Hybrid Intuitionistic Fuzzy Entropy-SWARA-COPRAS Method for Multi-Criteria Sustainable Biomass Crop Type Selection
Abstract
:1. Introduction
- This study conducts a survey through review of the existing literature and holding of interviews with experts with the aim of finding the key attribute for the assessment of the SBCT alternatives.
- It develops an integrated intuitionistic fuzzy entropy-SWARA-COPRAS model to evaluate the SBCT evaluation problem when the available information is uncertain.
- This paper proposes a novel combined weighting approach with entropy and SWARA to evaluate the criteria weights under an intuitionistic fuzzy environment.
- This study empirically studies the SBCT selection problem to evaluate the practicability and efficacy of the developed IF-entropy-SWARA-COPRAS methodology.
- This paper also involves comparative study and sensitivity investigation to assess the effectiveness and strength of the presented approach.
2. Proposed Methodology
2.1. Preliminaries
2.2. New IF-Entropy-SWARA-COPRAS Model
3. Result and Discussion
3.1. Case Study: SBCT Selection Problem
3.2. Comparison and Sensitivity Investigation
- In the IF-Entropy-SWARA-COPRAS model, both criteria types, i.e., benefit and cost, were taken in the evaluation. Taking these attributes with complex proportions provides more accurate data than only treating with the benefit or cost criteria. Hence, it improves the usefulness of the initial information and the correctness of the outcomes.
- In the IF-TOPSIS model [47,60], it is required to find the similarity/distance between each alternative and the IF-IS, which is a difficult process that diminishes the accuracy of the results, whereas the PF-COPRAS [61] can be obtained from the association of complex relations between options of the PF-DM with the PFWA operator. Here, the integrated IF-Entropy-SWARA-COPRAS model uses an easy and instinctive procedure that produces suitable, sensible, and comparatively exact results in assessing and choosing various SBCT options based on the performance tools. The IF-Entropy-SWARA-COPRAS model offers a notion of UGs to prefer the best options.
- In the Cobuloglu & Buyuktahtakın [12] and Buyukozkan & Gocer [61] models, the AHP tool is implemented for finding attributes’ weights, which is an intricate process [62]. In the Mishra et al. [49] model, the similarity-based weighting tool is utilized to compute the objective weights of attributes. In the presented IF-Entropy-SWARA-COPRAS model, an integrated weighting model—by joining the entropy-based tool for objective weight and the SWARA model for subjective weight—is discussed to obtain the attribute weights.
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Aspects | Criteria | Type | SBCT |
---|---|---|---|
Economic | Seeding (L1) | Benefit | Corn (P1) |
Biomass yield (L2) | Benefit | ||
Production and harvesting (L3) | Benefit | ||
Transportation and storage (L4) | Benefit | Wheat (P2) | |
Conversion rate (L5) | Benefit | ||
Robustness to risks (L6) | Cost | ||
Equipment and knowledge (L7) | Benefit | Miscanthus (P3) | |
Environmental | Soil quality impact (L8) | Benefit | |
Carbon emissions (L9) | Cost | ||
