Decision Making Under Uncertainty: A Z-Number-Based Regret Principle Ramiz Alekperov, Vugar Salahli, Rahib Imamguluyev Mathematics, 2025 Decision-making theory has developed over many decades at the intersection of economics, mathematics, psychology, and engineering. Its classical foundations include Bernoulli’s expected utility theory, von Neumann and Morgenstern’s rational choice theory, and the criteria proposed by Savage, Wald, Hurwicz, and others. However, in real-world contexts, decisions are made under uncertainty, incompleteness, and unreliability of information, which classical approaches do not adequately address. To overcome these limitations, modern multi-criteria decision-making methods such as Analytic Hierarchy Process (AHP), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VlseKriterijumska Optimizacija I Kompromisno Resenje (Compromise solution approach) (VIKOR), and ELimination Et Choix Traduisant la REalité (Elimination and Choice Expressing Reality) (ELECTRE), as well as their fuzzy and Z-number extensions, are widely applied to the modeling and evaluation of complex systems. These Z-number extensions are based on the concept of Z-numbers introduced by Lotfi Zadeh in 2011 to formalize higher-order uncertainty. This study introduces the Z-Regret principle, which extends Savage’s regret criterion through the use of Z-numbers. Supported by Rafik Aliev’s mathematical justifications concerning arithmetic operations on Z-numbers, the model evaluates regret not only as a loss relative to the best alternative but also by incorporating the degree of confidence and reliability of this evaluation. Calculations for the selection of digital advertising platforms in terms of performance assessment under various scenarios demonstrate that the Z-Regret principle enables more stable and well-founded decision-making under uncertainty.
Improvement of operational parameters of sub-surface work-over equipment Neftyanoe Khozyaystvo Oil Industry, 2002
RECENT SCHOLAR PUBLICATIONS
Detection of Anomalies in the Energy Consumption System by Soft-Computing Methods AR Balashirin, ST Togrul, R Mikayilova International Conference on Intelligent and Fuzzy Systems, 791-798 , 2025 2025 Citations: 1
The Role of Artificial Intelligence in the Pharmaceutical Supply Chain AR Balashirin, R Mikayilova, L Suleymanova International Conference on Intelligent and Fuzzy Systems, 465-473 , 2025 2025
Decision Making Under Uncertainty: A Z-Number-Based Regret Principle R Alekperov, V Salahli, R Imamguluyev Mathematics. https://doi.org/10.3390/math13223579 13 (22), 3579 , 2025 2025 Citations: 2
Development of the Architecture of an Intelligent Decision-Making System for Managing Commercial Enterprises T Abdullayev, R Alekperov, R Imamguluyev, V Salahlı International Conference on Theory and Application of Soft Computing … , 2024 2024
Detecting Anomalies in Data Using Z-numbers AR Balashirin, ST Togrul International Conference on Intelligent and Fuzzy Systems, 99-106 , 2024 2024 Citations: 2
Managing Factors for Sustainable Development in the Processing Industry: A Comparative Analysis of Growth Models AS Gahraman, HA Sadreddin, AR Balashirin, IK Abbas, AV Sajaddin International Conference on Smart Environment and Green Technologies, 61-67 , 2024 2024
The Use Of ERP And WMS Systems In The Wholesale And Retail Trade Of Pharmaceutical Products R Alekperov IOSR Journal of Computer Engineering (IOSR-JCE) e-ISSN: 2278-0661,p-ISSN … , 2024 2024
An approach to assessing the level of development of enterprises in order to introduce convergent technologies based on Z-numbers R Alekperov, R Mikayilova, S Shukurova International Conference on Theory and Applications of Fuzzy Systems and … , 2023 2023 Citations: 1
Correction to: The Use of Z-numbers to Assess the Level of Motivation of Employees, Taking into Account Non-formalized Motivational Factors AR Balashirin International Conference on Intelligent and Fuzzy Systems, C1-C1 , 2023 2023 Citations: 1
The use of Z-numbers to assess the level of motivation of employees, taking into account non-formalized motivational factors AR Balashirin International Conference on Intelligent and Fuzzy Systems, 354-362 , 2023 2023 Citations: 19
of Motivation of Employees, Taking into Account AR Balashirin Intelligent and Fuzzy Systems: Intelligence and Sustainable Future … , 2023 2023
The use of fuzzy numbers for the rational choice of the structure of the distribution channel of goods AR Balashirin International Conference on Theory and Applications of Fuzzy Systems and … , 2022 2022 Citations: 11
Assessment of the effectiveness of marketing activities of commercial enterprises using the theory of fuzzy sets A Ramiz, S Vuqar International Conference on Intelligent and Fuzzy Systems, 135-141 , 2022 2022 Citations: 18
The method of ranking business processes on weaknesses based on the theory of fuzzy sets A Ramiz International Conference on Intelligent and Fuzzy Systems, 128-134 , 2022 2022 Citations: 3
Using fuzzy Z-numbers when processing flexible queries R Alekperov International Conference on Intelligent and Fuzzy Systems, 435-444 , 2022 2022 Citations: 6
The Method of Ranking Business Processes on Weaknesses Based on the Theory A Ramiz Intelligent and Fuzzy Systems: Digital Acceleration and The New Normal … , 2022 2022
