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Articles 421 - 450 of 914
Full-Text Articles in Computer Sciences
How To Explain The Anchoring Formula In Behavioral Economics, Laxman Bokati, Vladik Kreinovich, Chon Van Le
How To Explain The Anchoring Formula In Behavioral Economics, Laxman Bokati, Vladik Kreinovich, Chon Van Le
Departmental Technical Reports (CS)
According to the traditional economics, the price that a person is willing to pay for an item should be uniquely determined by the value that this person will get from this item, it should not depend, e.g., on the asking price proposed by the seller. In reality, the price that a person is willing to pay does depend on the asking price; this is known as the anchoring effect. In this paper, we provide a natural justification for the empirical formula that describes this effect.
A "Fuzzy" Like Button Can Decrease Echo Chamber Effect, Olga Kosheleva, Vladik Kreinovich
A "Fuzzy" Like Button Can Decrease Echo Chamber Effect, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the big problems of the US political life is the echo chamber effect -- in spite of the abundance of materials on the web, many people only read materials confirming their own opinions. The resulting polarization often deadlocks the political situation and prevents politicians from reaching compromises needed to make needed changes. In this paper, we show, on a simplified model, that the echo chamber effect can be decreased if we simply replace the currently prevalent binary (yes-no) Like button on webpages with a more gradual ("fuzzy") one -- a button that will capture the relative degree of …
New (Simplified) Derivation Of Nash's Bargaining Solution, Nguyen Hoang Phuong, Laxman Bokati, Vladik Kreinovich
New (Simplified) Derivation Of Nash's Bargaining Solution, Nguyen Hoang Phuong, Laxman Bokati, Vladik Kreinovich
Departmental Technical Reports (CS)
According to the Nobelist John Nash, if a group of people wants to selects one of the alternatives in which all of them get a better deal than in a status quo situations, then they should select the alternative that maximizes the product of their utilities. In this paper, we provide a new (simplified) derivation of this result, a derivation which is not only simpler -- it also does not require that the preference relation between different alternatives be linear.
Towards Making Fuzzy Techniques More Adequate For Combining Knowledge Of Several Experts, Nguyen Hoang Phuong, Vladik Kreinovich
Towards Making Fuzzy Techniques More Adequate For Combining Knowledge Of Several Experts, Nguyen Hoang Phuong, Vladik Kreinovich
Departmental Technical Reports (CS)
In medical and other applications, expert often use rules with several conditions, each of which involve a quantity within the domain of expertise of a different expert. In such situations, to estimate the degree of confidence that all these conditions are satisfied, we need to combine opinions of several experts -- i.e., in fuzzy techniques, combine membership functions corresponding to different experts. In each area of expertise, different experts may have somewhat different membership functions describing the same natural-language ("fuzzy") term like small. It is desirable to present the user with all possible conclusions corresponding to all these membership functions. …
Decision Making Under Interval Uncertainty: Towards (Somewhat) More Convincing Justifications For Hurwicz Optimism-Pessimism Approach, Warattaya Chinnakum, Laura Berrout Ramos, Olugbenga Iyiola, Vladik Kreinovich
Decision Making Under Interval Uncertainty: Towards (Somewhat) More Convincing Justifications For Hurwicz Optimism-Pessimism Approach, Warattaya Chinnakum, Laura Berrout Ramos, Olugbenga Iyiola, Vladik Kreinovich
Departmental Technical Reports (CS)
In the ideal world, we know the exact consequences of each action. In this case, it is relatively straightforward to compare different possible actions and, as a result of this comparison, to select the best action. In real life, we only know the consequences with some uncertainty. A typical example is interval uncertainty, when we only know the lower and upper bounds on the expected gain. How can we compare such interval-valued alternatives? A usual way to compare such alternatives is to use the optimism-pessimism criterion developed by Nobelist Leo Hurwicz. In this approach, we maximize a weighted combination of …
Theoretical Explanation Of Recent Empirically Successful Code Quality Metrics, Vladik Kreinovich, Omar A. Masmali, Nguyen Hoang Phuong, Omar Badreddin
Theoretical Explanation Of Recent Empirically Successful Code Quality Metrics, Vladik Kreinovich, Omar A. Masmali, Nguyen Hoang Phuong, Omar Badreddin
Departmental Technical Reports (CS)
Millions of lines of code are written every day, and it is not practically possible to perfectly thoroughly test all this code on all possible situations. In practice, we need to be able to separate codes which are more probable to contain bugs -- and which thus need to be tested more thoroughly -- from codes which are less probable to contain flaws. Several numerical characteristics -- known as code quality metrics -- have been proposed for this separation. Recently, a new efficient class of code quality metrics have been proposed, based on the idea to assign consequent integers to …
Quantum (And More General) Models Of Research Collaboration, Oscar Galindo, Miroslav Svitek, Vladik Kreinovich
Quantum (And More General) Models Of Research Collaboration, Oscar Galindo, Miroslav Svitek, Vladik Kreinovich
Departmental Technical Reports (CS)
In the last decades, several papers have shown that quantum techniques can be successful in describing not only events in the micro-scale physical world -- for which they were originally invented -- but also in describing social phenomena, e.g., different economic processes. In our previous paper, we provide an explanation for this somewhat surprising successes. In this paper, we extend this explanation and show that quantum (and more general) techniques can also be used to model research collaboration.