Water quality/requirement (L10) | Benefit | Switchgrass (P4) | |
Biodiversity and wildlife (L11) | Benefit | ||
Invasiveness (L12) | Cost | ||
Social | Technological development (L13) | Benefit | Sugarcane (P5) |
Workforce requirement (L14) | Benefit | ||
Energy safety and welfare (L15) | Benefit | ||
Food competition (L16) | Benefit |
Linguistic Rating | IFN |
---|---|
Extremely skilled (ES) | (1.00, 0.00, 0.00) |
Very very skilled (VVS) | (0.95, 0.03, 0.02) |
Very skilled (VS) | (0.80, 0.15, 0.05) |
Skilled (S) | (0.60, 0.30, 0.10) |
Less skilled (LS) | (0.40, 0.55, 0.05) |
Very less skilled (VLS) | (0.30, 0.65, 0.05) |
Extremely less skilled (ELS) | (0.10, 0.85, 0.05) |
Linguistic Rating | IFN |
---|---|
Absolutely good (AG) | (0.95, 0.05) |
Very very good (VVG) | (0.85, 0.10) |
Very good | (0.80, 0.15) |
Good (G) | (0.70, 0.20) |
Pretty good (PG) | (0.60, 0.30) |
Medium (M) | (0.50, 0.40) |
Pretty poor (PP) | (0.40, 0.50) |
Poor (P) | (0.30, 0.60) |
Very poor (VP) | (0.20, 0.70) |
Very very poor (VVP) | (0.10, 0.80) |
Absolutely poor (AP) | (0.05, 0.95) |
DEs | E1 | E2 | E3 |
---|---|---|---|
Linguistic ratings | Very skilled (VS) (0.80, 0.15, 0.05) | Skilled (S) (0.60, 0.30, 0.10) | Less skilled (LS) (0.40, 0.55, 0.05) |
Weight | 0.4286 | 0.3367 | 0.2347 |
P1 | P2 | P3 | P4 | P5 | |
---|---|---|---|---|---|
L1 | (PP, P, PG) | (G, PG, M) | (VG, G, PG) | (G, PG, VG) | (M, M, PP) |
L2 | (PG, PG, M) | (VG, G, G) | (PG, G, PG) | (VG, VG, PG) | (G, PG, PG) |
L3 | (VP, P, PP) | (M, P, PP) | (G, M, P) | (VG, PG, PP) | (VVP, VP, P) |
L4 | (PP, M, M) | (M, PP, PP) | (P, M, PP) | (VG, G, PP) | (PP, VP, VVP) |
L5 | (P, VP, VP) | (PP, P, P) | (VG, M, PP) | (VG, VVG, PG) | (PP, P, P) |
L6 | (VVG, G, G) | (G, P, M) | (PP, PP, PG) | (M, G, P) | (VVG, G, P) |
L7 | (G, M, M) | (PG, PP, VP) | (M, P, VP) | (PG, P, M) | (VG, M, P) |
L8 | (PG, VG, VP) | (M, VP, P) | (VG, PP, P) | (VG, PG, VP) | (VG, P, M) |
L9 | (G, PP, P) | (P, VVP, PP) | (P, PP, VVP) | (P, PG, P) | (VG, PP, P) |
L10 | (VVG, M, G) | (G, PP, P) | (G, P, PP) | (VG, G, P) | (VVG, M, PG) |
L11 | (M, P, VVP) | (M, VVP, P) | (VP, PP, P) | (VG, P, PP) | (G, VP, PG) |
L12 | (VVG, PG, PP) | (PG, PP, VP) | (PG, VP, PP) | (PG, P, PP) | (VVG, G, M) |
L13 | (G, PG, P) | (P, PP, VP) | (G, VG, PP) | (G, PP, VG) | (VG, PG, M) |
L14 | (VG, G, PP) | (PG, M, VP) | (M, P, VVP) | (G, VP, PP) | (VVG, MP, P) |
L15 | (PG, PP, P) | (PG, P, PP) | (G, PP, P) | (VG, G, P) | (VG, M, P) |
L16 | (PG, G, P) | (M, M, P) | (PG, P, G) | (M, P, M) | (G, PG, M) |
P1 | P2 | P3 | P4 | P5 | |
---|---|---|---|---|---|
L1 | (0.568, 0.326) | (0.627, 0.270) | (0.730, 0.194) | (0.699, 0.214) | (0.478, 0.422) |
L2 | (0.578, 0.321) | (0.748, 0.177) | (0.637, 0.262) | (0.765, 0.176) | (0.646, 0.252) |
L3 | (0.285, 0.614) | (0.416, 0.483) | (0.565, 0.327) | (0.673, 0.251) | (0.185, 0.715) |
L4 | (0.459, 0.440) | (0.445, 0.454) | (0.397, 0.502) | (0.703, 0.219) | (0.273, 0.625) |
L5 | (0.244, 0.655) | (0.345, 0.555) | (0.648, 0.277) | (0.786, 0.154) | (0.345, 0.555) |
L6 | (0.777, 0.149) | (0.550, 0.341) | (0.454, 0.444) | (0.544, 0.348) | (0.728, 0.192) |
L7 | (0.598, 0.297) | (0.460, 0.435) | (0.375, 0.523) | (0.491, 0.405) | (0.635, 0.289) |
