Genelleştirilmiş Küme Değerli Nötrosofik Beşli Sayılar Üzerine ANP Metodu

Yıl 2025, Cilt: 8 Sayı: 4, 1544 - 1571, 16.09.2025

Abdullah Kargın

https://doi.org/10.47495/okufbed.1565028

Öz

Bu çalışmada, nötrosofik beşli sayılar üzerinde karar verme uygulamalarında ilk defa Analytic Network Process (ANP) yöntemi kullanılarak yeni bir yöntem geliştirildi. Bu yöntemin uygulama adımları ve güncel hayatta karşılaşılan problemlere nasıl uygulanacağı hakkında bilgi verildi. Böylece nötrosofik küme teorisinin yeni yapılarından biri olan nötrosofik beşli kümeler ile çok kriterli karar verme uygulamalarından biri olan ANP yönteminin birlikte kullanıldığı yeni bir yöntem geliştirildi. Bu yeni yöntem, klasik ANP yönteminin tutarlılık hesaplama, 3. ve 6. adımlarını içermektedir. Ayrıca bu uygulamanın kullanıldığı güncel hayattan örnek bir uygulama yapıldı. Örnek uygulamada yenilenebilir enerji kaynaklarının seçiminde çevresel, sosyal ve ekonomik kriterlerin birbirleri üzerindeki etkisi kurgusal veriler kullanılarak analiz edildi. Bu uygulama sonucunda çevresel kriterin daha etkili olduğu, bunu sırasıyla sosyal kriterin ve ekonomik kriterin takip ettiği sonucuna varıldı. Ayrıca, kriterler arasındaki karşılıklı bağımlılıklar kriterlerin ağırlıklarını değiştirdi. Kriterlerin ağırlıklarının değişmesine neden olan kriterlerin birbirine bağımlılıklarının karar verme sürecinde belirli bir sıralama değişikliğine yol açabileceği sonucuna varıldı. Ayrıca farklı operatörler ile elde edilen karşılaştırma matrislerinin tutarlılık oranlarının değişebileceği ve tutarsız bir matris ile tutarlı bir matris ile elde edilen önem sıralamalarının farklı olabileceği sonucuna da varıldı.

Anahtar Kelimeler

ANP Metod , Yenilenebilir Enerji Kaynakları , Nötrosofik Teori , Nötrosofik Beşli Sayılar , Karar Verme Uygulamaları

ANP Method on Generalized Set-Valued Neutrosophic Quintuple Numbers

Öz

In this study, a new method was developed by using the Analytic Network Process method (ANP) for the first time in decision making applications on neutrosophic quintuple numbers. Information about the application steps of this method and how to apply it to problems encountered in current life is given. Thus, a new method has been developed in which neutrosophic quintuple sets, one of the new structures of neutrosophic set theory, and ANP method, one of the applications of multi-criteria decision making, are used together. This new method includes consistency calculation, step 3 and step 6 of the classical ANP method. Also, an example application from current life was made. In the case study, the impact of environmental, social and economic criteria on each other in the selection of renewable energy sources was analyzed using fictitious data. As a result of this application, it was concluded that the environmental criterion was more effective, followed by the social criterion and the economic criterion, respectively. Moreover, the interdependencies between the criteria changed the weights of the criteria. It is concluded that the interdependencies of the criteria that cause changes in the weights of the criteria may lead to a certain ranking change in the decision-making process. It is also concluded that the consistency ratios of the comparison matrices obtained with different operators may vary and the importance rankings obtained with an inconsistent matrix and a consistent matrix may be different.

