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Technical Reports from 2024

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Why Linear and Sigmoid Last Layers Work Better in Classification, Lehel Dénes-Fazakas, Lásló Szilágyi, and Vladik Kreinovich

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Every Feasibly Computable Reals-to-Reals Function Is Feasibly Uniformly Continuous, Olga Kosheleva and Vladik Kreinovich

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From Normal Distribution to What? How to Best Describe Distributions with Known Skewness, Olga Kosheleva and Vladik Kreinovich

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Why Bernstein Polynomials: Yet Another Explanation, Olga Kosheleva and Vladik Kreinovich

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Fuzzy Ideas Explain Fechner Law and Help Detect Relation Between Objects in Video, Olga Kosheleva, Vladik Kreinovich, and Ahnaf Farhan

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McFadden's Discrete Choice and Softmax under Interval (and Other) Uncertainty: Revisited, Bartlomiej Jacek Kubica, Olga Kosheleva, and Vladik Kreinovich

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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

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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

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How Difficult Is It to Comprehend a Program That Has Significant Repetitions: Fuzzy-Related Explanations of Empirical Results, Christian Servin, Olga Kosheleva, and Vladik Kreinovich

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From Quantifying and Propagating Uncertainty to Quantifying and Propagating Both Uncertainty and Reliability: Practice-Motivated Approach to Measurement Planning and Data Processing, Niklas R. Winnewisser, Vladik Kreinovich, and Olga Kosheleva

Technical Reports from 2023

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How People Make Decisions Based on Prior Experience: Formulas of Instance-Based Learning Theory (ILBT) Follow from Scale Invariance, Palvi Aggarwal, Martine Ceberio, Olga Kosheleva, and Vladik Kreinovich

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How to Deal with Inconsistent Intervals: Utility-Based Approach Can Overcome the Limitations of the Purely Probability-Based Approach, Kittawit Autchariyapanitkul, Tomoe Entani, Olga Kosheleva, and Vladik Kreinovich

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How to Estimate Unknown Unknowns: From Cosmic Light to Election Polls, Talha Azfar, Vignesh Ponraj, Vladik Kreinovich, and Nguyen Hoang Phuong

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Why Sigmoid Transformation Helps Incorporate Logic Into Deep Learning: A Theoretical Explanation, Chitta Baral and Vladik Kreinovich

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Every ReLU-Based Neural Network Can Be Described by a System of Takagi-Sugeno Fuzzy Rules: A Theorem, Barnabas Bede, Olga Kosheleva, and Vladik Kreinovich

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Integrity First, Service Before Self, and Excellence: Core Values of US Air Force Naturally Follow from Decision Theory, Martine Ceberio, Olga Kosheleva, and Vladik Kreinovich

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Just-in-Accuracy: Mobile Approach to Uncertainty, Martine Ceberio, Christoph Q. Lauter, and Vladik Kreinovich

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How to Make Decision Under Interval Uncertainty: Description of All Reasonable Partial Orders on the Set of All Intervals, Tiago M. Costa, Olga Kosheleva, and Vladik Kreinovich

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Selecting the Most Adequate Fuzzy Operation for Explainable AI: Empirical Fact and Its Possible Theoretical Explanation, Orsolya Csiszar, Gábor Csiszar, Martine Ceberio, and Vladik Kreinovich

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Why Fuzzy Control Is Often More Robust (and Smoother): A Theoretical Explanation, Orsolya Csiszar, Gábor Csiszar, Olga Kosheleva, Martine Ceberio, and Vladik Kreinovich

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We Can Always Reduce a Non-Linear Dynamical System to Linear -- at Least Locally -- But Does It Help?, Orsolya Csiszar, Gábor Csiszar, Olga Kosheleva, Vladik Kreinovich, and Nguyen Hoang Phuong

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Which Activation Function Works Best for Training Artificial Pancreas: Empirical Fact and Its Theoretical Explanation, Lehel Dénes-Fazakas, Lásló Szilágyi, György Eigner, Olga Kosheleva, Martine Ceberio, and Vladik Kreinovich

