Bipolar neutrosophic soft sets and applications in decision making

Article

Ali, Mumtaz, Son, Le Hoang, Deli, Irfan and Tien, Nguyen Dang. 2017. "Bipolar neutrosophic soft sets and applications in decision making." Journal of Intelligent and Fuzzy Systems. 33 (6), pp. 4077-4087. https://doi.org/10.3233/JIFS-17999
Article Title

Bipolar neutrosophic soft sets and applications in decision making

ERA Journal ID581
Article CategoryArticle
AuthorsAli, Mumtaz (Author), Son, Le Hoang (Author), Deli, Irfan (Author) and Tien, Nguyen Dang (Author)
Journal TitleJournal of Intelligent and Fuzzy Systems
Journal Citation33 (6), pp. 4077-4087
Number of Pages11
Year2017
Place of PublicationNetherlands
ISSN1064-1246
1875-8967
Digital Object Identifier (DOI)https://doi.org/10.3233/JIFS-17999
Web Address (URL)https://www.iospress.nl/journal/journal-of-intelligent-fuzzy-systems/
Abstract

Neutrosophic set, proposed by Smarandache considers a truth membership function, an indeterminacy membership function and a falsity membership function. Soft set, proposed by Molodtsov is a mathematical framework which has the ability of independency of parameterizations inadequacy, syndrome of fuzzy set, rough set, probability. Those concepts have been utilized successfully to model uncertainty in several areas of application such as control, reasoning, game theory, pattern recognition, and computer vision. Nonetheless, there are many problems in real-world applications containing indeterminate and inconsistent information that cannot be effectively handled by the neutrosophic set and soft set. In this paper, we propose the notation of bipolar neutrosophic soft sets that combines soft sets and bipolar neutrosophic sets. Some algebraic operations of the bipolar neutrosophic set such as the complement, union, intersection are examined. We then propose an aggregation bipolar neutrosophic soft operator of a bipolar neutrosophic soft set and develop a decision making algorithm based on bipolar neutrosophic soft sets. Numerical examples are given to show the feasibility and effectiveness of the developed approach.

Keywordsalgebraic operations, bipolar neutrosophic soft sets, decision making, neutrosophic sets, soft sets
ANZSRC Field of Research 2020499999. Other mathematical sciences not elsewhere classified
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Byline AffiliationsSchool of Agricultural, Computational and Environmental Sciences
Vietnam National University, Vietnam
Aralik University, Turkiye
People’s Police University of Technology and Logistics, Vietnam
Institution of OriginUniversity of Southern Queensland
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Thao, Nguyen Xuan, Ali, Mumtaz and Smarandache, Florentin. 2019. "An intuitionistic fuzzy clustering algorithm based on a new correlation coefficient with application in medical diagnosis." Journal of Intelligent and Fuzzy Systems. 36 (1), pp. 189-198. https://doi.org/10.3233/JIFS-181084
Linguistic Approaches to Interval Complex Neutrosophic Sets in Decision Making
Dat, Luu Quoc, Thong, Nguyen Tho, Son, Le Hoang, Ali, Mumtaz, Smarandache, Florentin, Abdel-Basset, Mohamed and Long, Hoang Viet. 2019. "Linguistic Approaches to Interval Complex Neutrosophic Sets in Decision Making." IEEE Access. 7, pp. 38902-38917. https://doi.org/10.1109/ACCESS.2019.2902841
Dynamic interval valued neutrosophic set: Modeling decision making in dynamic environments
Thong, Nguyen Tho, Dat, Luu Quoc, Son, Le Hoang, Hoa, Nguyen Dinh, Ali, Mumtaz and Smarandache, Florentin. 2019. "Dynamic interval valued neutrosophic set: Modeling decision making in dynamic environments." Computers in Industry. 108, pp. 45-52. https://doi.org/10.1016/j.compind.2019.02.009
Fuzzy and neutrosophic modeling for link prediction in social networks
