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01-03-2024 | ORIGINAL PAPER

Multicriteria group decision-making based on Fermatean fuzzy fairly weighted and ordered weighted averaging operators

Authors: Tingting Liu, Kai Gao, Yuan Rong

Published in: Granular Computing | Issue 1/2024

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Abstract

The comprehensive evaluation of digital transformation capability (DTC) for enterprise can not only enhance its innovation capabilities, but also provide guidance for improving its digital transformation measures. Thus, this study constructs a comprehensive decision framework by incorporating the preference selection index (PSI), step-wise weights assessment ratio analysis (SWARA) and evaluation based on distance from average solution (EDAS) under Fermatean fuzzy circumstance. To begin with, we define the fairly operational laws of Fermatean fuzzy numbers (FFNs) and propound the Fermatean fuzzy fairly weighted averaging and Fermatean fuzzy ordered weighted averaging operators. Then we advance a fused FF-SWARA-PSI weight model for ascertaining the importance of criteria from the angle of subjective and objective and the principle of minimum relative information entropy is utilized to integrate the subjective weight identified by Fermatean fuzzy SWARA method and objective weighted identified by improved Fermatean fuzzy PSI method. Further, an improved EDAS method based on the proposed operator is propounded to prioritize the alternatives with Fermatean fuzzy information. Lastly, an empirical case that assesses the DTC for enterprise is carried out to confirm the feasibility and applicability of the proposed framework. The sensibility analysis is executed by analyzing the weight coefficients and parameters for discussing the robustness and stability of propounded framework. The feasibility and practicability of the suggested FF-PSI-SWARA-EDAS framework are also investigated through the comparison study with the extant methods.

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Akram M, Bibi R, Deveci M (2023a) An outranking approach with 2-tuple linguistic Fermatean fuzzy sets for multi-attribute group decision-making. Eng Appl Artif Intel. https://doi.org/10.1016/j.engappai.2023.105992CrossRef

Akram M, Ramzan N, Deveci M (2023b) Linguistic Pythagorean fuzzy CRITIC-EDAS method for multiple-attribute group decision analysis. Eng Appl Artif Intel. https://doi.org/10.1016/j.engappai.2022.105777CrossRef

Akram M, Muhiuddin G, Santos-Garcia G (2022) An enhanced VIKOR method for multi-criteria group decision-making with complex Fermatean fuzzy sets. Math Biosci Eng 19(7):7201–7231. https://doi.org/10.3934/mbe.2022340CrossRefPubMed

Alahmadi RAA, Ganie AH, Al-Qudah Y, Khalaf MMM, Ganie AH (2023) Multi-attribute decision-making based on novel Fermatean fuzzy similarity measure and entropy measure. Granular Comput. https://doi.org/10.1007/s41066-023-00378-xCrossRef

Alkan N, Kahraman C (2023) Prioritization of supply chain digital transformation strategies using multi-expert fermatean fuzzy analytic hierarchy process. Informatica 34(1):1–33. https://doi.org/10.15388/22-infor493MathSciNetCrossRef

Amman M, Rashid T, Ali A (2023) Fermatean fuzzy multi-criteria decision-making based on Spearman rank correlation coefficient. Granular Comput. https://doi.org/10.1007/s41066-023-00421CrossRef

Asante D, He Z, Adjei NO, Asante B (2020) Exploring the barriers to renewable energy adoption utilising MULTIMOORA-EDAS method. Energy Policy. https://doi.org/10.1016/j.enpol.2020.111479CrossRef

Ashraf S, Abbasi SN, Naeem M, Eldin SMM (2023) Novel decision aid model for green supplier selection based on extended EDAS approach under pythagorean fuzzy Z-numbers. Front Environ Sci. https://doi.org/10.3389/fenvs.2023.1137689CrossRef

Ashraf S, Rehman N, Hussain A, AlSalman H, Gumaei AH (2021) q-Rung orthopair fuzzy rough Einstein aggregation information-based edas method: applications in robotic agrifarming. Comput Intel Neurosc. https://doi.org/10.1155/2021/5520264CrossRef

Atanassov K, Gargov G (1989) Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343–349. https://doi.org/10.1016/0165-0114(89)90205-4MathSciNetCrossRef

Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96. https://doi.org/10.1016/S0165-0114(86)80034-3MathSciNetCrossRef

