A Mathematical Model for Nonlinear Optimization Which Attempts Membership Functions to Address the Uncertainties
Abstract
:1. Introduction
2. Literature Survey
3. Preliminaries
4. An Optimization Model for Fuzzy Nonlinear Programming
4.1. Formulation of the Fuzzy NLP with Equality Constraints
4.2. Computational Procedure
Remark
- A maximum point if starting with the principal major determinant of order then the last principal minor determinants of form an alternating sign pattern starting with
- A minimum point if starting with the principal minor determinant of order then the last principal minor determinants of having the sign of
5. Numerical Illustration
5.1. Case (i): NLP with Fuzzy Membership Functions
5.2. Case (ii): The Robust Ranking Approach for NLP with Fuzzy MFs
5.3. Models Performance Evaluation with Different Sets of Inputs
5.4. Comparison Analysis
6. Results and Discussion
- The decision-maker perception, the entire value of the fuzzy NLPP, will be higher than and less than .
- The decision-maker for the entire fuzzy NLPP estimations are going to be bigger than or sufficient to and less than or equivalent to .
- The extent of the favors of the decision-maker for the rest of the estimations of the entire fuzzy NLPP value has frequently been attained as below:
- Here x describes the significance of the entire NLPP, and also the perception of decision-makers for , where
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Fuzzy Input for Objective Functions’ Coefficient | Fuzy Inputs for Coefficients in Constiants’ and Right Side’s Value | Optimal Objective Value | Solutions | |
---|---|---|---|---|
Set-1 | [2,4,7,11]; [6.5,12.3,16,19.98]; [5,9,11.5,15.07] | [4,7,10,13]; [2.5,4.9,7.9,11]; [1.2,3.4,6.7,10.5] and [11.8,14.9,19.2,24.4] | 20.3700 | |
Set-2 | [0.4,1.13,2.31,5.56]; [16.15,22.39,26.78,29.59]; [5.98,7.99,10.54,13.67] | [1.56,2.67,6.64,9.88]; [2.35,3.89,6.99,8.92]; [5.22,7.41,9.27,10.53] and | 138.5768 | |
Set-3 | [-3.35,-0.93,-4.11,8.61]; [-5.11,-1.09,-3.11,10.19], [25.98,27.99,30.54,33.67] | [21.05,22.07,26.06,29.08], [12.03,13.09,16.09,18.02], [25.02,27.01,29.07,30.03] and [12,13,14,15] | 0.0178 | |
Set-4 | [63.89,70.31,79.91,85.13]; [45.11,51.98,63.44,0.97]; [75.21,87.23,90.44,99.92] | [29.68,34.55,39.13,41.45], [12.03,14.09,17.09,19.02], [11.12,12.17,14.19,18.71] and [111.2,122.1,134.9,148.7] | 412.3734 |
Optimum Values | The Existing Model Is Based on the Conventional Approach | The Proposed Model Is Based on the Conventional Approach in Terms of Fuzziness | The Proposed Model Is Based on the Robust Ranking Approach |
---|---|---|---|
2.8 | |||
0 | |||
1.4 | |||
1.4 | |||
Min Z | 9.8 |
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Kaliyaperumal, P.; Das, A. A Mathematical Model for Nonlinear Optimization Which Attempts Membership Functions to Address the Uncertainties. Mathematics 2022, 10, 1743. https://doi.org/10.3390/math10101743
Kaliyaperumal P, Das A. A Mathematical Model for Nonlinear Optimization Which Attempts Membership Functions to Address the Uncertainties. Mathematics. 2022; 10(10):1743. https://doi.org/10.3390/math10101743
Chicago/Turabian StyleKaliyaperumal, Palanivel, and Amrit Das. 2022. "A Mathematical Model for Nonlinear Optimization Which Attempts Membership Functions to Address the Uncertainties" Mathematics 10, no. 10: 1743. https://doi.org/10.3390/math10101743