Tuan, Tran Manh, Chuan, Pham Minh, Ali, Mumtaz, Ngan, Tran Thi, Mittal, Mamta and Son, Le Hoang. 2019. "Fuzzy and neutrosophic modeling for link prediction in social networks." Evolving Systems. 10, pp. 629-634. https://doi.org/10.1007/s12530-018-9251-y
Multi-step daily forecasting of reference evapotranspiration for different climates of India: A modern multivariate complementary technique reinforced with ridge regression feature selection
Malik, Anurag, Jamei, Mehdi, Ali, Mumtaz, Prasad, Ramendra, Karbasi, Masoud and Yaseen, Zaher Mundher. 2022. "Multi-step daily forecasting of reference evapotranspiration for different climates of India: A modern multivariate complementary technique reinforced with ridge regression feature selection." Agricultural Water Management. 272. https://doi.org/https://doi.org/10.1016/j.agwat.2022.107812
Designing a Multi-Stage Expert System for daily ocean wave energy forecasting: A multivariate data decomposition-based approach
Jamei, Mehdi, Ali, Mumtaz, Karbasi, Masoud, Xiang, Yong, Ahmadianfar, Iman and Yaseen, Zaher Mundher. 2022. "Designing a Multi-Stage Expert System for daily ocean wave energy forecasting: A multivariate data decomposition-based approach ." Applied Energy. 326, pp. 1-24. https://doi.org/10.1016/j.apenergy.2022.119925
Forecasting weekly reference evapotranspiration using Auto Encoder Decoder Bidirectional LSTM model hybridized with a Boruta-CatBoost input optimizer
Karbasi, Masoud, Jamei, Mehdi, Ali, Mumtaz, Malik, Anurag and Yaseen, Zaher Mundher. 2022. "Forecasting weekly reference evapotranspiration using Auto Encoder Decoder Bidirectional LSTM model hybridized with a Boruta-CatBoost input optimizer." Computers and Electronics in Agriculture. 198, pp. 1-17. https://doi.org/10.1016/j.compag.2022.107121
Fuzzy Equivalence on Standard and Rough Neutrosophic Sets and Applications to Clustering Analysis
Thao, Nguyen Xuan, Son, Le Hoang, Cuong, Bui Cong, Ali, Mumtaz and Lan, Luong Hong. 2018. "Fuzzy Equivalence on Standard and Rough Neutrosophic Sets and Applications to Clustering Analysis." Bhateja, Vikrant, Nguyen, Bao Le, Nguyen, Nhu Gia, Satapathy, Suresh Chandra and Le, Dac-Nhuong (ed.) 4th International Conference on Information Systems Design and Intelligent Applications (INDIA 2017). Da Nang, Vietnam 15 - 17 Jun 2017 Singapore. https://doi.org/10.1007/978-981-10-7512-4_82
Development of data-driven models for wind speed forecasting in Australia
Neupane, Ananta, Raj, Nawin, Deo, Ravinesh and Ali, Mumtaz. 2021. "Development of data-driven models for wind speed forecasting in Australia." Deo, R., Samui, Pijush and Roy, Sanjiban Sekhar (ed.) Predictive modelling for energy management and power systems engineering. Netherlands. Elsevier. pp. 143-190
Advanced extreme learning machines vs. deep learning models for peak wave energy period forecasting: A case study in Queensland, Australia
Ali, Mumtaz, Prasad, Ramendra, Xiang, Yong, Sankaran, Adarsh, Deo, Ravinesh C., Xiao, Fuyuan and Zhu, Shuyu. 2021. "Advanced extreme learning machines vs. deep learning models for peak wave energy period forecasting: A case study in Queensland, Australia." Renewable Energy. 177, pp. 1033-1044. https://doi.org/10.1016/j.renene.2021.06.052
Novel short-term solar radiation hybrid model: long short-term memory network integrated with robust local mean decomposition
Huynh, Anh Ngoc-Lan, Deo, Ravinesh C., Ali, Mumtaz, Abdulla, Shahab and Raj, Nawin. 2021. "Novel short-term solar radiation hybrid model: long short-term memory network integrated with robust local mean decomposition." Applied Energy. 298, pp. 1-19. https://doi.org/10.1016/j.apenergy.2021.117193
Low cost and centimeter-level global positioning system accuracy using real-time kinematic library and real-time kinematic gpsa