L8 | (0.627, 0.290) | (0.366, 0.531) | (0.612, 0.311) | (0.650, 0.272) | (0.622, 0.301) |
L9 | (0.538, 0.352) | (0.222, 0.677) | (0.295, 0.604) | (0.420, 0.475) | (0.612, 0.311) |
L10 | (0.735, 0.188) | (0.538, 0.352) | (0.530, 0.359) | (0.692, 0.229) | (0.717, 0.206) |
L11 | (0.357, 0.540) | (0.340, 0.556) | (0.612, 0.311) | (0.605, 0.317) | (0.553, 0.335) |
L12 | (0.711, 0.211) | (0.460, 0.435) | (0.444, 0.450) | (0.469, 0.427) | (0.749, 0.175) |
L13 | (0.584, 0.308) | (0.314, 0.585) | (0.692, 0.225) | (0.637, 0.271) | (0.687, 0.238) |
L14 | (0.703, 0.219) | (0.493, 0.403) | (0.357, 0.540) | (0.509, 0.378) | (0.657, 0.262) |
L15 | (0.477, 0.419) | (0.469, 0.427) | (0.538, 0.352) | (0.692, 0.229) | (0.623, 0.300) |
L16 | (0.586, 0.308) | (0.459, 0.440) | (0.549, 0.344) | (0.440, 0.459) | (0.627, 0.270) |
Attributes | E1 | E2 | E3 | Aggregated IFN | Score Value |
---|---|---|---|---|---|
L1 | VVP | VP | VP | (0.159, 0.741) | 0.209 |
L2 | M | M | PP | (0.478, 0.422) | 0.528 |
L3 | VP | VP | VP | (0.200, 0.700) | 0.250 |
L4 | VVP | VVP | VVP | (0.100, 0.800) | 0.150 |
L5 | P | VP | P | (0.268, 0.632) | 0.318 |
L6 | P | PP | P | (0.335, 0.564) | 0.386 |
L7 | PP | P | PP | (0.368, 0.532) | 0.418 |
L8 | PG | G | PG | (0.637, 0.262) | 0.688 |
L9 | VVP | VVP | VP | (0.125, 0.775) | 0.175 |
L10 | G | VG | G | (0.738, 0.182) | 0.778 |
L11 | VP | VP | P | (0.225, 0.675) | 0.275 |
L12 | PG | M | PG | (0.569, 0.331) | 0.619 |
L13 | PP | M | PP | (0.436, 0.464) | 0.486 |
L14 | M | M | PG | (0.526, 0.374) | 0.576 |
L15 | PG | M | G | (0.597, 0.301) | 0.648 |
L16 | VG | G | VVG | (0.786, 0.150) | 0.818 |
Attributes | Score Values | sj | kj | pj | |
---|---|---|---|---|---|
L16 | 0.818 | - | 1.000 | 1.000 | 0.0869 |
L10 | 0.778 | 0.040 | 1.040 | 0.9615 | 0.0836 |
L8 | 0.688 | 0.090 | 1.090 | 0.8821 | 0.0767 |
L15 | 0.648 | 0.040 | 1.040 | 0.8482 | 0.0737 |
L12 | 0.619 | 0.029 | 1.029 | 0.8243 | 0.0716 |
L14 | 0.576 | 0.043 | 1.043 | 0.7903 | 0.0687 |
L2 | 0.528 | 0.048 | 1.048 | 0.7541 | 0.0655 |
L13 | 0.486 | 0.042 | 1.042 | 0.7237 | 0.0629 |
L7 | 0.418 | 0.068 | 1.068 | 0.6776 | 0.0589 |
L6 | 0.386 | 0.032 | 1.032 | 0.6566 | 0.0571 |
L5 | 0.318 | 0.068 | 1.068 | 0.6148 | 0.0534 |
L11 | 0.275 | 0.043 | 1.043 | 0.5895 | 0.0512 |
L3 | 0.250 | 0.025 | 1.025 | 0.5751 | 0.0501 |
L1 | 0.209 | 0.041 | 1.041 | 0.5524 | 0.0480 |
L9 | 0.175 | 0.034 | 1.034 | 0.5342 | 0.0464 |
L4 | 0.150 | 0.025 | 1.025 | 0.5212 | 0.0453 |
Options | ||||||
---|---|---|---|---|---|---|
P1 | (0.482, 0.421) | 0.530 | (0.195, 0.757) | 0.219 | 0.635 | 80.342 |
P2 | (0.411, 0.492) | 0.459 | (0.098, 0.867) | 0.116 | 0.658 | 83.198 |
P3 | (0.493, 0.413) | 0.540 | (0.091, 0.877) | 0.107 | 0.756 | 95.556 |
P4 | (0.573, 0.342) | 0.616 | (0.113, 0.850) | 0.132 | 0.791 | 100.000 |
P5 | (0.504, 0.405) | 0.550 | (0.202, 0.753) | 0.224 | 0.653 | 82.574 |
0.0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 | |
---|---|---|---|---|---|---|---|---|---|---|---|
L1 | 0.058 | 0.057 | 0.056 | 0.055 | 0.054 | 0.053 | 0.052 | 0.051 | 0.050 | 0.049 | 0.048 |
L2 | 0.049 | 0.051 | 0.052 | 0.054 | 0.056 | 0.057 | 0.059 | 0.061 | 0.062 | 0.064 | 0.066 |
