Methodology for Interval-Valued Intuitionistic Fuzzy multiple attribute decision making and Applications to Performance Evaluation of Sustainable Microfinance Groups Lending
As an important supplement to my country's financial institutions, micro-loan companies serve "agriculture, rural areas and farmers", small and micro enterprises, and individuals, to a certain extent, alleviating the financing difficulties of such groups and regulating private finance. However, micro-loan companies only lend but do not deposit. In the process of lending, due to inadequate risk management, the risk problem has become increasingly prominent. With the continuous growth of the loan amount of rural credit and the continuous increase of microfinance groups lending customers, it faces certain problems in its risk management, which increases the risks of the company in all aspects. The performance evaluation of sustainable microfinance groups lending is a classical multiple attribute decision making (MADM) issues. In this given paper, the interval-valued intuitionistic fuzzy sets (IVIFSs), Hamacher operation sum and Hamacher operation product are introduced. The induced interval-valued intuitionistic fuzzy Hamacher power OWA (I-IVIFHPOWA) operator is built. Then, the I-IVIFHPOWA information operator is employed to solve MADM under IVIFSs. Finally, an example for performance evaluation of sustainable microfinance groups lending is used to test this new defined approach.
Y. Ni, H. Zhao, Z.S. Xu, Z.Y. Wang, Multiple attribute decision-making method based on projection model for dual hesitant fuzzy set, Fuzzy Optimization and Decision Making, 21 (2022) 263- 289.
M. Palanikumar, K. Arulmozhi, C. Jana, Multiple attribute decision-making approach for Pythagorean neutrosophic normal interval-valued fuzzy aggregation operators, Computational & Applied Mathematics, 41 (2022) 27.
T. Senapati, G.Y. Chen, R.R. Yager, Aczel-Alsina aggregation operators and their application to intuitionistic fuzzy multiple attribute decision making, International Journal of Intelligent Systems, 37 (2022) 1529-1551.
Y.M. Xing, M.S. Cao, Y.J. Liu, M. Zhou, J. Wu, A Choquet integral based interval Type-2 trapezoidal fuzzy multiple attribute group decision making for Sustainable Supplier Selection, Computers & Industrial Engineering, 165 (2022) 16.
W. Yang, Y.F. Pang, T-Spherical Fuzzy Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making, Mathematics, 10 (2022) 33.
H.S. Luo, L.J. Li, Y.K. Zhang, S.Y. Fang, X.Y. Chen, Link prediction in multiplex networks using a novel multiple-attribute decision-making approach, Knowledge-Based Systems, 219 (2021) 14.
M.B. Maisuria, D.M. Sonar, M.K. Rathod, Nanofluid selection used for coolant in heat exchanger by multiple attribute decision-making method, Journal of Mechanical Science and Technology, 35 (2021) 689-695.
A. Mousazadeh, M. Kafaee, M. Ashraf, Ranking of commercial photodiodes in radiation detection using multiple-attribute decision making approach, Nucl. Instrum. Methods Phys. Res. Sect. A-Accel. Spectrom. Dect. Assoc. Equip., 987 (2021) 5.
C. Shit, G. Ghorai, Multiple attribute decision-making based on different types of Dombi aggregation operators under Fermatean fuzzy information, Soft Computing, 25 (2021) 13869-13880.
M. Talafha, A. Alkouri, S. Alqaraleh, H. Zureigat, A. Aljarrah, Complex hesitant fuzzy sets and its applications in multiple attributes decision-making problems, Journal of Intelligent & Fuzzy Systems, 41 (2021) 7299-7327.
R. Verma, On intuitionistic fuzzy order-alpha divergence and entropy measures with MABAC method for multiple attribute group decision-making, Journal of Intelligent & Fuzzy Systems, 40 (2021) 1191-1217.
S.Z. Zeng, D.D. Luo, C.H. Zhang, X.S. Li, A Correlation-Based TOPSIS Method for Multiple Attribute Decision Making with Single-Valued Neutrosophic Information, International Journal of Information Technology & Decision Making, 19 (2020) 343-358.