Gianey, Hemant K., Ali, Mumtaz, Vijayakumar, Varadarajan, Sharma, Ashutosh and Kumar, Rajiv. 2021. "Low cost and centimeter-level global positioning system accuracy using real-time kinematic library and real-time kinematic gpsa." Recent Advances in Computer Science and Communications. 14 (2), pp. 360-367. https://doi.org/10.2174/2213275912666190328201322
Variational mode decomposition based random forest model for solar radiation forecasting: New emerging machine learning technology
Ali, Mumtaz, Prasad, Ramendra, Xiang, Yong, Khan, Mohsin, Farooque, Aitazaz Ahsan, Zong, Tianrui and Yaseen, Zaher Mundher. 2021. "Variational mode decomposition based random forest model for solar radiation forecasting: New emerging machine learning technology." Energy Reports. 7, pp. 6700-6717. https://doi.org/10.1016/j.egyr.2021.09.113
Forecasting standardized precipitation index using data intelligence models: regional investigation of Bangladesh
Yaseen, Zaher Mundher, Ali, Mumtaz, Sharafati, Ahmad, Al-Ansari, Nadhir and Shahid, Shamsuddin. 2021. "Forecasting standardized precipitation index using data intelligence models: regional investigation of Bangladesh." Scientific Reports. 11 (1), pp. 1-25. https://doi.org/10.1038/s41598-021-82977-9
Multifractal characterization and cross correlations of reference evapotranspiration time series of India
Adarsh, S., Nityanjaly, L. J., Pham, Quoc Bao, Sarang, R., Ali, Mumtaz and Nandhineekrishna, P.. 2021. "Multifractal characterization and cross correlations of reference evapotranspiration time series of India." European Physical Journal: Special Topics. 230 (21-22), pp. 3845-3859. https://doi.org/10.1140/epjs/s11734-021-00325-4
Self-supervised cross-iterative clustering for unlabeled plant disease images
Fang, Uno, Li, J., Lu, X., Gao, Longxiang, Ali, Mumtaz and Xiang, Yong. 2021. "Self-supervised cross-iterative clustering for unlabeled plant disease images." Neurocomputing. 456, pp. 36-48. https://doi.org/10.1016/j.neucom.2021.05.066
Spatiotemporal variability of multifractal properties of fineresolution daily gridded rainfall fields over India
Sankaran, Adarsh, Chavan, Sagar Rohidas, Ali, Mumtaz, Devarajan, Archana Devarajan, Dharan, Drisya Sasi and Khan, Muhammad Ismail. 2021. "Spatiotemporal variability of multifractal properties of fineresolution daily gridded rainfall fields over India." Natural Hazards. 106 (3), pp. 1951-1979. https://doi.org/10.1007/s11069-021-04523-0
Forecasting long-term precipitation for water resource management: a new multi-step data-intelligent modelling approach
Ali, Mumtaz, Deo, Ravinesh C., Xiang, Yong, Li, Ya and Yaseen, Zaher Mundher. 2020. "Forecasting long-term precipitation for water resource management: a new multi-step data-intelligent modelling approach." Hydrological Sciences Journal. 65 (16), pp. 2693-2708. https://doi.org/10.1080/02626667.2020.1808219
Modeling wheat yield with data-intelligent algorithms: artificial neural network versus genetic programming and minimax probability machine regression
Ali, Mumtaz and Deo, Ravinesh C.. 2020. "Modeling wheat yield with data-intelligent algorithms: artificial neural network versus genetic programming and minimax probability machine regression." Samui, Pijush, Bui, Dieu Tien, Chakraborty, Subrata and Deo, Ravinesh C. (ed.) Handbook of probabilistic models. Oxford, United Kingdom. Elsevier. pp. 37-87
Multifractal Cross Correlation Analysis of Agro-Meteorological Datasets (Including Reference Evapotranspiration) of California, United States
Sankaran, A., Krzyszczak, Jaromir, Baranowski, Piotr, Devarajan Sindhu, Archana, Nandhineekrishna Pradeep, Kumar, Lija Jayaprakash, Nityanjali, Thankamani, Vandana and Ali, Mumtaz. 2020. "Multifractal Cross Correlation Analysis of Agro-Meteorological Datasets (Including Reference Evapotranspiration) of California, United States." Atmosphere. 11 (10), pp. 1-24. https://doi.org/10.3390/atmos11101116