Which Are The Correct Membership Functions? Correct "And"- And "Or"- Operations? Correct Defuzzification Procedure?, Olga Kosheleva, Vladik Kreinovich, Shahnaz Shahbazova
Which Are The Correct Membership Functions? Correct "And"- And "Or"- Operations? Correct Defuzzification Procedure?, Olga Kosheleva, Vladik Kreinovich, Shahnaz Shahbazova
Departmental Technical Reports (CS)
Even in the 1990s, when many successful examples of fuzzy control appeared all the time, many users were somewhat reluctant to use fuzzy control. One of the main reasons for this reluctance was the perceived subjective character of fuzzy techniques -- for the same natural-language rules, different experts may select somewhat different membership functions and thus get somewhat different control/recommendation strategies. In this paper, we promote the idea that this selection does not have to be subjective. We can always select the "correct" membership functions, i.e., functions for which, on previously tested case, we got the best possible control. Similarly, …
Scale-Invariance And Fuzzy Techniques Explain The Empirical Success Of Inverse Distance Weighting And Of Dual Inverse Distance Weighting In Geosciences, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich
Scale-Invariance And Fuzzy Techniques Explain The Empirical Success Of Inverse Distance Weighting And Of Dual Inverse Distance Weighting In Geosciences, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich
Departmental Technical Reports (CS)
Once we measure the values of a physical quantity at certain spatial locations, we need to interpolate these values to estimate the value of this quantity at other locations x. In geosciences, one of the most widely used interpolation techniques is inverse distance weighting, when we combine the available measurement results with the weights inverse proportional to some power of the distance from x to the measurement location. This empirical formula works well when measurement locations are uniformly distributed, but it leads to biased estimates otherwise. To decrease this bias, researchers recently proposed a more complex dual inverse distance weighting …
How To Combine (Dis)Utilities Of Different Aspects Into A Single (Dis)Utility Value, And How This Is Related To Geometric Images Of Happiness, Laxman Bokati, Nguyen Hoang Phuong, Olga Kosheleva, Vladik Kreinovich
How To Combine (Dis)Utilities Of Different Aspects Into A Single (Dis)Utility Value, And How This Is Related To Geometric Images Of Happiness, Laxman Bokati, Nguyen Hoang Phuong, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, a user needs our help in selecting the best out of a large number of alternatives. To be able to help, we need to understand the user's preferences. In decision theory, preferences are described by numerical values known as utilities. It is often not feasible to ask to user to provide utilities of all possible alternatives, so we must be able to estimate these utilities based on utilities of different aspects of these alternatives. In this paper, we provide a general formula for combining utilities of aspects into a single utility value. The resulting formula …
How To Describe Conditions Like 2-Out-Of-5 In Fuzzy Logic: A Neural Approach, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
How To Describe Conditions Like 2-Out-Of-5 In Fuzzy Logic: A Neural Approach, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
In many medical applications, we diagnose a disease and/or apply a certain remedy if, e.g., two out of five conditions are satisfied. In the fuzzy case, i.e., when we only have certain degrees of confidence that each of n statement is satisfied, how do we estimate the degree of confidence that k out of n conditions are satisfied? In principle, we can get this estimate if we use the usual methodology of applying fuzzy techniques: we represent the desired statement in terms of "and" and "or", and use fuzzy analogues of these logical operations. The problem with this approach is …
How Quantum Cryptography And Quantum Computing Can Make Cyber-Physical Systems More Secure, Deepak Tosh, Oscar Galindo, Vladik Kreinovich, Olga Kosheleva
How Quantum Cryptography And Quantum Computing Can Make Cyber-Physical Systems More Secure, Deepak Tosh, Oscar Galindo, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
