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When Is A Single "And"-Condition Enough?, Olga Kosheleva, Vladik Kreinovich
When Is A Single "And"-Condition Enough?, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, there are several possible decisions. Any general recommendation means specifying, for each possible decision, conditions under which this decision is recommended. In some cases, a single "and"-condition is sufficient: e.g., a condition under which a patient is recommended to take aspirin is that "the patient has a fever and the patient does not have stomach trouble". In other cases, conditions are more complicated. A natural question is: when is a single "and"-condition enough? In this paper, we provide an answer to this question.
Which Fuzzy Implications Operations Are Polynomial? A Theorem Proves That This Can Be Determined By A Finite Set Of Inequalities, Sebastia Massanet, Olga Kosheleva, 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, Vladik Kreinovich
Departmental Technical Reports (CS)
To adequately represent human reasoning in a computer-based systems, it is desirable to select fuzzy operations that are as close to human reasoning as possible. In general, every real-valued function can be approximated, with any desired accuracy, by polynomials; it is therefore reasonable to use polynomial fuzzy operations as the appropriate approximations. We thus need to select, among all polynomial operations that satisfy corresponding properties -- like associativity -- the ones that best fit the empirical data. The challenge here is that properties like associativity mean satisfying infinitely many constraints (corresponding to infinitely many possible triples of values), while most …
Logical Inference Inevitably Appears: Fuzzy-Based Explanation, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich, Orsolya Csiszar
Logical Inference Inevitably Appears: Fuzzy-Based Explanation, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich, Orsolya Csiszar
Departmental Technical Reports (CS)
Many thousands years ago, our primitive ancestors did not have the ability to reason logically and to perform logical inference. This ability appeared later. A natural question is: was this appearance inevitable -- or was this a lucky incident that could have been missed? In this paper, we use fuzzy techniques to provide a possible answer to this question. Our answer is: yes, the appearance of logical inference in inevitable.
Is Fully Explainable Ai Even Possible: Fuzzy-Based Analysis, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich
Is Fully Explainable Ai Even Possible: Fuzzy-Based Analysis, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the main limitations of many current AI-based decision-making systems is that they do not provide any understandable explanations of how they came up with the produced decision. Taking into account that these systems are not perfect, that their decisions are sometimes far from good, the absence of an explanation makes it difficult to separate good decisions from suspicious ones. Because of this, many researchers are working on making AI explainable. In some applications areas -- e.g., in chess -- practitioners get an impression that there is a limit to understandability, that some decisions remain inhuman -- not explainable. …
Selecting The Most Adequate Fuzzy Operation For Explainable Ai: Empirical Fact And Its Possible Theoretical Explanation, Orsolya Csiszar, Gábor Csiszar, Martine Ceberio, Vladik Kreinovich
Selecting The Most Adequate Fuzzy Operation For Explainable Ai: Empirical Fact And Its Possible Theoretical Explanation, Orsolya Csiszar, Gábor Csiszar, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
A reasonable way to make AI results explainable is to approximate the corresponding deep-learning-generated function by a simple expression formed by fuzzy operations. Experiments on real data show that out of all easy-to-compute fuzzy operations, the best approximation is attained if we use an operation a + b − 0.5 ( limited to the interval [0,1]$. In this paper, we provide a possible theoretical explanation for this empirical result.
Interval-Valued And Set-Valued Extensions Of Discrete Fuzzy Logics, Belnap Logic, And Color Optical Computing, Victor L. Timchenko, Yury P. Kondratenko, Vladik Kreinovich
Interval-Valued And Set-Valued Extensions Of Discrete Fuzzy Logics, Belnap Logic, And Color Optical Computing, Victor L. Timchenko, Yury P. Kondratenko, Vladik Kreinovich
Departmental Technical Reports (CS)
It has been recently shown that in some applications, e.g., in ship navigation near a harbor, it is convenient to use combinations of basic colors -- red, green, and blue -- to represent different fuzzy degrees. In this paper, we provide a natural explanation for the efficiency of this empirical fact: namely, we show that it is reasonable to consider discrete fuzzy logics, it is reasonable to consider their interval-valued and set-valued extensions, and that a set-valued extension of the 3-values logic is naturally equivalent to the use of color combinations.