Introduction
-
Novel Fermatean fuzzy-WASPAS (FF-WASPAS) method based on score function and entropy measure is developed for solving complex MCDM problems.
-
An improved score function and entropy measure for FFSs are developed with their elegant properties. And, further employed to assess the criteria weights.
-
To display the feasibility and effectiveness of the developed methodology, a practical case study of HCW disposal location selection is presented in the FFSs context.
-
Comparative study is conferred to exemplify the validity and stability of the introduced framework.
Earlier works
Fermatean fuzzy sets
WASPAS method
References | Method | Application |
---|---|---|
Zavadskas et al. [58] | Single-valued neutrosophic WASPAS | Construction of alternative sites for waste incineration plant |
Turskis et al. [52] | Fuzzy AHP-WASPAS | Shopping center construction site selection |
Ghorabaee et al. [19] | Interval type-2 fuzzy WASPAS | Evaluation of green suppliers |
Deveci et al. [13] | Interval type-2 fuzzy- WASPAS-TOPSIS | Assessment of car-sharing station |
Mishra and Rani [33] | Interval-valued intuitionistic fuzzy WASPAS | Evaluation and selection of reservoir flood control management policies |
Mishra et al. [34] | Hesitant fuzzy WASPAS | Green supplier selection |
Schitea et al. [42] | Intuitionistic fuzzy WASPAS-COPRAS-EDAS | Hydrogen mobility roll-up site selection |
Rani and Mishra [41] | q-rung orthopair WASPAS | Alternative fuel technologies assessment |
Mohagheghi and Mousavi [35] | Interval-valued Pythagorean fuzzy D-WASPAS | Evaluation of sustainable project portfolios |
Mardani et al. [28] | Hesitant fuzzy-SWOT-SWARA-WASPAS | Assessment of digital technologies intervention to control the COVID-19 outbreak |
Rani et al. [43] | Intuitionistic fuzzy type-2 WASPAS | Physician selection |
Agarwal et al. [1] | Fuzzy SWARA-WASPAS | Evaluation of humanitarian supply chain management barriers |
Ali et al. [2] | Uncertain probabilistic linguistic WASPAS | Supplier selection |
Location selection and waste disposal system
Preliminaries
Improved score function and entropy measure within FFSs context
Novel Fermatean fuzzy Score function
Entropy measure for FFS
Proposed FF-WASPAS method for MCDM problems
Case study: healthcare waste disposal location (HCWDL) selection
Factors | Criteria | Type | References |
---|---|---|---|
Environmental | V1: Potential risk of intrusion and emission | Cost | Yazdani et al. [56] |
V2: Distance to the urban and city infrastructure and society | Benefit | ||
V3: Distance to a complex of waste sorting | Cost | ||
V4: Geographic and geologic circumstances | Benefit | ||
V5: The prevailing environmental friendly services (air, water, energy, and electricity supply) | Benefit | ||
Economic | V6: Land price (in m2) and other costs (transportation and maintenance) in the specific zone | Cost | |
V7: Possibility of future development | Benefit | ||
Social | V8: Availability of employees | Benefit | Yazdani et al. [56] |
V9: Sensitivity towards environment, local and territorial rules or protocols | Benefit | ||
V10: Level of satisfaction among residents to the location selection | Benefit | Yazdani et al. [56] |