L3 | 0.060 | 0.059 | 0.058 | 0.057 | 0.056 | 0.055 | 0.054 | 0.053 | 0.052 | 0.051 | 0.050 |
L4 | 0.070 | 0.068 | 0.065 | 0.063 | 0.060 | 0.058 | 0.055 | 0.053 | 0.050 | 0.048 | 0.045 |
L5 | 0.055 | 0.055 | 0.055 | 0.055 | 0.055 | 0.054 | 0.054 | 0.054 | 0.054 | 0.054 | 0.053 |
L6 | 0.060 | 0.060 | 0.059 | 0.059 | 0.059 | 0.058 | 0.058 | 0.058 | 0.058 | 0.057 | 0.057 |
L7 | 0.072 | 0.070 | 0.069 | 0.068 | 0.067 | 0.065 | 0.064 | 0.063 | 0.061 | 0.060 | 0.059 |
L8 | 0.061 | 0.063 | 0.064 | 0.066 | 0.067 | 0.069 | 0.071 | 0.072 | 0.074 | 0.075 | 0.077 |
L9 | 0.065 | 0.063 | 0.061 | 0.059 | 0.057 | 0.056 | 0.054 | 0.052 | 0.050 | 0.048 | 0.046 |
L10 | 0.055 | 0.058 | 0.060 | 0.063 | 0.066 | 0.069 | 0.072 | 0.075 | 0.078 | 0.081 | 0.084 |
L11 | 0.066 | 0.065 | 0.063 | 0.062 | 0.060 | 0.059 | 0.057 | 0.056 | 0.054 | 0.053 | 0.051 |
L12 | 0.067 | 0.068 | 0.068 | 0.069 | 0.069 | 0.070 | 0.070 | 0.070 | 0.071 | 0.071 | 0.072 |
L13 | 0.056 | 0.056 | 0.057 | 0.058 | 0.058 | 0.059 | 0.060 | 0.061 | 0.061 | 0.062 | 0.063 |
L14 | 0.065 | 0.065 | 0.066 | 0.066 | 0.067 | 0.067 | 0.067 | 0.068 | 0.068 | 0.068 | 0.069 |
L15 | 0.069 | 0.069 | 0.070 | 0.070 | 0.071 | 0.071 | 0.072 | 0.072 | 0.073 | 0.073 | 0.074 |
L16 | 0.072 | 0.074 | 0.075 | 0.077 | 0.078 | 0.080 | 0.081 | 0.082 | 0.084 | 0.085 | 0.087 |
Parameters | Mishra [60] | Buyukozkan & Gocer [61] | Cobuloglu and Buyuktahtakin [12] | Mishra et al. [49] | Proposed Method |
---|---|---|---|---|---|
Model | TOPSIS | COPRAS | AHP-based LLSM | ARAS | COPRAS |
Evaluation settings | IFSs | PFSs | FSs | PFSs | IFSs |
AOs | Averaging | Averaging | Averaging | Averaging | Averaging |
Prioritization scheme | Compromise degree | Compromise degree | Outranking degree | Utility theory | Utility theory |
Criteria weights | Objective weight assessment | Subjective weight by AHP | Subjective weight by AHP | Objective weight assessment | Integrated weight by objective and subjective weights |
MCDA | Group | Group | Group | Group | Group |
Does the preference tool consider nature of attributes | Yes | Yes | Yes | Yes | Yes |
DE’s weight | Calculated | Calculated | Calculated | Calculated (Using scoring tool) | Calculated (Using scoring tool) |
Types of normalization | Vector | Vector | Linear | Linear | Linear, vector |
Best SBCT option | P4 | P4 | P4 | P4 | P4 |
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Mardani, A.; Devi, S.; Alrasheedi, M.; Arya, L.; Singh, M.P.; Pandey, K. Hybrid Intuitionistic Fuzzy Entropy-SWARA-COPRAS Method for Multi-Criteria Sustainable Biomass Crop Type Selection. Sustainability 2023, 15, 7765. https://doi.org/10.3390/su15107765
Mardani A, Devi S, Alrasheedi M, Arya L, Singh MP, Pandey K. Hybrid Intuitionistic Fuzzy Entropy-SWARA-COPRAS Method for Multi-Criteria Sustainable Biomass Crop Type Selection. Sustainability. 2023; 15(10):7765. https://doi.org/10.3390/su15107765
Chicago/Turabian StyleMardani, Abbas, Sarita Devi, Melfi Alrasheedi, Leena Arya, Mrigendra Pratap Singh, and Kiran Pandey. 2023. "Hybrid Intuitionistic Fuzzy Entropy-SWARA-COPRAS Method for Multi-Criteria Sustainable Biomass Crop Type Selection" Sustainability 15, no. 10: 7765. https://doi.org/10.3390/su15107765