Anahtar Kelimeler

ANP Method , Renewable Energy Sources , Neutrosophic Theory , Neutrosophic Quintuple Numbers , Decision Making Applications

Kaynakça

• Abdel-Basset M., Gamal A., Son LH., Smarandache F. A bipolar neutrosophic multi criteria decision making framework for professional selection. Applied Sciences 2020; 10(4): 1202.
• Alkabaa AS., Taylan O., Guloglu B., Baik S., Sharma V., Mishra R., Upreti GA. Fuzzy ANP-based criticality analyses approach of reliability-centered maintenance for CNC lathe machine components. Journal of Radiation Research and Applied Sciences 2024; 17(1): 100738.
• Al-Tahan M., Davvaz B., Smarandache F., Al-Kaseasbeh S. Fundamental group and complete parts of neutrosophic quadruple hυ-groups. Neutrosophic Sets And Systems 2023; (53): 107-116.
• Bakhshizadeh A., Yazdani-Chamzini A., Benmaran ML., Šaparauskas J., Turskis Z. Extracting and prioritizing the attractiveness parameters of shopping centers under intuitionistic fuzzy numbers. International Journal of Strategic Property Management 2024; 28(2): 130-142.
• Borujeni SHA., Zare M., Saadabadi LA. Comparison of factors affecting the acceptance of the trenchless technology and open-trench method using ANP and AHP: case study in Iran. Journal of Construction Engineering and Management 2024; 150(1): 04023145.
• Büyüközkan G., Karabulut Y., Göçer F. Spherical fuzzy sets based integrated DEMATEL, ANP, VIKOR approach and its application for renewable energy selection in Türkiye. Applied Soft Computing Article 2024; (58): 111465 58.
• Chatterjee R., Majumdar P., Samanta SK. On some similarity measures and entropy on quadri-partitioned single valued neutrosophic sets. Journal of Intelligent & Fuzzy Systems 2016; (30): 2475-2485.
• Debnath S. Fuzzy quadri-partitioned neutrosophic soft matrix theory and its decision-making approach. Journal of Computational and Cognitive Engineering 2022; 1(2): 88-93.
• Garg H. A new exponential-logarithm-based single-valued neutrosophic set and their applications. Expert Systems with Applications 2024; (238): 121854.
• Gayen D., Chatterjee R., Roy S. A review on environmental impacts of renewable energy for sustainable development. International Journal of Environmental Science and Technology 2024; 21(5): 5285-5310.
• Hanafi AM., Moawed MA., Abdellatif OE. Advancing sustainable energy management: a comprehensive review of artificial intelligence techniques in building. Engineering Research Journal (Shoubra) 2024; 53(2): 26-46.
• Hussain S., Hussain J., Rosyida L., Broumi S. Quadri-partitioned neutrosophic soft graphs. In: S. Broumi (ed.) Handbook of Research on Advances and Applications of Fuzzy Sets and Logic. IGI Global 2022; 34, 771-795.
• Jana C., Pal M., Karaaslan F., Wang JQ. Trapezoidal neutrosophic aggregation operators and their application to the multi-attribute decision-making process. Scientia Iranica 2020, 27(3): 1655-1673.
• Kar A., Rai RN. QFD-Based hybrid neutrosophic MCDM approach with six sigma evaluation for sustainable product design in industry 4.0. Kybernetes 2024; DOI: 10.1108/K-09-2023-1757.
• Karaaslan F. Neutrosophic soft set with applications in decision making,” International Journal of Information Science and Intelligent System, 2015, 4(2): 1-20.
• Karaaslan F. Correlation coefficients of single-valued neutrosophic refined soft sets and their applications in clustering analysis. Neural Computing and Applications, 2017, 28(9): 2781-2793.
• Karaaslan A., Aydın S. Evaluation of renewable energy resources with multi-criteria decision-making techniques: Türkiye example. Atatürk University Journal of Economics and Administrative Sciences 2020; 34(4): 1351-1375.
• Kargın A., Dayan A., Şahin NM. Generalized hamming similarity measure based on neutrosophic quadruple numbers and its applications to law sciences. Neutrosophic Set and Systems 2021; (40): 45-67.