Probabilistic and artificial intelligence modelling of drought and agricultural crop yield in Pakistan
Ali, Mumtaz. 2019. Probabilistic and artificial intelligence modelling of drought and agricultural crop yield in Pakistan. PhD Thesis Doctor of Philosophy. University of Southern Queensland. https://doi.org/10.26192/S847-M467
Near real-time significant wave height forecasting with hybridized multiple linear regression algorithms
Ali, Mumtaz, Prasad, Ramendra, Xiang, Yong and Deo, Ravinesh C.. 2020. "Near real-time significant wave height forecasting with hybridized multiple linear regression algorithms." Renewable and Sustainable Energy Reviews. 132. https://doi.org/10.1016/j.rser.2020.110003
Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets
Smarandache, Florentin, Ali, Mumtaz and Khan, Mohsin. 2019. "Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets." Kahraman, Cengiz and Otay, Irem (ed.) Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets. Cham, Switzerland. Springer. pp. 25-42
Near real-time global solar radiation forecasting at multiple time-step horizons using the long short-term memory network
Huynh, Anh Ngoc‐Lan, Deo, Ravinesh C., An-Vo, Duc-Anh, Ali, Mumtaz, Raj, Nawin and Abdulla, Shahab. 2020. "Near real-time global solar radiation forecasting at multiple time-step horizons using the long short-term memory network." Energies. 13 (14). https://doi.org/10.3390/en13143517
Development of Advanced Computer Aid Model for Shear Strength of Concrete Slender Beam Prediction
Sharafati, Ahmad, Haghbin, Masoud, Aldlemy, Mohammed Suleman, Mussa, Mohamed H., Al Zand, Ahmed W., Ali, Mumtaz, Bhagat, Suraj Kumar, Al-Ansari, Nadhir and Yaseen, Zaher Mundher. 2020. "Development of Advanced Computer Aid Model for Shear Strength of Concrete Slender Beam Prediction." Applied Sciences. 10 (11), pp. 1-25. https://doi.org/10.3390/app10113811
A double decomposition-based modelling approach to forecast weekly solar radiation
Prasad, Ramendra, Ali, Mumtaz, Xiang, Yong and Khan, Huma. 2020. "A double decomposition-based modelling approach to forecast weekly solar radiation." Renewable Energy. 152, pp. 9-22. https://doi.org/10.1016/j.renene.2020.01.005
M-CFIS-R: Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing
Tuan, Tran Manh, Lan, Luong Thi Hong, Chou, Shuo-Yan, Ngan, Tran Thi, Son, Le Hoang, Giang, Nguyen Long and Ali, Mumtaz. 2020. "M-CFIS-R: Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing." Mathematics. 8 (5), pp. 1-24. https://doi.org/10.3390/math8050707
Complete ensemble empirical mode decomposition hybridized with random forest and kernel ridge regression model for monthly rainfall forecasts
Ali, Mumtaz, Prasad, Ramendra, Xiang, Yong and Yaseen, Z.. 2020. "Complete ensemble empirical mode decomposition hybridized with random forest and kernel ridge regression model for monthly rainfall forecasts." Journal of Hydrology. 584, pp. 1-15. https://doi.org/10.1016/j.jhydrol.2020.124647
The Generalized Neutrosophic Cubic Aggregation Operators and Their Application to Multi-Expert Decision-Making Method
Khan, Majid, Gulistan, Muhammad, Ali, Mumtaz and Chammam, Wathek. 2020. "The Generalized Neutrosophic Cubic Aggregation Operators and Their Application to Multi-Expert Decision-Making Method." Symmetry. 12 (4), pp. 1-15. https://doi.org/10.3390/sym12040496
Prediction of evaporation in arid and semi-arid regions: a comparative study using different machine learning models
Yaseen, Zaher Mundher, Al-Juboori, Al-Juboori, Beyaztasc, Ufuk, Al-Ansari, Nadhir, Chau, Kwok-Wing, Qi, Chongchong, Ali, Mumtaz, Salih, Sinan Q. and Shahid, Shamsuddin. 2020. "Prediction of evaporation in arid and semi-arid regions: a comparative study using different machine learning models." Engineering Applications of Computational Fluid Mechanics. 14 (1), pp. 70-89. https://doi.org/10.1080/19942060.2019.1680576