Aydemir SB, Gunduz SY (2020) Fermatean fuzzy TOPSIS method with Dombi aggregation operators and its application in multi-criteria decision making. J Intell Fuzzy Syst 39(1):851–869. https://doi.org/10.3233/jifs-191763CrossRef

Behzad M, Zolfani SH, Pamucar D, Behzad M (2020) A comparative assessment of solid waste management performance in the Nordic countries based on BWM-EDAS. J Clean Prod. https://doi.org/10.1016/j.jclepro.2020.122008CrossRef

Boskovic S, Svadlenka L, Jovcic S, Dobrodolac M, Simic V, Bacanin N (2023) An Alternative Ranking Order Method Accounting for Two-Step Normalization (AROMAN)-a case study of the electric vehicle selection problem. IEEE Access 11:39496–39507. https://doi.org/10.1109/access.2023.3265818CrossRef

Chen S-M, Jian W-S (2017) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups, similarity measures and PSO techniques. Inf Sci 391:65–79. https://doi.org/10.1016/j.ins.2016.11.004MathSciNetCrossRef

Chen S-M, Niou S-J (2011) Fuzzy multiple attributes group decision-making based on fuzzy preference relations. Expert Syst Appl 38(4):3865–3872. https://doi.org/10.1016/j.eswa.2010.09.047CrossRef

Chen S-M, Randyanto Y, Cheng S-H (2016) Fuzzy queries processing based on intuitionistic fuzzy social relational networks. Inf Sci 327:110–124. https://doi.org/10.1016/j.ins.2015.07.054MathSciNetCrossRef

Cuong BC (2014) Picture fuzzy sets. J Comput Sci Cybern 30:409–420

Darko AP, Liang D (2020) Some q-rung orthopair fuzzy Hamacher aggregation operators and their application to multiple attribute group decision making with modified EDAS method. Eng Appl Artif Intel. https://doi.org/10.1016/j.engappai.2019.103259CrossRef

Deng Z, Wang J (2022) New distance measure for Fermatean fuzzy sets and its application. Int J Intell Syst 37(3):1903–1930. https://doi.org/10.1002/int.22760CrossRef

Deveci M, Pamucar D, Cali U, Kantar E, Kolle K, Tande JO (2022) Hybrid q-Rung Orthopair Fuzzy Sets Based CoCoSo model for floating offshore wind farm site selection in norway. Csee J Power Energy Syst 8(5):1261–1280. https://doi.org/10.17775/cseejpes.2021.07700CrossRef

Fan X, Wang Y, Lu X (2023) Digital transformation drives sustainable innovation capability improvement in manufacturing enterprises: based on FsQCA and NCA Approaches. Sustain Basel. https://doi.org/10.3390/su15010542CrossRef

Ganie AH (2022) Multicriteria decision-making based on distance measures and knowledge measures of Fermatean fuzzy sets. Granular Comput 7(4):979–998. https://doi.org/10.1007/s41066-021-00309-8CrossRef

Garg H, Shahzadi G, Akram M (2020) Decision-making analysis based on Fermatean fuzzy yager aggregation operators with application in COVID-19 testing facility. Math Probl Eng. https://doi.org/10.1155/2020/7279027MathSciNetCrossRef

Gul M, Lo H-W, Yucesan M (2021) Fermatean fuzzy TOPSIS-based approach for occupational risk assessment in manufacturing. Complex Intell Syst 7(5):2635–2653. https://doi.org/10.1007/s40747-021-00417-7CrossRef

Gul S (2021) Fermatean fuzzy set extensions of SAW, ARAS, and VIKOR with applications in COVID-19 testing laboratory selection problem. Expert Syst. https://doi.org/10.1111/exsy.12769CrossRefPubMedPubMedCentral

Hadi A, Khan W, Khan A (2021) A novel approach to MADM problems using Fermatean fuzzy Hamacher aggregation operators. Int J Intell Syst 36(7):3464–3499. https://doi.org/10.1002/int.22423CrossRef

Karatop B, Taskan B, Adar E, Kubat C (2021) Decision analysis related to the renewable energy investments in Turkey based on a Fuzzy AHP-EDAS-Fuzzy FMEA approach. Comput Ind Eng. https://doi.org/10.1016/j.cie.2020.106958CrossRef