L1 | L2 | L3 | L4 | L5 | |
---|---|---|---|---|---|
V1 | \(\mho_{1}\): (0.40, 0.70) \(\mho_{2}\): (0.45, 0.60) \(\mho_{3}\): (0.50, 0.72) | \(\mho_{1}\): (0.30, 0.75) \(\mho_{2}\): (0.35, 0.75) \(\mho_{3}\): (0.40, 0.80) | \(\mho_{1}\): (0.40, 0.65) \(\mho_{2}\): (0.50, 0.70) \(\mho_{3}\): (0.55, 0.72) | \(\mho_{1}\): (0.30, 0.75) \(\mho_{2}\): (0.50, 0.70) \(\mho_{3}\): (0.45, 0.65) | \(\mho_{1}\): (0.58, 0.70) \(\mho_{2}\): (0.50, 0.75) \(\mho_{3}\): (0.52, 0.72) |
V2 | \(\mho_{1}\): (0.55, 0.70) \(\mho_{2}\): (0.65, 0.69) \(\mho_{3}\): (0.50, 0.72) | \(\mho_{1}\): (0.65, 0.50) \(\mho_{2}\): (0.70, 0.58) \(\mho_{3}\): (0.68, 0.55) | \(\mho_{1}\): (0.65, 0.58) \(\mho_{2}\): (0.60, 0.52) \(\mho_{3}\): (0.62, 0.54) | \(\mho_{1}\): (0.58, 0.55) \(\mho_{2}\): (0.60, 0.50) \(\mho_{3}\): (0.55, 0.65) | \(\mho_{1}\): (0.60, 0.55) \(\mho_{2}\): (0.60, 0.52) \(\mho_{3}\): (0.68, 0.60) |
V3 | \(\mho_{1}\): (0.70, 0.40) \(\mho_{2}\): (0.65, 0.50) \(\mho_{3}\): (0.55, 0.50) | \(\mho_{1}\): (0.70, 0.50) \(\mho_{2}\): (0.72, 0.55) \(\mho_{3}\): (0.68, 0.55) | \(\mho_{1}\): (0.64, 0.67) \(\mho_{2}\): (0.65, 0.60) \(\mho_{3}\): (0.69, 0.58) | \(\mho_{1}\): (0.70, 0.69) \(\mho_{2}\): (0.62, 0.65) \(\mho_{3}\): (0.68, 0.60) | \(\mho_{1}\): (0.70, 0.64) \(\mho_{2}\): (0.64, 0.58) \(\mho_{3}\): (0.62, 0.55) |
V4 | \(\mho_{1}\): (0.65, 0.50) \(\mho_{2}\): (0.60, 0.55) \(\mho_{3}\): (0.70, 0.50) | \(\mho_{1}\): (0.67, 0.55) \(\mho_{2}\): (0.72, 0.58) \(\mho_{3}\): (0.68, 0.52) | \(\mho_{1}\): (0.70, 0.50) \(\mho_{2}\): (0.65, 0.58) \(\mho_{3}\): (0.62, 0.55) | \(\mho_{1}\): (0.64, 0.60) \(\mho_{2}\): (0.70, 0.55) \(\mho_{3}\): (0.65, 0.54) | \(\mho_{1}\): (0.64, 0.51) \(\mho_{2}\): (0.69, 0.65) \(\mho_{3}\): (0.61, 0.54) |
V5 | \(\mho_{1}\): (0.70, 0.60) \(\mho_{2}\): (0.65, 0.59) \(\mho_{3}\): (0.68, 0.52) | \(\mho_{1}\): (0.72, 0.55) \(\mho_{2}\): (0.68, 0.50) \(\mho_{3}\): (0.65, 0.52) | \(\mho_{1}\): (0.70, 0.56) \(\mho_{2}\): (0.65, 0.62) \(\mho_{3}\): (0.67, 0.60) | \(\mho_{1}\): (0.65, 0.60) \(\mho_{2}\): (0.66, 0.55) \(\mho_{3}\): (0.68, 0.60) | \(\mho_{1}\): (0.66, 0.54) \(\mho_{2}\): (0.65, 0.56) \(\mho_{3}\): (0.63, 0.57) |
V6 | \(\mho_{1}\): (0.55, 0.72) \(\mho_{2}\): (0.53, 0.78) \(\mho_{3}\): (0.57, 0.75) | \(\mho_{1}\): (0.50, 0.68) \(\mho_{2}\): (0.45, 0.72) \(\mho_{3}\): (0.40, 0.75) | \(\mho_{1}\): (0.50, 0.76) \(\mho_{2}\): (0.55, 0.75) \(\mho_{3}\): (0.58, 0.70) | \(\mho_{1}\): (0.55, 0.72) \(\mho_{2}\): (0.63, 0.70) \(\mho_{3}\): (0.58, 0.75) | \(\mho_{1}\): (0.58, 0.76) \(\mho_{2}\): (0.55, 0.72) \(\mho_{3}\): (0.60, 0.74) |
V7 | \(\mho_{1}\): (0.70, 0.62) \(\mho_{2}\): (0.69, 0.65) \(\mho_{3}\): (0.69, 0.62) | \(\mho_{1}\): (0.70, 0.66) \(\mho_{2}\): (0.72, 0.63) \(\mho_{3}\): (0.74, 0.62) | \(\mho_{1}\): (0.70, 0.60) \(\mho_{2}\): (0.65, 0.62) \(\mho_{3}\): (0.68, 0.66) | \(\mho_{1}\): (0.67, 0.55) \(\mho_{2}\) (0.68, 0.58) \(\mho_{3}\): (0.69, 0.60) | \(\mho_{1}\): (0.62, 0.57) \(\mho_{2}\): (0.65, 0.54) \(\mho_{3}\): (0.62, 0.56) |