S.H. Zhou, X. Ji, X.H. Xu, A hierarchical selection algorithm for multiple attributes decision making with large-scale alternatives, Information Sciences, 521 (2020) 195-208.
J. Campbell, H. Ahmad, S. Claflin, B. Taylor, I. van der Mei, R. Norman, G. Chen, L. Laslett, S. Simpson-Yap, G. Henson, A. Palmer, A multi-instrument comparison study of six multi-attribute utility instruments for a large cohort of Australians with multiple sclerosis: implications for resource allocation decision making, Qual. Life Res., 30 (2021) S45-S46.
J.P. Fan, F. Yan, M.Q. Wu, GLDS method for multiple attribute group decision making under 2-Tuple linguistic neutrosophic environment, Journal of Intelligent & Fuzzy Systems, 40 (2021) 11523-11538.
L.A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965) 338-356.
K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986) 87-96.
K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy-sets, Fuzzy Sets and Systems, 31 (1989) 343-349.
W.Z. Wang, Z.J. Wang, An Approach to Multi-Attribute Interval-Valued Intuitionistic Fuzzy Decision Making with Incomplete Weight Information, in: 5th International Conference on Fuzzy Systems and Knowledge Discovery, Ieee Computer Soc, Jinan, PEOPLES R CHINA, 2008, pp. 346-350.
Z.J. Wang, W.Z. Wang, K.W. Li, Ieee, Multi-Attribute Decision Making Models and Methods under Interval-Valued Intuitionistic Fuzzy Environment, in: 20th Chinese Control and Decision Conference, Ieee, Yantai, PEOPLES R CHINA, 2008, pp. 2420-2425.
Z.J. Wang, K.W. Li, W.Z. Wang, An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights, Information Sciences, 179 (2009) 3026-3040.
L.S. Zhang, S.Z. Gao, Ieee, A novel weights generating approach for multiple attribute decision making under interval-valued intuitionistic fuzzy environment, in: 29th Chinese Control And Decision Conference (CCDC), Ieee, Chongqing, PEOPLES R CHINA, 2017, pp. 4406-4409.
R. Davoudabadi, S.M. Mousavi, V. Mohagheghi, A new last aggregation method of multi-attributes group decision making based on concepts of TODIM, WASPAS and TOPSIS under interval-valued intuitionistic fuzzy uncertainty, Knowledge and Information Systems, 62 (2020) 1371-1391.
Z.L. Yue, Deriving decision maker's weights based on distance measure for interval-valued intuitionistic fuzzy group decision making, Expert Systems with Applications, 38 (2011) 11665-11670.
J. Ye, Multiple attribute group decision-making methods with unknown weights in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting, International Journal of General Systems, 42 (2013) 489-502.
S.L. Zhang, J. Tang, F.Y. Meng, R.P. Yuan, A Group Decision Making Method with Interval-Valued Intuitionistic Fuzzy Preference Relations and Its Application in the Selection of Cloud Computing Vendors for SMEs, Informatica, 32 (2021) 163-193.
Z.L. Yue, Y.Y. Jia, An application of soft computing technique in group decision making under interval-valued intuitionistic fuzzy environment, Applied Soft Computing, 13 (2013) 2490-2503.
S.P. Wan, G.L. Xu, J.Y. Dong, A novel method for group decision making with interval-valued Atanassov intuitionistic fuzzy preference relations, Information Sciences, 372 (2016) 53-71.
S.P. Wan, G.L. Xu, J.Y. Dong, An Atanassov intuitionistic fuzzy programming method for group decision making with interval-valued Atanassov intuitionistic fuzzy preference relations, Applied Soft Computing, 95 (2020) 15.