Kersuliene V, Zavadskas EK, Turskis Z (2010) SELECTION OF RATIONAL DISPUTE RESOLUTION METHOD BY APPLYING NEW STEP-WISE WEIGHT ASSESSMENT RATIO ANALYSIS (SWARA). J Bus Econ Manag 11(2):243–258. https://doi.org/10.3846/jbem.2010.12CrossRef

Keshavarz-Ghorabaee M, Amiri M, Hashemi-Tabatabaei M, Zavadskas EK, Kaklauskas A (2020) A New Decision-Making Approach Based on Fermatean Fuzzy Sets and WASPAS for Green Construction Supplier Evaluation. Mathematics-Basel. https://doi.org/10.3390/math8122202CrossRef

Keshavarz Ghorabaee M, Zavadskas EK, Olfat L, Turskis Z (2015) Multi-Criteria Inventory Classification Using a New Method of Evaluation Based on Distance from Average Solution (EDAS). Informatica 26(3):435–451. https://doi.org/10.15388/Informatica.2015.57CrossRef

Kumar K, Chen S-M (2021) Multiattribute decision making based on the improved intuitionistic fuzzy Einstein weighted averaging operator of intuitionistic fuzzy values. Inf Sci 568:369–383. https://doi.org/10.1016/j.ins.2021.03.020MathSciNetCrossRef

Kumar K, Chen S-M (2022a) Group decision making based on advanced intuitionistic fuzzy weighted Heronian mean aggregation operator of intuitionistic fuzzy values. Inf Sci 601:306–322. https://doi.org/10.1016/j.ins.2022.04.001CrossRef

Kumar K, Chen S-M (2022b) Group decision making based on q-rung orthopair fuzzy weighted averaging aggregation operator of q-rung orthopair fuzzy numbers. Inf Sci 598:1–18. https://doi.org/10.1016/j.ins.2022.03.032CrossRef

Lai H, Liao H, Long Y, Zavadskas EK (2022) A Hesitant Fermatean Fuzzy CoCoSo Method for Group Decision-Making and an Application to Blockchain Platform Evaluation. Int J Fuzzy Syst 24(6):2643–2661. https://doi.org/10.1007/s40815-022-01319-7CrossRef

Liang W-Z, Zhao G-Y, Luo S-Z (2018) An Integrated EDAS-ELECTRE Method With Picture Fuzzy Information for Cleaner Production Evaluation in Gold Mines. Ieee Access 6:65747–65759. https://doi.org/10.1109/access.2018.2878747CrossRef

Liao N, Gao H, Lin R, Wei G, Chen X (2023) An extended EDAS approach based on cumulative prospect theory for multiple attributes group decision making with probabilistic hesitant fuzzy information. Artif Intell Rev 56(4):2971–3003. https://doi.org/10.1007/s10462-022-10244-yCrossRef

Lin M, Wang H, Xu Z, Yao Z, Huang J (2018) Clustering algorithms based on correlation coefficients for probabilistic linguistic term sets. Int J Intell Syst 33(12):2402–2424. https://doi.org/10.1002/int.22040CrossRef

Liu P, Chen S-M, Wang Y (2020) Multiattribute group decision making based on intuitionistic fuzzy partitioned Maclaurin symmetric mean operators. Inf Sci 512:830–854. https://doi.org/10.1016/j.ins.2019.10.013MathSciNetCrossRef

Luqman A, Shahzadi G (2023) Multi-attribute decision-making for electronic waste recycling using interval-valued Fermatean fuzzy Hamacher aggregation operators. Granular Comput. https://doi.org/10.1007/s41066-023-00363-4CrossRef

Mahapatra SK, Satapathy A (2023) Parametric analysis of erosion wear of sponge iron slag-filled ramie-epoxy composites using Taguchi and preference selection index methods. Proc Inst Mech Eng Part E J Process Mech Eng. https://doi.org/10.1177/09544089231193927CrossRef

Maniya K, Bhatt MG (2010) A selection of material using a novel type decision-making method: Preference selection index method. Mater Des 31(4):1785–1789. https://doi.org/10.1016/j.matdes.2009.11.020CrossRef

Martyn K, Kadzinski M (2023) Deep preference learning for multiple criteria decision analysis. Eur J Oper Res 305(2):781–805. https://doi.org/10.1016/j.ejor.2022.06.053MathSciNetCrossRef

Mishra AR, Chen S-M, Rani P (2023a) Multicriteria decision making based on novel score function of Fermatean fuzzy numbers, the CRITIC method, and the GLDS method. Inf Sci 623:915–931. https://doi.org/10.1016/j.ins.2022.12.031CrossRef