• Kungumaraj E. An evaluation of triangular neutrosophic pert analysis for real-life project time and cost estimation. Neutrosophic Sets and Systems 2024; 63(1): 5.
• Li T., Rui Y., Zhao S., Zhang Y., Zhu H. A quantitative digital twin maturity model for underground infrastructure based on D-ANP. Tunnelling and Underground Space Technology 2024; (146): 105612.
• Liao H., Mi X., Xu Z., Xu J., Herrera F. Intuitionistic fuzzy analytic network process. IEEE Transactions on Fuzzy Systems 2018; 26(5): 2578-2590.
• Lyu HM., Yin ZY., Zhou A., Shen SL. Sensitivity analysis of typhoon-induced floods in coastal cities using improved ANP-GIS. International Journal of Disaster Risk Reduction 2024; (104): 104344.
• Mahmood T., Azam M., Hayat K., Özer Ö., Rehman U. Classification of helium hard disk drives by employing multi-attribute decision making approach relying on bipolar complex fuzzy dombi geometric Heronian mean operators. PLOS One, 2025
• Mary SA. Quadri partitioned neutrosophic soft set. International Research Journal on Advanced Science Hub 2021; (3): 106-112.
• Mikhailov L., Singh MG. Fuzzy analytic network process and its application to the development of decision support systems, IEEE transactions on systems, man, and cybernetics, part c. Applications and Reviews 2003; 33(1): 33-41.
• Mousavi SR., Sepehri M., Najafi SE. A framework for improving patient satisfaction by reducing the length of stay in the operation suite using the combined DEMATEL-ANP model. decision making. Applications in Management and Engineering 2024; 7(2): 197-220.
• Nalbant KG., Özdemir Ş., Özdemir Y. Evaluating the campus climate factors using an interval type-2 fuzzy ANP. Sigma Journal of Engineering and Natural Sciences 2024; 42(1): 89-98.
• Onwusinkwue S., Osasona F., Ahmad IAI., Anyanwu AC., Dawodu SO., Obi OC., Hamdan A. Artificial intelligence (AI) in renewable energy: a review of predictive maintenance and energy optimization. World Journal of Advanced Research and Reviews 2024; 21(1): 2487-2499.
• Özer Ö. Hamacher prioritized aggregation operators based on complex picture fuzzy sets and their applications in decision-making problems, J. Math. Comput. Sci., 2022; 1(1): 33–54.
• Panimalar A., Mohana K., Parvathi R. Mathematical morphological operations for quadri-partitioned neutrosophic set. International Journal of Neutrosophic Science 2023; 23(2): 77.
• Pouyakian M., Shafikhani AA., Najafi AA., Afshar-Najafi B., Kavousi A. Utilising the fuzzy analytic network process technique to prioritise safety challenges ın construction projects. International Journal of Critical Infrastructures 2024; 20(1): 16-32.
• Qing K., Du Y., Huang Q., Duan C., Hu W. Energy scheduling for microgrids with renewable energy sources considering an adjustable convex hull based uncertainty set. Renewable Energy 2024; (220): 119611.
• Rather KN., Mahalik MK., Mallick H. Do renewable energy sources perfectly displace non-renewable energy sources? evidence from Asia–pacific economies. Environmental Science and Pollution Research 2024; 31(17): 25706-25720.
• Saaty TL. Axiomatic foundation of the analytic hierarchy process. Management Science 1986; 32(7): 841-855.
• Şahin B., Soylu A. Intuitionistic fuzzy analytical network process models for maritime supply chain. Applied Soft Computing 2020; (96): 106614.
• Şahin M. Neutro-sigma algebras and anti-sigma algebras. Neutrosophic Sets and Systems 2022; 51(1): 56.
• Şahin M., Kargın A. Bipolar neutrosophic quintuple numbers and bipolar set valued neutrosophic quintuple numbers. in: G. Özyazıcı, M. Ceritoğlu (ed.), V. International Sciences and Innovation Congress 2022a; sayfa no:516-531, Ankara.