For cyber-physical systems, cyber-security is vitally important. There are many cyber-security tools that make communications secure -- e.g., communications between sensors and the computers processing the sensor's data. Most of these tools, however, are based on RSA encryption, and it is known that with quantum computing, this encryption can be broken. It is therefore desirable to use an unbreakable alternative -- quantum cryptography -- for such communications. In this paper, we discuss possible consequences of this option. We also explain how quantum computers can help even more: namely, they can be used to optimize the system's design -- in particular, …
Why Squashing Functions In Multi-Layer Neural Networks, Julio Urenda, Orsoly Csiszár, Gábor Csiszár, József Dombi, Olga Kosheleva, Vladik Kreinovich, György Eigner
Why Squashing Functions In Multi-Layer Neural Networks, Julio Urenda, Orsoly Csiszár, Gábor Csiszár, József Dombi, Olga Kosheleva, Vladik Kreinovich, György Eigner
Departmental Technical Reports (CS)
Most multi-layer neural networks used in deep learning utilize rectified linear neurons. In our previous papers, we showed that if we want to use the exact same activation function for all the neurons, then the rectified linear function is indeed a reasonable choice. However, preliminary analysis shows that for some applications, it is more advantageous to use different activation functions for different neurons -- i.e., select a family of activation functions instead, and select the parameters of activation functions of different neurons during training. Specifically, this was shown for a special family of squashing functions that contain rectified linear neurons …
A Mystery Of Human Biological Development -- Can It Be Used To Speed Up Computations?, Olga Kosheleva, Vladik Kreinovich
A Mystery Of Human Biological Development -- Can It Be Used To Speed Up Computations?, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
For many practical problems, the only known algorithms for solving them require non-feasible exponential time. To make computations feasible, we need an exponential speedup. A reasonable way to look for such possible speedup is to search for real-life phenomena where such a speedup can be observed. A natural place to look for such a speedup is to analyze the biological activities of human beings -- since we, after all, solve many complex problems that even modern super-fast computers have trouble solving. Up to now, this search was not successful -- e.g., there are people who compute much faster than others, …
How To Gauge The Quality Of A Testing Method When Ground Truth Is Known With Uncertainty, Nicholas Gray, Scott Ferson, Vladik Kreinovich
How To Gauge The Quality Of A Testing Method When Ground Truth Is Known With Uncertainty, Nicholas Gray, Scott Ferson, Vladik Kreinovich
Departmental Technical Reports (CS)
The quality of a testing method is usually measured by using sensitivity, specificity, and/or precision. To compute each of these three characteristics, we need to know the ground truth, i.e., we need to know which objects actually have the tested property. In many applications (e.g., in medical diagnostics), the information about the objects comes from experts, and this information comes with uncertainty. In this paper, we show how to take this uncertainty into account when gauging the quality of testing methods.
Need For Simplicity And Everything Is A Matter Of Degree: How Zadeh's Philosophy Is Related To Kolmogorov Complexity, Quantum Physics, And Deep Learning, Vladik Kreinovich, Olga Kosheleva, Andres Ortiz-Muñoz
Need For Simplicity And Everything Is A Matter Of Degree: How Zadeh's Philosophy Is Related To Kolmogorov Complexity, Quantum Physics, And Deep Learning, Vladik Kreinovich, Olga Kosheleva, Andres Ortiz-Muñoz
Departmental Technical Reports (CS)
Many people remember Lofti Zadeh's mantra -- that everything is a matter of degree. This was one of the main principles behind fuzzy logic. What is somewhat less remembered is that Zadeh also used another important principle -- that there is a need for simplicity. In this paper, we show that together, these two principles can generate the main ideas behind such various subjects as Kolmogorov complexity, quantum physics, and deep learning. We also show that these principles can help provide a better understanding of an important notion of space-time causality.