V8 | \(\mho_{1}\): (0.68, 0.55) \(\mho_{2}\): (0.70, 0.50) \(\mho_{3}\): (0.65, 0.55) | \(\mho_{1}\): (0.69, 0.55) \({J}\)2: (0.72, 0.62) \(\mho_{3}\): (0.70, 0.50) | \(\mho_{1}\): (0.68, 0.50) \(\mho_{2}\): (0.70, 0.55) \(\mho_{3}\): (0.72, 0.50) | \(\mho_{1}\): (0.68, 0.50) \(\mho_{2}\): (0.65, 0.52) \(\mho_{3}\): (0.60, 0.56) | \(\mho_{1}\): (0.65, 0.58) \(\mho_{2}\): (0.60, 0.56) \(\mho_{3}\): (0.60, 0.50) |
V9 | \(\mho_{1}\): (0.58, 0.55) \(\mho_{2}\): (0.65, 0.55) \(\mho_{3}\): (0.62, 0.60) | \(\mho_{1}\): (0.67, 0.59) \(\mho_{2}\): (0.73, 0.55) \(\mho_{3}\): (0.71, 0.54) | \(\mho_{1}\): (0.68, 0.55) \(\mho_{2}\): (0.64, 0.50) \(\mho_{3}\): (0.69, 0.55) | \(\mho_{1}\): (0.68, 0.54) \(\mho_{2}\): (0.63, 0.56) \(\mho_{3}\): (0.61, 0.52) | \(\mho_{1}\): (0.65, 0.55) \({J}\)2: (0.63, 0.57) \(\mho_{3}\): (0.62, 0.55) |
V10 | \(\mho_{1}\): (0.70, 0.55) \(\mho_{2}\): (0.68, 0.55) \(\mho_{3}\): (0.60, 0.57) | \(\mho_{1}\): (0.68, 0.65) \(\mho_{2}\): (0.74, 0.65) \(\mho_{3}\): (0.70, 0.62) | \(\mho_{1}\): (0.70, 0.68) \(\mho_{2}\): (0.65, 0.64) \(\mho_{3}\): (0.65, 0.50) | \(\mho_{1}\): (0.68, 0.62) \(\mho_{2}\): (0.68, 0.60) \(\mho_{3}\): (0.64, 0.55) | \(\mho_{1}\): (0.62, 0.60) \(\mho_{2}\): (0.65, 0.55) \(\mho_{3}\): (0.68, 0.60) |
L1 | L2 | L3 | L4 | L5 | |
---|---|---|---|---|---|
V1 | (0.465, 0.676) | (0.363, 0.766) | (0.503, 0.687) | (0.446, 0.701) | (0.551, 0.721) |
V2 | (0.363, 0.766) | (0.694, 0.539) | (0.640, 0.549) | (0.593, 0.566) | (0.644, 0.557) |
V3 | (0.661, 0.460) | (0.717, 0.531) | (0.676, 0.618) | (0.685, 0.647) | (0.673, 0.591) |
V4 | (0.668, 0.514) | (0.708, 0.548) | (0.677, 0.539) | (0.681, 0.565) | (0.666, 0.557) |
V5 | (0.694, 0.569) | (0.703, 0.525) | (0.690, 0.590) | (0.679, 0.585) | (0.663, 0.556) |
V6 | (0.564, 0.747) | (0.468, 0.714) | (0.559, 0.736) | (0.605, 0.724) | (0.592, 0.742) |
V7 | (0.710, 0.628) | (0.736, 0.638) | (0.694, 0.625) | (0.696, 0.575) | (0.646, 0.558) |
V8 | (0.695, 0.535) | (0.720, 0.551) | (0.716, 0.514) | (0.663, 0.525) | (0.634, 0.546) |
V9 | (0.634, 0.566) | (0.721, 0.561) | (0.686, 0.535) | (0.659, 0.539) | (0.650, 0.556) |
V10 | (0.682, 0.557) | (0.725, 0.640) | (0.685, 0.603) | (0.684, 0.590) | (0.666, 0.585) |
L1 | L2 | L3 | L4 | L5 | |
---|---|---|---|---|---|
V1 | (0.676, 0.465) | (0.766, 0.363) | (0.687, 0.503) | (0.701, 0.446) | (0.721, 0.551) |
V2 | (0.363, 0.766) | (0.694, 0.539) | (0.640, 0.549) | (0.593, 0.566) | (0.644, 0.557) |
V3 | (0.460, 0.661) | (0.531, 0.717) | (0.618, 0.676) | (0.647, 0.685) | (0.591, 0.673) |
V4 | (0.668, 0.514) | (0.708, 0.548) | (0.677, 0.539) | (0.681, 0.565) | (0.666, 0.557) |
V5 | (0.694, 0.569) | (0.703, 0.525) | (0.690, 0.590) | (0.679, 0.585) | (0.663, 0.556) |
V6 | (0.747, 0.564) | (0.714, 0.468) | (0.736, 0.559) | (0.724, 0.605) | (0.742, 0.592) |
V7 | (0.710, 0.628) | (0.736, 0.638) | (0.694, 0.625) | (0.696, 0.575) | (0.646, 0.558) |
V8 | (0.695, 0.535) | (0.720, 0.551) | (0.716, 0.514) | (0.663, 0.525) | (0.634, 0.546) |
V9 | (0.634, 0.566) | (0.721, 0.561) | (0.686, 0.535) | (0.659, 0.539) | (0.650, 0.556) |
V10 | (0.682, 0.557) | (0.725, 0.640) | (0.685, 0.603) | (0.684, 0.590) | (0.666, 0.585) |
Location options | FF-WSM | FF-WPM | FF-WASPAS | Ranking | ||
---|---|---|---|---|---|---|
