Technical Reports from 2014
From Interval-Valued Probabilities to Interval-Valued Possibilities: Case Studies of Interval Computation under Constraints, Luis C. Gutierrez, Martine Ceberio, Vladik Kreinovich, Rebekah L. Gruver, Mariana Peña, Mathew J. Rister, Abraham Saldaña, John Vasquez, Janelle Ybarra, and Salem Benferhat
A Simple Probabilistic Explanation of Term Frequency-Inverse Document Frequency (tf-idf) Heuristic (and Variations Motivated by This Explanation), Lukas Havrlant and Vladik Kreinovich
F-Transform Enhancement of the Sampling Theorem and Reconstruction of Noisy Signals, Michal Holčapek, Irina Perfilieva, and Vladik Kreinovich
How to Understand Connections Based on Big Data: From Cliques to Flexible Granules, Ali Jalal-Kamali, M. Shahriar Hossain, and Vladik Kreinovich
A Feasible Algorithm for Checking n-Scissors Congruence of Polyhedra in Rd, Olga Kosheleva and Vladik Kreinovich
Decision Making under Interval Uncertainty: What Can and What Cannot Be Computed in Linear Time and in Real Time, Olga Kosheleva and Vladik Kreinovich
Deep Mathematical Results Are The Ones That Connect Seemingly Unrelated Areas: Towards A Formal Proof Of Gian-Carlo Rota's Thesis, Olga Kosheleva and Vladik Kreinovich
For Each Mathematical Statement, Only Finitely Many of Its Generalizations Are Useful: A Formal Proof of E. Bishop's Idea, Olga Kosheleva and Vladik Kreinovich
How to Compare Different Range Estimations: A Symmetry-Based Approach, Olga Kosheleva and Vladik Kreinovich
Kekule's Benzene Structure: A Case Study of Teaching Usefulness of Symmetry, Olga Kosheleva and Vladik Kreinovich
Observable Causality Implies Lorentz Group: Alexandrov-Zeeman-Type Theorem for Space-Time Regions, Olga Kosheleva and Vladik Kreinovich
Simpler-to-Describe Cases are Often More Difficult to Prove: A Possible Explanation, Olga Kosheleva and Vladik Kreinovich
Towards a Formal Description of Understandability (Causality, Pre-Requisites): From Prosorov's Phonocentric Topology to More General Interior (Closure) Structures, Olga Kosheleva and Vladik Kreinovich
Zipf's Law and 7 Plus Minus 2 Principle Lead to a Possible Explanation of Daniel's Law, Olga Kosheleva and Vladik Kreinovich
Fitts's Law: Towards a Geometric Explanation, Olga Kosheleva, Vladik Kreinovich, and Octavio Lerma
Formalizing the Informal, Precisiating the Imprecise: How Fuzzy Logic Can Help Mathematicians and Physicists by Formalizing Their Intuitive Ideas, Olga Kosheleva, Renata Reiser, and Vladik Kreinovich
If Many Physicists Are Right and No Physical Theory Is Perfect, Then by Using Physical Observations, We Can Feasibly Solve Almost All Instances of Each NP-Complete Problem, Olga Kosheleva, Michael Zakharevich, and Vladik Kreinovich
Asymptotically Optimal Algorithm for Checking Whether a Given Vector Is a Solution to a Given Interval-Quantifier Linear System, Vladik Kreinovich
Constructive Mathematics in St. Petersburg, Russia: A (Somewhat Subjective) View from Within, Vladik Kreinovich
Dealing with Uncertainties in Computing: from Probabilistic and Interval Uncertainty to Combination of Different Types of Uncertainty, Vladik Kreinovich
Interval computations and interval-related statistical techniques: estimating uncertainty of the results of data processing and indirect measurements, Vladik Kreinovich
In Category Of Sets And Relations, It Is Possible To Describe Functions In Purely Category Terms, Vladik Kreinovich, Martine Ceberio, and Quentin Brefort
Among Several Successful Algorithms, Simpler Ones Usually Work Better: A Possible Explanation of an Empirical Observation, Vladik Kreinovich and Olga Kosheleva
Is the World Itself Fuzzy? Physical Arguments for -- and Unexpected Computational Consequences of -- Zadeh's Vision, Vladik Kreinovich and Olga Kosheleva
Logic of Scientific Discovery: How Physical Induction Affects What Is Computable, Vladik Kreinovich and Olga Kosheleva
