Technical Reports from 2025
Best Strategies for Bilingual Education: How Can We Explain Their Success?, Claudia Cabrera, Olga Kosheleva, Christian Servin, and Vladik Kreinovich
All We (and LLMs) Need Is Fuzzy: An Argument, Olga Kosheleva and Vladik Kreinovich
Gurevich's Quizani Dialogs as an Example of Explainable Mathematics, and How This Is Related to Quantum Space-Time Ideas that Can Speed Up Computations, Olga Kosheleva and Vladik Kreinovich
How to Share a Success, How to Share a Crisis, and How All This Is Related to Fuzzy, Olga Kosheleva and Vladik Kreinovich
"At Least k out of n" under Fuzzy Uncertainty: Efficient Algorithm for General "And"-Operations, Olga Kosheleva, Vladik Kreinovich, and Klaus-Peter Adlassnig
Why um and u*log(u) Are the Most Effective Nonlinear Functions in Fuzzy Clustering: Theoretical Explanation of the Empirical Fact, Olga Kosheleva, Vladik Kreinovich, and Yuchi Kanzawa
Why Convex Combinations of Interval Endpoints: Related Explanations for Cases of Data Processing and Decision Making, Christian Servin, Olga Kosheleva, and Vladik Kreinovich
Why Interval-Valued (and Type-2) Fuzzy Methods Are Often More Effective, Christian Servin, Olga Kosheleva, and Vladik Kreinovich
From Machine Learning to Human Learning: What Can Pedagogy Learn from AI Successes, Victor L. Timchenko, Yury P. Kondratenko, Olga Kosheleva, and Vladik Kreinovich
How to Deal with High-Impact Low-Probability Events: Theoretical Explanation of the Empirically Successful Fuzzy-Like Technique, Juan Ulloa, Aaron Velasco, Olga Kosheleva, and Vladik Kreinovich
7 Plus Minus 2 Law Revisited: Alternative Geometric Explanation, Mayan Arithmetic, and Using 9- and 18-Based Numbers in Jewish Tradition, Julio C. Urenda, Olga Kosheleva, and Vladik Kreinovich
Egyptian Triangle and Geometry of Airplane Wings: A Simplified Explanation, Julio C. Urenda, Olga Kosheleva, and Vladik Kreinovich
Unfortunately, the Universal Predictor Cannot Be Made Constructive, Julio C. Urenda, Olga Kosheleva, and Vladik Kreinovich
Ultrathin-Layer Strain-Based Electronic Devices: From-First-Principles Derivation of the Corresponding Equation, Julio C. Urenda and Vladik Kreinovich
A Natural Extension of F-Transform to Triangular and Triangulated Domains Necessitates the Use of Triangular Membership Functions, Hana Zámečiková, Irina Perfilieva, Olga Kosheleva, and Vladik Kreinovich
Technical Reports from 2024
Data Fusion Is More Complex Than Data Processing: A Proof, Robert Alvarez, Salvador Ruiz, Martine Ceberio, and Vladik Kreinovich
Shapley Value under Interval Uncertainty and Partial Information, Kittawit Autchariyapanikul, Olga Kosheleva, and Vladik Kreinovich
Stochastic Dominance: Cases of Interval and P-Box Uncertainty, Kittawit Autchariyapanikul, Olga Kosheleva, and Vladik Kreinovich
Paradox of Causality and Paradoxes of Set Theory, Alondra Baquier, Bradley Beltran, Gabriel Miki-Silva, Olga Kosheleva, and Vladik Kreinovich
How to Make a Neural Network Learn from a Small Number of Examples -- and Learn Fast: An Idea, Chitta Baral and Vladik Kreinovich
How to Check Continuity Based on Approximate Measurement Results, Inese Bula and Vladik Kreinovich
Towards an Optimal Design: What Can We Recommend to Elon Musk?, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich, and Hung T. Nguyen
Number Representation With Varying Number of Bits, Anuradha Choudhury, Md Ahsanul Haque, Saeefa Rubaiyet Nowmi, Ahmed Ann Noor Ryen, Sabrina Saika, and Vladik Kreinovich
Why Linear and Sigmoid Last Layers Work Better in Classification, Lehel Dénes-Fazakas, Lásló Szilágyi, and Vladik Kreinovich
How to Make a Decision under Interval Uncertainty If We Do Not Know the Utility Function, Jeffrey Escamilla and Vladik Kreinovich