• Şahin M., Kargın A. Bipolar neutrosophic valued neutrosophic crisp Sets. in: M. Faisal, A. Amanzholova (ed.), IV. International Ankara Multidisciplinary Studies Congress 2022b, sayfa no: 494-507, Ankara.
• Şahin M., Kargın A. Interval neutrosophic quintuple numbers and interval set valued neutrosophic quintuple numbers. in: G. Özyazıcı, M. Ceritoğlu (ed.), V. International Sciences and Innovation Congress 2022c; sayfa no: 532-547, Ankara
• Şahin M., Kargın A., Doğan K. Generalized set valued neutrosophic quintuple numbers. in: P. A. Gürel, K. Beşaltı (ed.), 9th Ankara International Congress on Scientific Research 2023; sayfa no: 55-62. Ankara.
• Şahin M., Kargın A., Doğan K. Neutrosophic quintuple numbers and set valued neutrosophic quintuple numbers. in: M. Şahin, A. Amanzholova (ed.), III. Başkent International Conference on Multidisciplinary Studies 2022; sayfa no: 605-614, Ankara.
• Şahin M., Kargın A., Kılıç A. Generalized set valued neutrosophic quadruple sets and numbers. in: F. Smarandache, M. Şahin, V. Uluçay, A. Kargın (ed.), Quadruple neutrosophic theory and applications, Pons Publishing House, Brussels 2020; 2, 23-40.
• Şahin M., Kargın A., Uz MS. Generalized euclid measures based on generalized set valued neutrosophic quadruple numbers and multi criteria decision making applications. Neutrosophic Sets and Systems 2021; (47): 573-600.
• Sayed ET., Olabi AG., Alami AH., Radwan A., Mdallal A., Rezk A., Abdelkareem MA. Renewable energy and energy storage systems. Energies 2023; 16(3): 1415.
• Shoaei M., Noorollahi Y., Hajinezhad A., Moosavian SF. A review of the applications of artificial intelligence in renewable energy systems: an approach-based study. Energy Conversion and Management 2024; (306): 118207.
• Slamaa AA., El-Ghareeb HA., Saleh AA. A roadmap for migration system-architecture decision by neutrosophic-ANP and benchmark for enterprise resource planning systems. IEEE Access 2021; (9): 48583-48604.
• Smarandache F. Neutrosophic quadruple numbers, refined neutrosophic quadruple numbers, absorbance law, and the multiplication of neutrosophic quadruple numbers. Neutrosophic Set and Systems 2015; (10): 96-98.
• Smarandache F. Neutrosophy: neutrosophic probability, set and logic. Amer. Research Press Reheboth, USA, 1998.
• Talaat M., Elkholy MH., Alblawi A., Said T. Artificial intelligence applications for microgrids integration and management of hybrid renewable energy sources. Artificial Intelligence Review 2023; 56(9): 10557-10611.
• Vaz-Patto CM., Ferreira FA., Govindan K., Ferreira NC. Rethinking urban quality of life: unveiling causality links using cognitive mapping, neutrosophic logic and DEMATEL. European Journal Of Operational Research 2024; 316(1): 310-328.
• Voskoglou MG., Smarandache F., Mohamed M. Q-rung neutrosophic sets and topological spaces. Neutrosophic Systems with Applications 2024; (15): 58-66.
• Wang H., Smarandache F., Zhang Y., Sunderraman R. Single valued neutrosophic sets. Multispace and Multistructure 2010; (4): 410-413.
• Wilberforce T., Olabi AG., Sayed ET., Mahmoud M., Alami AH., Abdelkareem MA. The state of renewable energy source envelopes in urban areas. International Journal of Thermofluids 2024; (21): 100581.
• Yang Y., Li H., Zhang Z., Liu X. Interval-valued intuitionistic fuzzy analytic network process. Information Sciences 2020; (526): 102-118.
• Zaied ANH., Ismail M., Gamal A. An integrated of neutrosophic-ANP technique for supplier selection. Neutrosophic Sets and Systems 2019; (27): 237-244. Zhang Y., Wang S., Liu J., Liu D., Li T., Wu W. A corrosion assessment methodology based on triangular intuitionistic fuzzy comprehensive evaluation (TIFCE) with analytic network process (TIFANP): an application to external corrosion of the storage tank floor. Expert Systems with Applications 2024; (238): 121896.