Mishra AR, Mardani A, Rani P, Zavadskas EK (2020) A novel EDAS approach on intuitionistic fuzzy set for assessment of health-care waste disposal technology using new parametric divergence measures. J Clean Prod. https://doi.org/10.1016/j.jclepro.2020.122807CrossRef

Mishra AR, Rani P (2021) Multi-criteria healthcare waste disposal location selection based on Fermatean fuzzy WASPAS method. Complex Intell Syst 7(5):2469–2484. https://doi.org/10.1007/s40747-021-00407-9CrossRef

Mishra AR, Rani P, Cavallaro F, Hezam IMM, Lakshmi J (2023b) An Integrated Intuitionistic Fuzzy Closeness Coefficient-Based OCRA Method for Sustainable Urban Transportation Options Selection. Axioms. https://doi.org/10.3390/axioms12020144CrossRef

Niu W, Rong Y, Yu L, Huang L (2022) A Novel Hybrid Group Decision Making Approach Based on EDAS and Regret Theory under a Fermatean Cubic Fuzzy Environment. Math Basel. https://doi.org/10.3390/math10173116CrossRef

Opricovic S, Tzeng GH (2004) Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 156(2):445–455. https://doi.org/10.1016/s0377-2217(03)00020-1CrossRef

Rani P, Mishra AR (2021) Fermatean fuzzy Einstein aggregation operators-based MULTIMOORA method for electric vehicle charging station selection. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2021.115267CrossRef

Rong Y, Liu Y, Pei Z (2020) Complex q-rung orthopair fuzzy 2-tuple linguistic Maclaurin symmetric mean operators and its application to emergency program selection. Int J Intell Syst 35(11):1749–1790. https://doi.org/10.1002/int.22271CrossRef

Rong Y, Liu Y, Pei Z (2022a) A novel multiple attribute decision-making approach for evaluation of emergency management schemes under picture fuzzy environment. Int J Mach Learn Cybern 13(3):633–661. https://doi.org/10.1007/s13042-021-01280-1CrossRef

Rong Y, Yu L (2023) Decision Support System for Prioritization of Offshore Wind Farm Site by Utilizing Picture Fuzzy Combined Compromise Solution Group Decision Method, Entropy

Rong Y, Yu L, Niu W, Liu Y, Senapati T, Mishra AR (2022b) MARCOS approach based upon cubic Fermatean fuzzy set and its application in evaluation and selecting cold chain logistics distribution center. Eng Appl Artif Intel. https://doi.org/10.1016/j.engappai.2022.105401CrossRef

Roubens M (1982) Preference relations on actions and criteria in multicriteria decision making. Eur J Oper Res 10(1):51–55. https://doi.org/10.1016/0377-2217(82)90131-XMathSciNetCrossRef

Saha A, Pamucar D, Gorcun OF, Mishra AR (2023) Warehouse site selection for the automotive industry using a fermatean fuzzy-based decision-making approach. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2022.118497CrossRef

Senapati T, Yager RR (2019) Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods. Eng Appl Artif Intel 85:112–121. https://doi.org/10.1016/j.engappai.2019.05.012CrossRef

Senapati T, Yager RR (2020) Fermatean fuzzy sets. J Amb Intel Hum Comp 11(2):663–674. https://doi.org/10.1007/s12652-019-01377-0CrossRef

Shahri MM, Jahromi AE, Houshmand M (2021) Failure Mode and Effect Analysis using an integrated approach of clustering and MCDM under pythagorean fuzzy environment. J Loss Prev Process Ind. https://doi.org/10.1016/j.jlp.2021.104591CrossRef

Shit C, Ghorai G (2021) Multiple attribute decision-making based on different types of Dombi aggregation operators under Fermatean fuzzy information. Soft Comput 25(22):13869–13880. https://doi.org/10.1007/s00500-021-06252-9CrossRef

Simic V, Dabic-Miletic S, Tirkolaee EB, Stevic Z, Deveci M, Senapati T (2023a) Neutrosophic CEBOM-MACONT model for sustainable management of end-of-life tires. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2023.110399CrossRef

Simic V, Milovanovic B, Pantelic S, Pamucar D, Tirkolaee EB (2023b) Sustainable route selection of petroleum transportation using a type-2 neutrosophic number based ITARA-EDAS model. Inf Sci 622:732–754. https://doi.org/10.1016/j.ins.2022.11.105CrossRef

