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A Hybrid Framework for Selecting Food Waste Treatment Techniques Using q-Rung Orthopair Fuzzy CRITIC-Generalized TODIM Method

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Abstract

Evaluation and prioritization are indispensable for selecting the appropriate FWTT (food waste treatment technique). Previous research shows that the decision methods are suitable for selecting FWTTs. Nevertheless, current literature on choosing FWTTs seldom considers the impact of experts’ bounded rational behavior and interactive criteria, especially with uncertain information. This article proposes a q-ROFS (q-rung orthopair fuzzy set)-generalized TODIM (an acronym in Portuguese for interactive and multi-criteria decision-making method)-based hybrid framework for coping with the selection problem of FWTTs. In the information fusion process, the fuzziness and ambiguity of information are expressed by the q-ROFS. Then, the q-ROFS-CRITIC (criteria importance through inter-criteria correlation) method is introduced to calculate the criteria weights considering the interactive criteria. Next, the q-ROFS-generalized TODIM framework is presented to rank the alternative techniques considering the experts’ bounded rational behavior. Finally, a real case of selecting FWTTs with q-ROFSs is performed to examine the applicability and feasibility of this framework. The result shows that the alternative \(f_{2}\) (anaerobic digestion) has the highest priority for food waste treatment with the largest overall dominance degree value. After that, a sensitivity study of different parameters and comparative analysis with similar selection methods are organized to elaborate on the reasonability of the provided framework.

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Abbreviations

AD:

Anaerobic digestion

CP:

Composting

CRITIC:

Criteria importance through inter-criteria correlation

EDAS:

Distance from average solution

FAO:

Food and agriculture organization

FFS:

Fermatean fuzzy set

FW:

Food waste

FWTT:

Food waste treatment technique

HD:

Degree of hesitancy

IFS:

Intuitionistic fuzzy set

IN:

Incineration

LF:

Landfill

MCDM:

Multi-criteria decision-making

MULTIMOORA:

Multi-attribute multi-objective optimization with the ratio analysis

PFS:

Pythagorean fuzzy set

q-ROFS:

Q-rung orthopair fuzzy set

TODIM:

Acronym in Portuguese for interactive and multi-criteria decision-making

WA:

Weighted averaging

\(\tilde{P}\) :

A q-ROFS

\(\gamma_{{\tilde{P}}} \left( x \right)\) :

Degree of membership

\(\delta_{{\widetilde{P}}} \left( x \right)\) :

Degree of non-membership

\(\mu_{{\widetilde{P}}} \left( x \right)\) :

Degree of hesitancy

\(S\left( {\tilde{g}} \right)\) :

Score function

\(H\left( {\tilde{g}} \right)\) :

Accuracy function

\(\widehat{d}\left( {g_{1} ,g_{2} } \right)\) :

Distance between two fuzzy numbers

\(v^{t}\) :

A group of experts

\(f_{i}\) :

Each alternative

\(f_{1}\) :

CP

\(f_{2}\) :

AD

\(f_{3}\) :

IN

\(f_{4}\) :

LF

\(z_{j}\) :

Each criterion

\(\widetilde{{A^{t} }}\) :

Q-ROFS evaluation matrix

\(\overline{{\widetilde{{a_{{_{ij} }}^{t} }}}}\) :

Mean values of the individual matrix

\(B\) :

Similarity measure

\(w_{t}\) :

Weights of experts

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{A}\) :

Group decision matrix

\(a^{\prime}_{ij}\) :

Score matrix

\(\sigma_{j}\) :

Standard deviation value

\(r_{{jj^{\prime}}}\) :

Correlation coefficient

\(w_{j}\) :

Criteria weights

\(l_{j}\) :

Quantity of information on criteria

\(\Phi_{j} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\) :

Dominance grade

\(\Phi \left( {f_{i} } \right)\) :

Overall dominance degree

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Acknowledgements

This work was supported by the Social Science Planning Project of Anhui province (AHSKQ2021D56).

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Authors and Affiliations

  1. School of Economics and Management, Anhui Normal University, Wuhu, 241002, Anhui, China

    Yushuo Cao, Xuzhong Wu, Ling Ding & Weizhong Wang

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Appendix

Appendix

See Tables 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, and 28.

Table 17 The dominance degree \(\Phi_{2} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\)
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Table 18 The dominance degree \(\Phi_{3} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\)
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Table 19 The dominance degree \(\Phi_{4} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\)
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Table 20 The dominance degree \(\Phi_{5} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\)
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Table 21 The dominance degree \(\Phi_{6} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\)
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Table 22 The dominance degree \(\Phi_{7} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\)
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Table 23 The dominance degree \(\Phi_{8} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\)
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Table 24 The dominance degree \(\Phi_{9} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\)
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Table 25 The dominance degree \(\Phi_{10} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\)
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Table 26 The dominance degree \(\Phi_{11} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\)
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Table 27 The dominance degree \(\Phi_{12} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\)
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Table 28 The dominance degree \(\Phi_{13} \left( {f_{i} ,f_{{i^{\prime}}} } \right)\)
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Cao, Y., Wu, X., Ding, L. et al. A Hybrid Framework for Selecting Food Waste Treatment Techniques Using q-Rung Orthopair Fuzzy CRITIC-Generalized TODIM Method. Int. J. Fuzzy Syst. 26, 1916–1935 (2024). https://doi.org/10.1007/s40815-024-01714-2

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