Technical Reports from 2023
Why Softmax? Because It Is the Only Consistent Approach to Probability-Based Classification, Anatole Lokshin and Vladik Kreinovich
Complex Numbers Explain Why in Chinese Tradition, 4 Is Bad But 8 Is Good, Luc Longpre, Olga Kosheleva, and Vladik Kreinovich
Designing an Optimal Medicine Cocktail Is NP-Hard, Luc Longpre and Vladik Kreinovich
Towards Decision Making Under Interval Uncertainty, Juan A. Lopez and Vladik Kreinovich
Which Fuzzy Implications Operations Are Polynomial? A Theorem Proves That This Can Be Determined by a Finite Set of Inequalities, Sebastia Massanet, Olga Kosheleva, and Vladik Kreinovich
Why Fractional Fuzzy, Mehran Mazandarani, Olga Kosheleva, and Vladik Kreinovich
How to Make Machine Learning Financial Recommendations More Fair: Theoretical Explanation, Tho M. Nguyen, Saeid Tizpaz-Niari, and Vladik Kreinovich
Linear Regression under Partial Information, Tho M. Nguyen, Saeid Tizpaz-Niari, and Vladik Kreinovich
Local-Global Support for Earth Sciences: Economic Analysis, Uyen Hoang Pham, Aaron Velasco, and Vladik Kreinovich
Foundations of Neural Networks Explain the Empirical Success of the "Surrogate" Approach to Ordinal Regression -- and Recommend What Next, Salvador Robles, Martine Ceberio, and Vladik Kreinovich
Why Resilient Modulus Is Proportional to the Square Root of Unconfined Compressive Strength (UCS): A Qualitative Explanation, Edgar Daniel Rodriguez Velasquez and Vladik Kreinovich
Why Inverse Layers in Pavement? Why Zipper Fracking? Why Interleaving in Education? A General Explanation, Edgar Daniel Rodriguez Velasquez, Aaron Velasco, Olga Kosheleva, and Vladik Kreinovich
Everything Is a Matter of Degree: The Main Idea Behind Fuzzy Logic Is Useful in Geosciences and in Authorship, Christian Servin, Aaron Velasco, Edgar Daniel Rodriguez Velasquez, and Vladik Kreinovich
If Everything is a Matter of Degree, Why Do Crisp Techniques Often Work Better?, Miroslav Svitek, Olga Kosheleva, and Vladik Kreinovich
Is Fully Explainable AI Even Possible: Fuzzy-Based Analysis, Miroslav Svitek, Olga Kosheleva, and Vladik Kreinovich
The World Is Cognizable: An Argument Based on Hoermander's Theorem, Miroslav Svitek, Olga Kosheleva, and Vladik Kreinovich
What Do Goedel's Theorem and Arrow's Theorem Have in Common: A Possible Answer to Arrow's Question, Miroslav Svitek, Olga Kosheleva, and Vladik Kreinovich
When Is It Beneficial to Merge Two Companies? When Is it Beneficial to Start a Research Collaboration?, Miroslav Svitek, Olga Kosheleva, and Vladik Kreinovich
How to Combine Probabilistic and Fuzzy Uncertainty: Theoretical Explanation of Clustering-Related Empirical Result, Lázló Szilágyi, Olga Kosheleva, and Vladik Kreinovich
From Fuzzy to Mobile Fuzzy, Victor L. Timchenko, Yuriy P. Kondratenko, Olga Kosheleva, and Vladik Kreinovich
Towards a Psychologically Natural Relation Between Colors and Fuzzy Degrees, Victor L. Timchenko, Yuriy P. Kondratenko, Olga Kosheleva, Vladik Kreinovich, and Nguyen Hoang Phuong
Interval-Valued and Set-Valued Extensions of Discrete Fuzzy Logics, Belnap Logic, and Color Optical Computing, Victor L. Timchenko, Yury P. Kondratenko, and Vladik Kreinovich
Natural Color Interpretation of Interval-Valued Fuzzy Degrees, Victor L. Timchenko, Yury P. Kondratenko, Vladik Kreinovich, and Olga Kosheleva
Why Unit Two-Variable-Per-Inequality (UTVPI) Constraints Are So Efficient to Handle: Intuitive Explanation, Saeid Tizpaz-Niari, Martine Ceberio, Olga Kosheleva, and Vladik Kreinovich