Sutrisno A, Kumar V (2022) Supply chain sustainability risk decision support model using integrated Preference Selection Index (PSI) method and prospect theory. J Adv Manag Res 19(2):316–346. https://doi.org/10.1108/jamr-06-2021-0193CrossRef

Sutrisno A, Kumar V (2023) Supply chain sustainability risk assessment model using integration of the preference selection index (PSI) and the Shannon entropy. Int J Quality Reliab Manag 40(3):674–708. https://doi.org/10.1108/ijqrm-06-2021-0191CrossRef

Tan J, Liu Y, Senapati T, Garg H, Rong Y (2022) An extended MABAC method based on prospect theory with unknown weight information under Fermatean fuzzy environment for risk investment assessment in B&R. J Amb Intel Hum Comp. https://doi.org/10.1007/s12652-022-03769-1CrossRef

Wang W, Han X, Ding W, Wu Q, Chen X, Deveci M (2023a) A Fermatean fuzzy Fine-Kinney for occupational risk evaluation using extensible MARCOS with prospect theory. Eng Appl Artif Intel. https://doi.org/10.1016/j.engappai.2022.105518CrossRef

Wang Y, Jiang Z, Li X, Chen Y, Cui X, Wang S (2023b) Research on antecedent configurations of enterprise digital transformation and enterprise performance from the perspective of dynamic capability. Finance Res Lett. https://doi.org/10.1016/j.frl.2023.104170CrossRef

Wei D, Meng D, Rong Y, Liu Y, Garg H, Pamucar D (2022) Fermatean Fuzzy Schweizer-Sklar Operators and BWM-entropy-based combined compromise solution approach: an application to green supplier selection. Entropy. https://doi.org/10.3390/e24060776MathSciNetCrossRefPubMedPubMedCentral

Wen Z, Liao H, Zavadskas EK (2020) MACONT: mixed aggregation by comprehensive normalization technique for multi-criteria analysis. Informatica 31(4):857–880. https://doi.org/10.15388/20-infor417MathSciNetCrossRef

Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE T Fuzzy Syst 22(4):958–965. https://doi.org/10.1109/tfuzz.2013.2278989CrossRef

Yager RR (2017) Generalized orthopair fuzzy sets. IEEE T Fuzzy Syst 25(5):1222–1230. https://doi.org/10.1109/tfuzz.2016.2604005CrossRef

Yazdani M, Zarate P, Zavadskas EK, Turskis Z (2019) A combined compromise solution (CoCoSo) method for multi-criteria decision-making problems. Manag Decis 57(9):2501–2519. https://doi.org/10.1108/md-05-2017-0458CrossRef

Zadeh LA (1965) Fuzzy sets. Inform Control 8(3):338–353. https://doi.org/10.1016/S0019-9958(65)90241-XCrossRef

Zavadskas EK, Turskis Z, Antucheviciene J, Zakarevicius A (2012) Optimization of Weighted Aggregated Sum Product Assessment. Elektronika Ir Elektrotechnika 122(6):3–6. https://doi.org/10.5755/j01.eee.122.6.1810CrossRef

Zhang N, Su W, Zhang C, Zeng S (2022) Evaluation and selection model of community group purchase platform based on WEPLPA-CPT-EDAS method. Comput Ind Eng. https://doi.org/10.1016/j.cie.2022.108573CrossRefPubMedPubMedCentral

Zhang X, Li Z, Li G (2023) Impacts of blockchain-based digital transition on cold supply chains with a third-party logistics service provider. Transport Res Part E-Logist Transport Rev. https://doi.org/10.1016/j.tre.2023.103014CrossRef

Zou X-Y, Chen S-M, Fan K-Y (2020) Multiple attribute decision making using improved intuitionistic fuzzy weighted geometric operators of intuitionistic fuzzy values. Inf Sci 535:242–253. https://doi.org/10.1016/j.ins.2020.05.011MathSciNetCrossRef

Title: Multicriteria group decision-making based on Fermatean fuzzy fairly weighted and ordered weighted averaging operators
Authors: Tingting Liu
Kai Gao
Yuan Rong
Publication date: 01-03-2024
Publisher: Springer International Publishing
Published in: Granular Computing / Issue 1/2024
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI: https://doi.org/10.1007/s41066-023-00427-5

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