\({\mathbb{C}}_{i}^{(1)}\) | \({\mathbb{S}}\left( {{\mathbb{C}}_{i}^{(1)} } \right)\) | \({\mathbb{C}}_{i}^{(2)}\) | \({\mathbb{S}}\left( {{\mathbb{C}}_{i}^{(2)} } \right)\) | \({\mathbb{C}}_{i} \left( \lambda =0.5 \right)\) | ||
L1 | (0.670, 0.557, 0.807) | 0.353 | (0.644, 0.582, 0.813) | 0.320 | 0.336 | 5 |
L2 | (0.721, 0.536, 0.779) | 0.417 | (0.720, 0.553, 0.771) | 0.413 | 0.415 | 1 |
L3 | (0.690, 0.564, 0.790) | 0.374 | (0.688, 0.569, 0.788) | 0.371 | 0.373 | 2 |
L4 | (0.679, 0.564, 0.798) | 0.361 | (0.675, 0.571, 0.797) | 0.356 | 0.359 | 3 |
L5 | (0.671, 0.565, 0.803) | 0.353 | (0.668, 0.566, 0.805) | 0.349 | 0.351 | 4 |
Comparative study
-
The WASPAS approach, a utility scoring model for MCDM, selects an option which has the maximum score (or the utmost utility), whereas the previous approaches, which are compromising degree procedures, prefer an option which is nearest to the ideal solution.
-
WASPAS is a combination of the WSM and WPM. The accuracy of the WASPAS approach is more consistent than WSM and WPM. This method facilitates us to achieve the maximum accuracy of assessment, utilizing the introduced framework for optimization of weighted aggregated mapping.
-
In the proposed model, the criteria weights are computed-based on proposed entropy and score function and are given in FFNs, whereas in Yazdani et al. [56], the criteria weights are estimated based on BWM and are mentioned in terms of IRNs. On the other hand, FF-TOPSIS and FF-WPM models, the criteria weights are assumed, which leaves no room for managing the ambiguity.
-
The proposed framework could offer a more precise description under an uncertain environment because of evaluating the criteria and DMs’ weights and utilizing them in the process of the proposed method. In addition, two other considered as central features in the procedure of this method lead the computational results to a reliable solution. These features comprise the last aggregation method to evade the loss of data and to tailor the introduced framework based on FFSs information.
Implementation and discussions
-
The government hospitals (GHs) require solid support skills to protect adequate funding from the state administration to start utilizing the facilities of common waste management facilities (CWMFs). The state health structures development project can show a key impact in the application of bio-medical waste (BMW) guidelines by the GHs.
-
The pollution control board (PCB) also wants to performance as a facilitator between the GHs and the CWMFs more efficiently so as to fast agreement can be touched between the two systems.
-
Diverse kinds of posters are being utilized by two CMFWs in the state. These can origin misperceptions among hospital employees, specifically among those who reformed their CMFW. The PCB should certify that diverse messages are not conversed by the CMFWs to the hospitals.
-
The non-use of uniform color bins may source misperception among the lower-level employee, which may consequence in preventable mix-ups of segregated waste. Therefore, the PCB and CWMFs should assert that the hospitals and other systems follow to uniform color coding for both bins and plastic materials that they use.