H.Y. Zhang, M.G. Dong, W.X. Zhang, X.X. Song, A.T. PRess, Inclusion measure and similarity measure of intuitionistic and interval-valued fuzzy sets, in: 2007 International Conference on Intelligent Systems and Knowledge Engineering, Atlantis Press, Southwest Jiaotong Univ, Chengdu, PEOPLES R CHINA, 2007.
C.P. Wei, P. Wang, Y.Z. Zhang, Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications, Information Sciences, 181 (2011) 4273-4286.
W.K.W. Ismail, L. Abdullah, A New Cosine Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Their Applications, in: 20th National Symposium on Mathematical Sciences, Amer Inst Physics, Univ Kebangsaan Malaysia, Sch Math Sci, Putrajaya, MALAYSIA, 2012, pp. 292-298.
B. Farhadinia, A.I. Ban, Developing new similarity measures of generalized intuitionistic fuzzy numbers and generalized interval-valued fuzzy numbers from similarity measures of generalized fuzzy numbers, Mathematical and Computer Modelling, 57 (2013) 812-825.
K. Hu, J.Q. Li, The Entropy and Similarity Measure of Interval Valued Intuitionistic Fuzzy Sets and Their Relationship, International Journal of Fuzzy Systems, 15 (2013) 279-288.
H.M. Zhang, L.Y. Yu, New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets, Information Sciences, 245 (2013) 181-196.
A.R. Mishra, P. Rani, K.R. Pardasani, A. Mardani, Z. Stevic, D. Pamucar, A novel entropy and divergence measures with multi-criteria service quality assessment using interval-valued intuitionistic fuzzy TODIM method, Soft Computing, 24 (2020) 11641-11661.
P. Rani, D. Jain, Information Measures-Based Multi-criteria Decision-Making Problems for Interval-Valued Intuitionistic Fuzzy Environment, Proceedings of the National Academy of Sciences India Section a-Physical Sciences, 90 (2020) 535-546.
H. Nguyen, Ieee, A Novel Similarity Measure Based on Generalized Score Function For Interval-valued Intuitionistic Fuzzy Sets With Applications, in: IEEE CIS International Conference on Fuzzy Systems (FUZZ-IEEE), Ieee, Electr Network, 2021.
Sonia, P. Tiwari, P. Gupta, Novel distance, similarity and entropy measures for interval valued intuitionistic fuzzy soft set, Journal of Intelligent & Fuzzy Systems, 43 (2022) 3067-3086.
F.K. Bo, J. He, H.R. Li, Q. Fu, Interval-valued intuitionistic fuzzy MADM method based on TOPSIS and grey correlation analysis (vol 17, pg 5584, 2020), Mathematical Biosciences and Engineering, 17 (2020) 6699-6701.
F. Dammak, L. Baccour, A.M. Alimi, A new ranking method for TOPSIS and VIKOR under interval valued intuitionistic fuzzy sets and possibility measures, Journal of Intelligent & Fuzzy Systems, 38 (2020) 4459-4469.
K. Deveci, R. Cin, A. Kagizman, A modified interval valued intuitionistic fuzzy CODAS method and its application to multi-criteria selection among renewable energy alternatives in Turkey, Applied Soft Computing, 96 (2020) 18.
A. Tiwari, Q.M.D. Lohani, P.K. Muhuri, Ieee, Interval-valued Intuitionistic Fuzzy TOPSIS method for Supplier Selection Problem, in: IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Ieee, Electr Network, 2020.
D. Zindani, S.R. Maity, S. Bhowmik, Interval-valued intuitionistic fuzzy TODIM method based on Schweizer-Sklar power aggregation operators and their applications to group decision making, Soft Computing, 24 (2020) 14091-14133.
Q. Wang, Research on teaching quality evaluation of college english based on the CODAS method under interval-valued intuitionistic fuzzy information, Journal of Intelligent & Fuzzy Systems, 41 (2021) 1499-1508.
M.W. Zhao, G.W. Wei, C. Wei, J. Wu, Y. Wei, Extended CPT-TODIM method for interval-valued intuitionistic fuzzy MAGDM and its application to urban ecological risk assessment, Journal of Intelligent & Fuzzy Systems, 40 (2021) 4091-4106.