What If the Resulting Interval Is Too Wide: From a Heuristic Fuzzy-Technique Idea to a Mathematically Justified Approach, Marc Fina and Vladik Kreinovich
Training Neural Networks on Interval Data: Unexpected Results and Their Explanation, Edwin Tomy George, Vladik Kreinovich, Christoph Lauter, Martine Ceberio, and Luc Jaulin
Towards a More Subtle (and Hopefully More Adequate) Fuzzy "And"-Operation: Normalization-Invariant Multi-Input Aggregation Operators, Yusuf Güven and Vladik Kreinovich
For Discrete-Time Linear Dynamical Systems under Interval Uncertainty, Predicting Two Moments Ahead Is NP-Hard, Luc Jaulin, Olga Kosheleva, and Vladik Kreinovich
Every Feasibly Computable Reals-to-Reals Function Is Feasibly Uniformly Continuous, Olga Kosheleva and Vladik Kreinovich
For 2 x n Cases, Proportional Fitting Problem Reduces to a Single Equation, Olga Kosheleva and Vladik Kreinovich
From Normal Distribution to What? How to Best Describe Distributions with Known Skewness, Olga Kosheleva and Vladik Kreinovich
How to Make AI More Reliable, Olga Kosheleva and Vladik Kreinovich
How to Propagate Uncertainty via AI Algorithms, Olga Kosheleva and Vladik Kreinovich
If Subsequent Results Are Too Easy to Obtain, the Proof Most Probably Has Errors: Explanation of the Empirical Observation, Olga Kosheleva and Vladik Kreinovich
Is Energy Local? Counterintuitive Non-Locality of Energy in General Relativity Can Be Naturally Explained on the Newtonian Level, Olga Kosheleva and Vladik Kreinovich
What to Do If an Inflexible Tolerance Problem Has No Solutions: Probabilistic Justification of Piegat's Semi-Heuristic Idea, Olga Kosheleva and Vladik Kreinovich
Why Bernstein Polynomials: Yet Another Explanation, Olga Kosheleva and Vladik Kreinovich
Why Empirical Membership Functions Are Well-Approximated by Piecewise Quadratic Functions: Theoretical Explanation for Empirical Formulas of Novak's Fuzzy Natural Logic, Olga Kosheleva and Vladik Kreinovich
Why Fully Consistent Quantum Field Theories Require that the Space-Time Be at Least 10-Dimensional: A Commonsense Field-Based Explanation, Olga Kosheleva and Vladik Kreinovich
Fuzzy Ideas Explain Fechner Law and Help Detect Relation Between Objects in Video, Olga Kosheleva, Vladik Kreinovich, and Ahnaf Farhan
Logarithmic Number System Is Optimal for AI Computations: Theoretical Explanation of Empirical Success, Olga Kosheleva, Vladik Kreinovich, Christoph Lauter, and Kristalys Ruiz-Rohena
Two Is Enough, but Three (or More) Is Better: in AI and Beyond, Olga Kosheleva, Vladik Kreinovich, Victor L. Timchenko, and Yury P. Kondratenko
McFadden's Discrete Choice and Softmax under Interval (and Other) Uncertainty: Revisited, Bartlomiej Jacek Kubica, Olga Kosheleva, and Vladik Kreinovich
Is Alaska Negative-Tax Arrangement Fair? Almost: Mathematical Analysis, Chon Van Le and Vladik Kreinovich
There Is Still Plenty of Room at the Bottom: Feynman's Vision of Quantum Computing 65 Years Later, Alexis Lupo, Vladik Kreinovich, Victor L. Timchenko, and Yuriy P. Kondratenko
How to Fairly Allocate Safety Benefits of Self-Driving Cars, Fernando Munoz, Christian Servin, and Vladik Kreinovich
Why Kolmolgorov-Arnold Networks (KAN) Work So Well: A Qualitative Explanation, Hung T. Nguyen, Vladik Kreinovich, and Olga Kosheleva
Why Pavement Cracks Are Mostly Longitudinal, Sometimes Transversal, and Rarely of Other Directions: A Geometric Explanation, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, and Vladik Kreinovich
How Can We Explain Empirical Formulas for Shrinkage Cracking of Cement-Stabilized Pavement Layers, Edgar Daniel Rodriguez Velasquez and Vladik Kreinovich