50 Years of Fuzzy: from Discrete to Continuous to -- Where?, Vladik Kreinovich, Hung T. Nguyen, Olga Kosheleva, and Rujira Ouncharoen
From Mean and Median Income to the Most Adequate Way of Taking Inequality Into Account, Vladik Kreinovich, Hung T. Nguyen, and Rujira Ouncharoen
How to Estimate Forecasting Quality: A System-Motivated Derivation of Symmetric Mean Absolute Percentage Error (SMAPE) and Other Similar Characteristics, Vladik Kreinovich, Hung T. Nguyen, and Rujira Ouncharoen
Log-Periodic Power Law as a Predictor of Catastrophic Events: A New Mathematical Justification, Vladik Kreinovich, Hung T. Nguyen, and Songsak Sriboonchitta
Need for Data Processing Naturally Leads to Fuzzy Logic (and Neural Networks): Fuzzy Beyond Experts and Beyond Probabilities, Vladik Kreinovich, Hung T. Nguyen, and Songsak Sriboonchitta
What If We Only Have Approximate Stochastic Dominance?, Vladik Kreinovich, Hung T. Nguyen, and Songsak Sriboonchitta
A Simple Geometric Model Provides a Possible Quantitative Explanation of the Advantages of Immediate Feedback in Student Learning, Octavio Lerma, Olga Kosheleva, and Vladik Kreinovich
Interleaving Enhances Learning: A Possible Geometric Explanation, Octavio Lerma, Olga Kosheleva, and Vladik Kreinovich
Why Injecting Fine Dust into a Tornado Is More Promising Than Injecting Coarse Dust: A Geometric Explanation, Octavio Lerma, Olga Kosheleva, and Vladik Kreinovich
Increased Climate Variability Is More Visible Than Global Warming: A General System-Theory Explanation, Octavio Lerma, Craig Tweedie, and Vladik Kreinovich
Every SUE Function is a Ratio of Two Multi-Linear Functions, Joe Lorkowski, Olga Kosheleva, and Vladik Kreinovich
How to Modify Grade Point Average (GPA) to Make It More Adequate, Joe Lorkowski, Olga Kosheleva, and Vladik Kreinovich
When Can We Reduce Multi-Variable Range Estimation Problem to Two Fewer-Variable Problems?, Joe Lorkowski, Olga Kosheleva, Luc Longpre, and Vladik Kreinovich
Fuzzy Logic Ideas Can Help in Explaining Kahneman and Tversky's Empirical Decision Weights, Joe Lorkowski and Vladik Kreinovich
Granularity Helps Explain Seemingly Irrational Features of Human Decision Making, Joe Lorkowski and Vladik Kreinovich
How Much For an Interval? a Set? a Twin Set? a p-Box? A Kaucher Interval? Towards an Economics-Motivated Approach to Decision Making Under Uncertainty, Joe Lorkowski and Vladik Kreinovich
How to Gauge Unknown Unknowns: A Possible Theoretical Explanation of the Usual Safety Factor of 2, Joe Lorkowski and Vladik Kreinovich
Interval and Symmetry Approaches to Uncertainty -- Pioneered by Wiener -- Helps Explain Many Seemingly Irrational Human Behaviors: A Case Study, Joe Lorkowski and Vladik Kreinovich
Likert-Type Fuzzy Uncertainty From A Traditional Decision Making Viewpoint: How Symmetry Helps Explain Human Decision Making (Including Seemingly Irrational Behavior), Joe Lorkowski and Vladik Kreinovich
Towards Decision Making under Interval, Set-Valued, Fuzzy, and Z-Number Uncertainty: A Fair Price Approach, Joe Lorkowski, Vladik Kreinovich, and Rafik Aliev
How to Fully Represent Expert Information about Imprecise Properties in a Computer System -- Random Sets, Fuzzy Sets, and Beyond: An Overview, Hung T. Nguyen and Vladik Kreinovich
Using Second-Order Probabilities to Make Maximum Entropy Approach to Copulas More Reasonable, Hung T. Nguyen, Vladik Kreinovich, and Berlin Wu
r-Bounded Fuzzy Measures are Equivalent to epsilon-Possibility Measures, Karen A. Richart-Ruiz, Olga Kosheleva, and Vladik Kreinovich
How to Assign Weights to Different Factors in Vulnerability Analysis: Towards a Justification of a Heuristic Technique, Beverly Rivera, Irbis Gallegos, and Vladik Kreinovich
From Numerical Probabilities to Linguistic Probabilities: A Theoretical Justification of Empirical Granules Used in Risk Management, Beverly Rivera, Francisco Zapata, and Vladik Kreinovich