D. Zindani, S.R. Maity, S. Bhowmik, Complex interval-valued intuitionistic fuzzy TODIM approach and its application to group decision making, Journal of Ambient Intelligence and Humanized Computing, 12 (2021) 2079-2102.
Z.S. Xu, J. Chen, On geometric aggregation ove interval-valued intuitionistic fuzzy information, in: 4th International Conference on Fuzzy Systems and Knowledge Discovery, Ieee Computer Soc, Haikou, PEOPLES R CHINA, 2007, pp. 466-+.
G.W. Wei, W.D. Yi, Induced Interval-Valued Intuitionistic Fuzzy OWG Operator, in: 5th International Conference on Fuzzy Systems and Knowledge Discovery, Ieee Computer Soc, Jinan, PEOPLES R CHINA, 2008, pp. 605-609.
X.W. Qi, C.Y. Liang, J.L. Zhang, Some Generalized Dependent Aggregation Operators with Interval-Valued Intuitionistic Fuzzy Information and Their Application to Exploitation Investment Evaluation, Journal of Applied Mathematics, (2013) 24.
F.W. Zhang, W.W. Huang, J. Sun, Z.D. Liu, Y.H. Zhu, K.T. Li, S.H. Xu, Q. Li, Generalized Fuzzy Additive Operators on Intuitionistic Fuzzy Sets and Interval-Valued Intuitionistic Fuzzy Sets and Their Application, Ieee Access, 7 (2019) 45734-45743.
E. Bolturk, M. Gulbay, C. Kahraman, Sustainable energy selection based on interval-valued intuitionistic fuzzy and neutrosophic aggregation operators, Journal of Intelligent & Fuzzy Systems, 39 (2020) 6553-6563.
P. Kakati, S. Borkotokey, Generalized interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral operators for multicriteria decision making, Iranian Journal of Fuzzy Systems, 17 (2020) 121-139.
L.P. Wu, G.W. Wei, J. Wu, C. Wei, Some Interval-Valued Intuitionistic Fuzzy Dombi Heronian Mean Operators and their Application for Evaluating the Ecological Value of Forest Ecological Tourism Demonstration Areas, International Journal of Environmental Research and Public Health, 17 (2020) 31.
Y. Rong, Y. Liu, Z. Pei, Interval-Valued Intuitionistic Fuzzy Generalised Bonferroni Mean Operators for Multi-attribute Decision Making, International Journal of Fuzzy Systems, 23 (2021) 1728-1754.
T. Senapati, G.Y. Chen, R. Mesiar, R.R. Yager, Novel Aczel-Alsina operations-based interval-valued intuitionistic fuzzy aggregation operators and their applications in multiple attribute decision-making process, International Journal of Intelligent Systems, 37 (2022) 5059-5081.
T. Senapati, R. Mesiar, V. Simic, A. Iampan, R. Chinram, R. Ali, Analysis of Interval-Valued Intuitionistic Fuzzy Aczel-Alsina Geometric Aggregation Operators and Their Application to Multiple Attribute Decision-Making, Axioms, 11 (2022) 22.
X. Xu, An integrated methodology for selecting the building material suppliers with interval-valued intuitionistic fuzzy information, Journal of Intelligent & Fuzzy Systems,, (2022) https://doi.org/10.3233/JIFS-221001.
J. Ye, Multicriteria decision-making method using the Dice similarity measure based on the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets, Applied Mathematical Modelling, 36 (2012) 4466-4472.
J. Ye, Generalized Dice measures for multiple attribute decision making under intuitionistic and interval-valued intuitionistic fuzzy environments, Neural Computing & Applications, 30 (2018) 3623-3632.
Y. Tang, L.L. Wen, G.W. Wei, Approaches to multiple attribute group decision making based on the generalized Dice similarity measures with intuitionistic fuzzy information, International Journal of Knowledge-Based and Intelligent Engineering Systems, 21 (2017) 85-95.