Monthly rainfall forecasting with Markov Chain Monte Carlo simulations integrated with statistical bivariate copulas
Ali, Mumtaz, Deo, Ravinesh C., Downs, Nathan J. and Maraseni, Tek. 2020. "Monthly rainfall forecasting with Markov Chain Monte Carlo simulations integrated with statistical bivariate copulas." Samui, Pijush, Bui, Dieu Tien, Chakraborty, Subrata and Deo, Ravinesh C. (ed.) Handbook of probabilistic models. Oxford, United Kingdom. Elsevier. pp. 89-105
Improving SPI-derived drought forecasts incorporating synoptic-scale climate indices in multi-phase multivariate empirical mode decomposition model hybridized with simulated annealing and kernel ridge regression algorithms
Ali, Mumtaz, Deo, Ravinesh C., Maraseni, Tek and Downs, Nathan J.. 2019. "Improving SPI-derived drought forecasts incorporating synoptic-scale climate indices in multi-phase multivariate empirical mode decomposition model hybridized with simulated annealing and kernel ridge regression algorithms." Journal of Hydrology. 576, pp. 164-184. https://doi.org/10.1016/j.jhydrol.2019.06.032
Significant wave height forecasting via an extreme learning machine model integrated with improved complete ensemble empirical mode decomposition
Ali, Mumtaz and Prasad, Ramendra. 2019. "Significant wave height forecasting via an extreme learning machine model integrated with improved complete ensemble empirical mode decomposition." Renewable and Sustainable Energy Reviews. 104, pp. 281-295. https://doi.org/10.1016/j.rser.2019.01.014
Designing a multi-stage multivariate empirical mode decomposition coupled with ant colony optimization and random forest model to forecast monthly solar radiation
Prasad, Ramendra, Ali, Mumtaz, Kwan, Paul and Khan, Huma. 2019. "Designing a multi-stage multivariate empirical mode decomposition coupled with ant colony optimization and random forest model to forecast monthly solar radiation." Applied Energy. 236, pp. 778-792. https://doi.org/10.1016/j.apenergy.2018.12.034
Logic connectives of complex fuzzy sets
Ngan, Tran Thi, Lan, Luong Thi Hong, Ali, Mumtaz, Tamir, Dan, Son, Le Hoang, Tuan, Tran Manh, Rishe, Naphtali and Kandel, Abe. 2018. "Logic connectives of complex fuzzy sets." Romanian Journal of Information Science and Technology. 21 (4), pp. 344-357.
A novel approach for fuzzy clustering based on neutrosophic association matrix
Long, Hoang Viet, Ali, Mumtaz, Son, Le Hoang, Khan, Mohsin and Tu, Doan Ngoc. 2019. "A novel approach for fuzzy clustering based on neutrosophic association matrix." Computers and Industrial Engineering. 127, pp. 687-697. https://doi.org/10.1016/j.cie.2018.11.007
Systematic review of decision making algorithms in extended neutrosophic sets
Khan, Mohsin, Son, Le Hoang, Ali, Mumtaz, Chau, Hoang Thi Minh, Na, Nguyen Thi Nhu and Smarandache, Florentin. 2018. "Systematic review of decision making algorithms in extended neutrosophic sets." Symmetry. 10 (8), pp. 1-28. https://doi.org/10.3390/sym10080314
Global Solar Radiation Prediction Using Hybrid Online Sequential Extreme Learning Machine Model
Hou, Muzhou, Zhang, Tianle, Weng, Futian, Ali, Mumtaz, Al-Ansari, Nadhir and Yaseen, Zaher Mundher. 2018. "Global Solar Radiation Prediction Using Hybrid Online Sequential Extreme Learning Machine Model." Energies. 11 (12), pp. 1-19. https://doi.org/10.3390/en11123415
New Soft Set Based Class of Linear Algebraic Codes
Ali, Mumtaz, Khan, Huma, Son, Le Hoang, Smarandache, Florentin and Kandasamy, W. B. Vasantha. 2018. "New Soft Set Based Class of Linear Algebraic Codes." Symmetry. 10 (10), pp. 1-10. https://doi.org/10.3390/sym10100510
H-max distance measure of intuitionistic fuzzy sets in decision making
Ngan, Roan Thi, Son, Le Hoang, Cuong, Bui Cong and Ali, Mumtaz. 2018. "H-max distance measure of intuitionistic fuzzy sets in decision making." Applied Soft Computing. 69, pp. 393-425. https://doi.org/10.1016/j.asoc.2018.04.036