Why Spiking Neural Networks Are Efficient: A Theorem, Michael Beer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Why Spiking Neural Networks Are Efficient: A Theorem, Michael Beer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Current artificial neural networks are very successful in many machine learning applications, but in some cases they still lag behind human abilities. To improve their performance, a natural idea is to simulate features of biological neurons which are not yet implemented in machine learning. One of such features is the fact that in biological neural networks, signals are represented by a train of spikes. Researchers have tried adding this spikiness to machine learning and indeed got very good results, especially when processing time series (and, more generally, spatio-temporal data). In this paper, we provide a theoretical explanation for this empirical …
Joule's 19th Century Energy Conservation Meta-Law And The 20th Century Physics (Quantum Mechanics And General Relativity): 21st Century Analysis, Vladik Kreinovich, Olga Kosheleva
Joule's 19th Century Energy Conservation Meta-Law And The 20th Century Physics (Quantum Mechanics And General Relativity): 21st Century Analysis, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
Joule's Energy Conservation Law was the first "meta-law": a general principle that all physical equations must satisfy. It has led to many important and useful physical discoveries. However, a recent analysis seems to indicate that this meta-law is inconsistent with other principles -- such as the existence of free will. We show that this conclusion about inconsistency is based on a seemingly reasonable -- but simplified -- analysis of the situation. We also show that a more detailed mathematical and physical analysis of the situation reveals that not only Joule's principle remains true -- it is actually strengthened: it is …
Why Gamma Distribution Of Seismic Inter-Event Times: A Theoretical Explanation, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich
Why Gamma Distribution Of Seismic Inter-Event Times: A Theoretical Explanation, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that the distribution of seismic inter-event times is well described by the Gamma distribution. Recently, this fact has been used to successfully predict major seismic events. In this paper, we explain that the Gamma distribution of seismic inter-event times can be naturally derived from the first principles.
Finitely Generated Sets Of Fuzzy Values: If "And" Is Exact, Then "Or" Is Almost Always Approximate, And Vice Versa -- A Theorem, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Finitely Generated Sets Of Fuzzy Values: If "And" Is Exact, Then "Or" Is Almost Always Approximate, And Vice Versa -- A Theorem, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the traditional fuzzy logic, experts' degrees of confidence are described by numbers from the interval [0,1]. Clearly, not all the numbers from this interval are needed: in the whole history of the Universe, there will be only countably many statements and thus, only countably many possible degree, while the interval [0,1] is uncountable. It is therefore interesting to analyze what is the set S of actually used values. The answer depends on the choice of "and"-operations (t-norms) and "or"-operations (t-conorms). For the simplest pair of min and max, any finite set will do -- as long as it is …
Fuzzy Logic Explains The Usual Choice Of Logical Operations In 2-Valued Logic, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Fuzzy Logic Explains The Usual Choice Of Logical Operations In 2-Valued Logic, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the usual 2-valued logic, from the purely mathematical viewpoint, there are many possible binary operations. However, in commonsense reasoning, we only use a few of them: why? In this paper, we show that fuzzy logic can explain the usual choice of logical operations in 2-valued logic.
Which Distributions (Or Families Of Distributions) Best Represent Interval Uncertainty: Case Of Permutation-Invariant Criteria, Michael Beer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Which Distributions (Or Families Of Distributions) Best Represent Interval Uncertainty: Case Of Permutation-Invariant Criteria, Michael Beer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we only know the interval containing the quantity of interest, we have no information about the probability of different values within this interval. In contrast to the cases when we know the distributions and can thus use Monte-Carlo simulations, processing such interval uncertainty is difficult -- crudely speaking, because we need to try all possible distributions on this interval. Sometimes, the problem can be simplified: namely, it is possible to select a single distribution (or a small family of distributions) whose analysis provides a good understanding of the situation. The most known case is when we …
Why A Classification Based On Linear Approximation To Dynamical Systems Often Works Well In Nonlinear Cases, Julio Urenda, Vladik Kreinovich
Why A Classification Based On Linear Approximation To Dynamical Systems Often Works Well In Nonlinear Cases, Julio Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
It can be proven that linear dynamical systems exhibit either stable behavior, or unstable behavior, or oscillatory behavior, or transitional behavior. Interesting, the same classification often applies to nonlinear dynamical systems as well. In this paper, we provide a possible explanation for this phenomenon, i.e., we explain why a classification based on linear approximation to dynamical systems often works well in nonlinear cases.
Smaller Standard Deviation For Initial Weights Improves Performance Of Classifying Neural Networks: A Theoretical Explanation Of Unexpected Simulation Results, Diego Aguirre, Philip Hassoun, Rafael Lopez, Crystal Serrano, Marcoantonio R. Soto, Andrea Torres, Vladik Kreinovich
Smaller Standard Deviation For Initial Weights Improves Performance Of Classifying Neural Networks: A Theoretical Explanation Of Unexpected Simulation Results, Diego Aguirre, Philip Hassoun, Rafael Lopez, Crystal Serrano, Marcoantonio R. Soto, Andrea Torres, Vladik Kreinovich
Departmental Technical Reports (CS)
Numerical experiments show that for classifying neural networks, it is beneficial to select a smaller deviation for initial weights that what is usually recommended. In this paper, we provide a theoretical explanation for these unexpected simulation results.
