Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness
In real-life scenarios, there are many mathematical tools to handle incomplete and imprecise data. One of them is the fuzzy approach. The main issue with addressing nonlinear interval programming (NIP) problems is that the optimal solution to the problem is a decision made under uncertainty that has...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-07-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/14/3123 |
| _version_ | 1797588443105067008 |
|---|---|
| author | Pavan Kumar Hamiden Abd El-Wahed Khalifa |
| author_facet | Pavan Kumar Hamiden Abd El-Wahed Khalifa |
| author_sort | Pavan Kumar |
| collection | DOAJ |
| description | In real-life scenarios, there are many mathematical tools to handle incomplete and imprecise data. One of them is the fuzzy approach. The main issue with addressing nonlinear interval programming (NIP) problems is that the optimal solution to the problem is a decision made under uncertainty that has a risk of not satisfying the feasibility and optimality criteria. Some strategies handle this kind of problem using classical terminology such as optimal solution and feasible solution. These strategies are insufficient for efficient analysis since the properties of the solution in an uncertain environment are ignored. Therefore, in the proposed approach, more suitable terminologies were suggested for the analysis process. In addition, it combines parametric treatment and interactive methodology. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming (MODP) issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the <i>α</i>-pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named the decomposition approach (DP), is presented for achieving a subset for the parametric space that contains the same <i>α</i>-pareto optimal solution. For a better understanding of the suggested concept, a numerical example is provided. |
| first_indexed | 2024-03-11T00:52:05Z |
| format | Article |
| id | doaj.art-b9e5112efb0341e59aab2d8d80a013a3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T00:52:05Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b9e5112efb0341e59aab2d8d80a013a32023-11-18T20:20:54ZengMDPI AGMathematics2227-73902023-07-011114312310.3390/math11143123Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving FuzzinessPavan Kumar0Hamiden Abd El-Wahed Khalifa1School of Advanced Science and Languages, VIT Bhopal University, Sehore 466116, IndiaDepartment of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi ArabiaIn real-life scenarios, there are many mathematical tools to handle incomplete and imprecise data. One of them is the fuzzy approach. The main issue with addressing nonlinear interval programming (NIP) problems is that the optimal solution to the problem is a decision made under uncertainty that has a risk of not satisfying the feasibility and optimality criteria. Some strategies handle this kind of problem using classical terminology such as optimal solution and feasible solution. These strategies are insufficient for efficient analysis since the properties of the solution in an uncertain environment are ignored. Therefore, in the proposed approach, more suitable terminologies were suggested for the analysis process. In addition, it combines parametric treatment and interactive methodology. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming (MODP) issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the <i>α</i>-pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named the decomposition approach (DP), is presented for achieving a subset for the parametric space that contains the same <i>α</i>-pareto optimal solution. For a better understanding of the suggested concept, a numerical example is provided.https://www.mdpi.com/2227-7390/11/14/3123optimizationmulti-objective dynamic programmingfuzzy setspiecewise quadratic fuzzy numbersclose interval approximationoptimization algorithm |
| spellingShingle | Pavan Kumar Hamiden Abd El-Wahed Khalifa Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness Mathematics optimization multi-objective dynamic programming fuzzy sets piecewise quadratic fuzzy numbers close interval approximation optimization algorithm |
| title | Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness |
| title_full | Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness |
| title_fullStr | Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness |
| title_full_unstemmed | Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness |
| title_short | Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness |
| title_sort | enhancing decomposition approach for solving multi objective dynamic non linear programming problems involving fuzziness |
| topic | optimization multi-objective dynamic programming fuzzy sets piecewise quadratic fuzzy numbers close interval approximation optimization algorithm |
| url | https://www.mdpi.com/2227-7390/11/14/3123 |
| work_keys_str_mv | AT pavankumar enhancingdecompositionapproachforsolvingmultiobjectivedynamicnonlinearprogrammingproblemsinvolvingfuzziness AT hamidenabdelwahedkhalifa enhancingdecompositionapproachforsolvingmultiobjectivedynamicnonlinearprogrammingproblemsinvolvingfuzziness |