Method for diagnostics and selection of the type of market structure of commodity markets based on fuzzy set theory R Mikayilova, R Alekperov International Conference on Theory and Application of Soft Computing … , 2021 2021 Citations: 1
Development and Implementation of an Algorithm for Processing Fuzzy Queries to Relational Databases R Alekperov International Conference on Intelligent and Fuzzy Systems, 892-900 , 2021 2021
Determination of the level of development of commodity markets by segmentation of economic regions based on the theory of fuzzy sets R Mikayilova, R Alekperov International Conference on Intelligent and Fuzzy Systems, 121-128 , 2021 2021 Citations: 3
Representation Of Fuzzy Queries In The Form Of A Multi-Criteria Decision Matrix Using Z-Numbers R Alekperov 2021
MOST CITED SCHOLAR PUBLICATIONS
The use of Z-numbers to assess the level of motivation of employees, taking into account non-formalized motivational factors AR Balashirin International Conference on Intelligent and Fuzzy Systems, 354-362 , 2023 2023 Citations: 19
Assessment of the effectiveness of marketing activities of commercial enterprises using the theory of fuzzy sets A Ramiz, S Vuqar International Conference on Intelligent and Fuzzy Systems, 135-141 , 2022 2022 Citations: 18
The use of fuzzy numbers for the rational choice of the structure of the distribution channel of goods AR Balashirin International Conference on Theory and Applications of Fuzzy Systems and … , 2022 2022 Citations: 11
A method for forecasting the demand for pharmaceutical products in a distributed pharmacy network based on an integrated approach using fuzzy logic and neural networks ARB Oglu, IIT Kizi International Conference on Intelligent and Fuzzy Systems, 998-1007 , 2020 2020 Citations: 11
Neural network modeling and estimation of the effectiveness of the financing policy impact on the socio-economic development of the socio-educational system AR Balashirin, IK Akbar International Conference on Theory and Applications of Fuzzy Systems and … , 2018 2018 Citations: 9
Application of neural networks for segmentation of catering services market within the overall system of consumer market on the model of restaurant business with the aim to … AR Balashirin, II Tarlan International Conference on Theory and Applications of Fuzzy Systems and … , 2018 2018 Citations: 8
Processing of fuzzy queries and software implementation to a relational database of wholesale and retail commercial enterprises K Kilic, T Abdullayev, R Alakbarov, N Kilic Procedia Computer Science 102, 490-494 , 2016 2016 Citations: 8
Разработка автоматизированной системы для прогнозирования показателей бурения на основе нейронных моделей РБ Алекперов, и др. Нефтяное хозяйство, 40-42 , 2001 2001 Citations: 8
Using fuzzy Z-numbers when processing flexible queries R Alekperov International Conference on Intelligent and Fuzzy Systems, 435-444 , 2022 2022 Citations: 6
Solution of the retail marketing problem of rational choice of the location of trade enterprises using the method of hierarchy analysis and fuzzy set theory A Veliyev, T Abdullayev, R Alekperov, V Salahli International Conference on Theory and Applications of Fuzzy Systems and … , 2020 2020 Citations: 6
Estimation of potential locations of trade objects on the basis of fuzzy set theory ARB Oglu, SVM Oglu International Conference on Intelligent and Fuzzy Systems, 228-237 , 2020 2020 Citations: 6
The method of ranking business processes on weaknesses based on the theory of fuzzy sets A Ramiz International Conference on Intelligent and Fuzzy Systems, 128-134 , 2022 2022 Citations: 3
Determination of the level of development of commodity markets by segmentation of economic regions based on the theory of fuzzy sets R Mikayilova, R Alekperov International Conference on Intelligent and Fuzzy Systems, 121-128 , 2021 2021 Citations: 3
Decision Making Under Uncertainty: A Z-Number-Based Regret Principle R Alekperov, V Salahli, R Imamguluyev Mathematics. https://doi.org/10.3390/math13223579 13 (22), 3579 , 2025 2025 Citations: 2
Detecting Anomalies in Data Using Z-numbers AR Balashirin, ST Togrul International Conference on Intelligent and Fuzzy Systems, 99-106 , 2024 2024 Citations: 2
Processing Of Fuzzy Logic Queries In Corporate Information System TS Abdullayev, RB Alekperov, KS Kilic Journals of Qafqaz University, Mathematics and Computer Science 34, 105-113 , 2012 2012 Citations: 2
Detection of Anomalies in the Energy Consumption System by Soft-Computing Methods AR Balashirin, ST Togrul, R Mikayilova International Conference on Intelligent and Fuzzy Systems, 791-798 , 2025 2025 Citations: 1
An approach to assessing the level of development of enterprises in order to introduce convergent technologies based on Z-numbers R Alekperov, R Mikayilova, S Shukurova International Conference on Theory and Applications of Fuzzy Systems and … , 2023 2023 Citations: 1
Correction to: The Use of Z-numbers to Assess the Level of Motivation of Employees, Taking into Account Non-formalized Motivational Factors AR Balashirin International Conference on Intelligent and Fuzzy Systems, C1-C1 , 2023 2023 Citations: 1
Method for diagnostics and selection of the type of market structure of commodity markets based on fuzzy set theory R Mikayilova, R Alekperov International Conference on Theory and Application of Soft Computing … , 2021 2021 Citations: 1