Cotton yield prediction with Markov Chain Monte Carlo-based simulation model integrated with genetic programing algorithm: a new hybrid copula-driven approach
Ali, Mumtaz, Deo, Ravinesh C., Downs, Nathan J. and Maraseni, Tek. 2018. "Cotton yield prediction with Markov Chain Monte Carlo-based simulation model integrated with genetic programing algorithm: a new hybrid copula-driven approach." Agricultural and Forest Meteorology. 263, pp. 428-448. https://doi.org/10.1016/j.agrformet.2018.09.002
Multi-stage committee based extreme learning machine model incorporating the influence of climate parameters and seasonality on drought forecasting
Ali, Mumtaz, Deo, Ravinesh C., Downs, Nathan J. and Maraseni, Tek. 2018. "Multi-stage committee based extreme learning machine model incorporating the influence of climate parameters and seasonality on drought forecasting." Computers and Electronics in Agriculture. 152, pp. 149-165. https://doi.org/10.1016/j.compag.2018.07.013
Multi-stage hybridized online sequential extreme learning machine integrated with Markov Chain Monte Carlo copula-Bat algorithm for rainfall forecasting
Ali, Mumtaz, Deo, Ravinesh C., Downs, Nathan J. and Maraseni, Tek. 2018. "Multi-stage hybridized online sequential extreme learning machine integrated with Markov Chain Monte Carlo copula-Bat algorithm for rainfall forecasting." Atmospheric Research. 213, pp. 450-464. https://doi.org/10.1016/j.atmosres.2018.07.005
An ensemble-ANFIS based uncertainty assessment model for forecasting multi-scalar standardized precipitation index
Ali, Mumtaz, Deo, Ravinesh C., Downs, Nathan J. and Maraseni, Tek. 2018. "An ensemble-ANFIS based uncertainty assessment model for forecasting multi-scalar standardized precipitation index." Atmospheric Research. 207, pp. 155-180. https://doi.org/10.1016/j.atmosres.2018.02.024
Link prediction in co-authorship networks based on hybrid content similarity metric
Chuan, Pham Minh, Son, Le Hoang, Ali, Mumtaz, Khang, Tran Dinh, Huong, Le Thanh and Dey, Nilanjan. 2018. "Link prediction in co-authorship networks based on hybrid content similarity metric." Applied Intelligence. 48 (8), pp. 2470-2486. https://doi.org/10.1007/s10489-017-1086-x
A neutrosophic recommender system for medical diagnosis based on algebraic neutrosophic measures
Ali, Mumtaz, Son, Le Hoang, Thanh, Nguyen Dang and Minh, Nguyen Van. 2018. "A neutrosophic recommender system for medical diagnosis based on algebraic neutrosophic measures." Applied Soft Computing. 71, pp. 1054-1071. https://doi.org/10.1016/j.asoc.2017.10.012
Segmentation of dental X-ray images in medical imaging using neutrosophic orthogonal matrices
Ali, Mumtaz, Son, Le Hoang, Khan, Mohsin and Tung, Nguyen Thanh. 2017. "Segmentation of dental X-ray images in medical imaging using neutrosophic orthogonal matrices." Expert Systems with Applications. 91, pp. 434-441. https://doi.org/10.1016/j.eswa.2017.09.027
Interval Complex Neutrosophic Set: Formulation and Applications in Decision-Making
Ali, Mumtaz, Dat, Luu Quoc, Son, Le Hoang and Smarandache, Florentin. 2018. "Interval Complex Neutrosophic Set: Formulation and Applications in Decision-Making." International Journal of Fuzzy Systems. 20 (3), pp. 986-999. https://doi.org/10.1007/s40815-017-0380-4
δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis
Ngan, Roan Thi, Ali, Mumtaz and Son, Le Hoang. 2018. "δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis." Applied Intelligence. 48 (2), pp. 499-525. https://doi.org/10.1007/s10489-017-0986-0
A novel clustering algorithm in a neutrosophic recommender system for medical diagnosis
Thanh, Nguyen Dang, Ali, Mumtaz and Son, Le Hoang. 2017. "A novel clustering algorithm in a neutrosophic recommender system for medical diagnosis." Cognitive Computation. 9 (4), pp. 526-544. https://doi.org/10.1007/s12559-017-9462-8