How to Best Retrain a Neural Network If We Added One More Input Variable, Saeid Tizpaz-Niari and Vladik Kreinovich
Fast -- Asymptotically Optimal -- Methods for Determining the Optimal Number of Features, Saied Tizpaz-Niari, Luc Longpré, Olga Kosheleva, and Vladik Kreinovich
Why Micro-Funding? Why Small Businesses Are Important? Analysis Based on First Principles, Hein D. Tran, Edwin Tomy George, and Vladik Kreinovich
Fuzzy Techniques Explain the Effectiveness of ReLU Activation Function in Deep Learning, Julio C. Urenda, Olga Kosheleva, and Vladik Kreinovich
Methodological Lesson of Pythagorean Triples, Julio C. Urenda, Olga Kosheleva, and Vladik Kreinovich
Why Deep Learning Is Under-Determined? Why Usual Numerical Methods for Solving Partial Differential Equations Do Not Preserve Energy? The Answers May Be Related to Chevalley-Warning Theorem (and Thus to Fermat Last Theorem), Julio C. Urenda, Olga Kosheleva, and Vladik Kreinovich
Logical Inference Inevitably Appears: Fuzzy-Based Explanation, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich, and Orsolya Csiszar
Giant Footprints of Buddha and Generalized Limits, Julio C. Urenda and Vladik Kreinovich
Topological Explanation of Why Complex Numbers Are Needed in Quantum Physics, Julio C. Urenda and Vladik Kreinovich
Usually, Either Left and Right Brains Are Equally Active or Only One of Them Is Active: First-Principles Explanation, Julio C. Urenda and Vladik Kreinovich
Why Attitudes Are Usually Mutual: A Possible Mathematical Explanation, Julio C. Urenda and Vladik Kreinovich
Why Gliding Symmetry Used to Be Prevalent in Biology But Practically Disappeared, Julio C. Urenda and Vladik Kreinovich
Low-Probability High-Impact Events Are Even More Important Than It Is Usually Assumed, Aaron Velasco, Olga Kosheleva, and Vladik Kreinovich
Why 6-Labels Uncertainty Scale in Geosciences: Probability-Based Explanation, Aaron Velasco, Julio C. Urenda, Olga Kosheleva, and Vladik Kreinovich
Dialogs Re-enacted Across Languages, Version 2, Nigel G. Ward, Jonathan E. Avila, Emilia Rivas, and Divette Marco
How to Propagate Interval (and Fuzzy) Uncertainty: Optimism-Pessimism Approach, Vinícius F. Wasques, Olga Kosheleva, and Vladik Kreinovich
People Prefer More Information About Uncertainty, But Perform Worse When Given This Information: An Explanation of the Paradoxical Phenomenon, Jieqiong Zhao, Olga Kosheleva, and Vladik Kreinovich
Technical Reports from 2022
How to Make Inflation Optimal and Fair, Sean Aguilar and Vladik Kreinovich
Why Best-Worst Method Works Well, Sean Aguilar and Vladik Kreinovich
Why Decision Paralysis, Sean Aguilar and Vladik Kreinovich
Why Seneca Effect?, Sean R. Aguilar and Vladik Kreinovich
Hunting Habits of Predatory Birds: Theoretical Explanation of an Empirical Formula, Adilene Alaniz, Jiovani Hernandez, Andres D. Munoz, and Vladik Kreinovich
Why Rectified Linear Unit is Efficient in Machine Learning: One More Explanation, Barnabas Bede, Vladik Kreinovich, and Uyen Pham
Why Constraint Interval Arithmetic Works Well: A Theorem Explains Empirical Success, Barnabas Bede, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, and Vladik Kreinovich
How to elicit complex-valued fuzzy degrees, Laxman Bokati, Olga Kosheleva, and Vladik Kreinovich
Why Rarity Score Is a Good Evaluation of a Non-Fungible Token, Laxman Bokati, Olga Kosheleva, and Vladik Kreinovich