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Why Bump Reward Function Works Well In Training Insulin Delivery Systems, Lehel Dénes-Fazakas, Lásló Szilágyi, Gyorgy Eigner, Olga Kosheleva, Vladik Kreinovich, and Nguyen Hoang Phuong

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Algebraic Product Is the Only "And-Like"-Operation for Which Normalized Intersection Is Associative: A Proof, Thierry Denœx and Vladik Kreinovich

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Conflict Situations Are Inevitable When There Are Many Participants: A Proof Based on the Analysis of Aumann-Shapley Value, Sofia Holguin and Vladik Kreinovich

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Fuzzy Mathematics under Non-Minimal "And"-Operations (t-Norms): Equivalence leads to Metric, Order Leads to Kinematic Metric, Topology Leads to Area or Volume, Purbita Jana, Olga Kosheleva, and Vladik Kreinovich

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Causality: Hypergraphs, Matter of Degree, Foundations of Cosmology, Cliff Joslyn, Andres Ortiz-Muñoz, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, and Vladik Kreinovich

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SUCCESS (Studying Underlying Characteristics of Computing and Engineering Student Success) Survey: Non-Cognitive and Affective Profiles in Engineering and Computing Students at UTEP (2018-2022), Sanga Kim, Christian Teran Lopez, Andres Segura, and Gabriel Miki

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How to Efficiently Propagate P-Box Uncertainty, Olga Kosheleva and Vladik Kreinovich

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If We Add Axiom of Choice to Constructive Analysis, We Get Classical Arithmetic: An Exercise in Reverse Constructive Mathematics, Olga Kosheleva and Vladik Kreinovich

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Industry-Academia Collaboration: Main Challenges and What Can We Do, Olga Kosheleva and Vladik Kreinovich

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Smooth Non-Additive Integrals and Measures and Their Potential Applications, Olga Kosheleva and Vladik Kreinovich

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What Was More Frequently Used -- "And" or "Or": Based on Analysis of European Languages, Olga Kosheleva and Vladik Kreinovich

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When Is a Single "And"-Condition Enough?, Olga Kosheleva and Vladik Kreinovich

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Wormholes, Superfast Computations, and Selivanov's Theorem, Olga Kosheleva and Vladik Kreinovich

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How to Select A Model If We Know Probabilities with Interval Uncertainty, Vladik Kreinovich

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From Type-2 Fuzzy to Type-2 Intervals and Type-2 Probabilities, Vladik Kreinovich, Olga Kosheleva, and Luc Longpré

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Which Random-Set Representation of a Fuzzy Set Is the Simplest?, Vladik Kreinovich, Olga Kosheleva, and Hung T. Nguyen

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Uncertainty Quantification for Results of AI-Based Data Processing: Towards More Feasible Algorithms, Christoph Q. Lauter, Martine Ceberio, Vladik Kreinovich, and Olga Kosheleva

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Approximate Stochastic Dominance Revisited, Chon Van Le, Olga Kosheleva, and Vladik Kreinovich

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Why Softmax? Because It Is the Only Consistent Approach to Probability-Based Classification, Anatole Lokshin and Vladik Kreinovich

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Complex Numbers Explain Why in Chinese Tradition, 4 Is Bad But 8 Is Good, Luc Longpre, Olga Kosheleva, and Vladik Kreinovich

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Designing an Optimal Medicine Cocktail Is NP-Hard, Luc Longpre and Vladik Kreinovich

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Towards Decision Making Under Interval Uncertainty, Juan A. Lopez and Vladik Kreinovich

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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

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Why Fractional Fuzzy, Mehran Mazandarani, Olga Kosheleva, and Vladik Kreinovich

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How to Make Machine Learning Financial Recommendations More Fair: Theoretical Explanation, Tho M. Nguyen, Saeid Tizpaz-Niari, and Vladik Kreinovich

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Linear Regression under Partial Information, Tho M. Nguyen, Saeid Tizpaz-Niari, and Vladik Kreinovich

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Local-Global Support for Earth Sciences: Economic Analysis, Uyen Hoang Pham, Aaron Velasco, and Vladik Kreinovich

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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