A. Khalid, M. Abbas, Distance Measures and Operations in Intuitionistic and Interval-Valued Intuitionistic Fuzzy Soft Set Theory, International Journal of Fuzzy Systems, 17 (2015) 490-497.
J. Ye, Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision-making, International Journal of General Systems, 42 (2013) 883-891.
P. Gupta, P. Tiwari, Measures of Cosine Similarity intended for Fuzzy sets, Intuitionistic and Interval-Valued Intuitionistic Fuzzy sets with Application in Medical Diagnoses, in: 3rd International Conference on Computing for Sustainable Global Development (INDIACom), Ieee, New Delhi, INDIA, 2016, pp. 1846-1849.
D.H. Liu, X.H. Chen, D. Peng, Interval-Valued Intuitionistic Fuzzy Ordered Weighted Cosine Similarity Measure and Its Application in Investment Decision-Making, Complexity, (2017) 11.
R. Verma, J.M. Merigo, A New Decision Making Method Using Interval-Valued Intuitionistic Fuzzy Cosine Similarity Measure Based on the Weighted Reduced Intuitionistic Fuzzy Sets, Informatica, 31 (2020) 399-433.
M. Sinn, Sequential Group Lending: A Mechanism to Raise the Repayment Rate in Microfinance, Economica, 80 (2013) 326-344.
T. Allen, Optimal (partial) group liability in microfinance lending, Journal of Development Economics, 121 (2016) 201-216.
A. Haldar, J.E. Stiglitz, Group Lending, Joint Liability, and Social Capital: Insights From the Indian Microfinance Crisis, Polit. Soc., 44 (2016) 459-497.
N.K. Kumar, Dynamic Incentives in Microfinance Group Lending: An Empirical Analysis of Progressive Lending Mechanism (vol 2, pg 1, 2012), Sage Open, 6 (2016) 1.
Y.Y. Xu, W.L. Cheng, L.Y. Zhang, Switching from Group Lending to Individual Lending: The Experience at China's Largest Microfinance Institution, Emerging Markets Finance and Trade, 56 (2020) 1989-2006.
R.R. Yager, D.P. Filev, Induced ordered weighted averaging operators, IEEE Transactions on Systems, Man, Cybernetics, Part B, 29 (1999) 141-150.
Z.-S. Xu, J. Chen, Approach to group decision making based on interval-valued intuitionistic judgment matrices, Systems Engineering-Theory Practice, 27 (2007) 126-133.
H.W. Liu, G.J. Wang, Multi-criteria decision-making methods based on intuitionistic fuzzy sets, European Journal of Operational Research, 179 (2007) 220-233.
P.D. Liu, Some Hamacher Aggregation Operators Based on the Interval-Valued Intuitionistic Fuzzy Numbers and Their Application to Group Decision Making, Ieee Transactions on Fuzzy Systems, 22 (2014) 83-97.
S.X. Shi, Performance evaluation of urban ecological environment construction with interval-valued intuitionistic fuzzy information, Journal of Intelligent & Fuzzy Systems, 32 (2017) 1119-1127.
R.R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision-making, Ieee Transactions on Systems Man and Cybernetics, 18 (1988) 183-190.
Z.X. Su, G.P. Xia, M.Y. Chen, Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making, International Journal of General Systems, 40 (2011) 805-835.
X.Y. Zhao, S. Tang, S.L. Yang, K.D. Huang, Extended VIKOR method based on cross-entropy for interval-valued intuitionistic fuzzy multiple criteria group decision making, Journal of Intelligent & Fuzzy Systems, 25 (2013) 1053-1066.
F.B. Yeni, G. Ozcelik, Interval-Valued Atanassov Intuitionistic Fuzzy CODAS Method for Multi Criteria Group Decision Making Problems, Group Decision and Negotiation, 28 (2019) 433-452.
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