Status Quo Bias Actually Helps Decision Makers To Take Nonlinearity Into Account: An Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich
Status Quo Bias Actually Helps Decision Makers To Take Nonlinearity Into Account: An Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the main motivations for designing computer models of complex systems is to come up with recommendations on how to best control these systems. Many complex real-life systems are so complicated that it is not computationally possible to use realistic nonlinear models to find the corresponding optimal control. Instead, researchers make recommendations based on simplified -- e.g., linearized -- models. The recommendations based on these simplified models are often not realistic but, interestingly, they can be made more realistic if we "tone them down" -- i.e., consider predictions and recommendations which are close to the current status quo state. …
Confirmation Bias In Systems Engineering: A Pedagogical Example, Griselda Acosta, Eric Smith, Vladik Kreinovich
Confirmation Bias In Systems Engineering: A Pedagogical Example, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the biases potentially affecting systems engineers is the confirmation bias, when instead of selecting the best hypothesis based on the data, people stick to the previously-selected hypothesis until it is disproved. In this paper, on a simple example, we show how important is to take care of this bias: namely, that because of this bias, we need twice as many experiments to switch to a better hypothesis.
A Natural Explanation For The Minimum Entropy Production Principle, Griselda Acosta, Eric Smith, Vladik Kreinovich
A Natural Explanation For The Minimum Entropy Production Principle, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
It is well known that, according to the second law of thermodynamics, the entropy of a closed system increases (or at least stays the same). In many situations, this increase is the smallest possible. The corresponding minimum entropy production principle was first formulated and explained by a future Nobelist Ilya Prigogine. Since then, many possible explanations of this principle appeared, but all of them are very technical, based on complex analysis of differential equations describing the system's dynamics. Since this phenomenon is ubiquitous for many systems, it is desirable to look for a general system-based explanation, explanation that would not …
Why Matrix Factorization Works Well In Recommender Systems: A Systems-Based Explanation, Griselda Acosta, Manuel Hernandez, Natalia Villanueva-Rosales, Eric Smith, Vladik Kreinovich
Why Matrix Factorization Works Well In Recommender Systems: A Systems-Based Explanation, Griselda Acosta, Manuel Hernandez, Natalia Villanueva-Rosales, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
Many computer-based services use recommender systems that predict our preferences based on our degree of satisfaction with the past selections. One of the most efficient techniques making recommender systems successful is matrix factorization. While this technique works well, until now, there was no general explanation of why it works. In this paper, we provide such an explanation.
In Alsina Et Al. Derivation Of Min-Max Fuzzy Logic From Distributivity, All Conditions Are Necessary: A Proof, Vladik Kreinovich, Ildar Batyrshin, Nailya Kubysheva
In Alsina Et Al. Derivation Of Min-Max Fuzzy Logic From Distributivity, All Conditions Are Necessary: A Proof, Vladik Kreinovich, Ildar Batyrshin, Nailya Kubysheva
Departmental Technical Reports (CS)
In their 1983 paper, C. Alsina, E. Trillas, and L. Valverde proved that distributivity, monotonicity, and boundary conditions imply that the "and"-operation is min and the "or"-operation is max. In this paper, we show that all these conditions are necessary for Alsina et al. result to be true.
Beyond P-Boxes And Interval-Valued Moments: Natural Next Approximations To General Imprecise Probabilities, Olga Kosheleva, Vladik Kreinovich
Beyond P-Boxes And Interval-Valued Moments: Natural Next Approximations To General Imprecise Probabilities, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
To make an adequate decision, we need to know the probabilities of different consequences of different actions. In practice, we only have partial information about these probabilities -- this situation is known as imprecise probabilities. A general description of all possible imprecise probabilities requires using infinitely many parameters. In practice, the two most widely used few-parametric approximate descriptions are p-boxes (bounds on the values of the cumulative distribution function) and interval-valued moments (i.e., bounds on moments). In some situations, these approximations are not sufficiently accurate. So, we need more accurate more-parametric approximations. In this paper, we explain what are the …