Engineering Commons^™

Estimating Risk Under Interval Uncertainty: Sequential And Parallel Algorithms, Vladik Kreinovich, Hung T. Nguyen, Songsak Sriboonchitta

Departmental Technical Reports (CS)

In traditional econometrics, the quality of an individual investment -- and of the investment portfolio -- is characterized by its expected return and its risk (variance). For an individual investment or portfolio, we can estimate the future expected return and a future risk by tracing the returns x₁, ..., x_n of this investment (and/or similar investments) over the past years, and computing the statistical characteristics based on these returns. The return (per unit investment) is defined as the selling of the corresponding financial instrument at the ends of, e.g., a one-year period, divided by the buying price …

Intelligence Techniques Are Needed To Further Enhance The Advantage Of Groups With Diversity In Problem Solving, Oscar Castillo, Patricia Melin, J. Esteban Gamez, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In practice, there are many examples when the diversity in a group enhances the group's ability to solve problems -- and thus, leads to more efficient groups, firms, schools, etc. Several papers, starting with the pioneering research by Scott E. Page from the University of Michigan at Ann Arbor, provide a theoretical justification for this known empirical phenomenon. However, when the general advise of increasing diversity is transformed into simple-to-follow algorithmic rules (like quotas), the result is not always successful. In this paper, we prove that the problem of designing the most efficient group is computationally difficult (NP-hard). Thus, in …

Mathematical Justification Of Spectral/Covariance Techniques: On The Example Of Arc Detection, Jan Beck, David Nemir, Vladik Kreinovich

Departmental Technical Reports (CS)

Detecting arcing faults is an important but difficult-to-solve practical problem. Many existing methods of arc detection are based upon acquiring a signal that is proportional to current and then making an analysis of the signal's power spectrum (or, equivalently, its covariance function). Since the power spectrum, i.e., the absolute values of the Fourier transform, carries only partial information about the signal, a natural question is: why should we restrict ourselves to the use of this partial information? A related question is caused by the fact that even the most efficient methods still miss some arcing faults and/or lead to false …

Computing With Tensors: Potential Applications Of Physics-Motivated Mathematics To Computer Science, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we explain what are tensors and how tensors can help in computing.

A New Simplified Derivation Of Nash Bargaining Solution, Tanja Magoc, Vladik Kreinovich

Departmental Technical Reports (CS)

In the 1950s, the Nobel Prize winner John F. Nash has shown that under certain conditions, the best solution to the bargaining problem is when the product of the (increase in) utilities is the largest. Nash's derivation assumed that we are looking for strategies that assign a single situation to each bargaining situation. In this paper, we propose a simplified derivation of Nash bargaining solution that does not requires this assumption.

An Aspect-Based Approach To Checking Design Constraints At Run-Time, Yoonsik Cheon, Carmen Avila, Steve Roach, Cuauhtemoc Munoz, Neith Estrada, Valeria Fierro, Jessica Romo

Departmental Technical Reports (CS)

Design decisions and constraints of a software system can be specified precisely using a formal notation such as the Object Constraint Language (OCL). However, they are not executable, and assuring the conformance of an implementation to its design is hard. The inability of expressing design constraints in an implementation and checking them at runtime invites, among others, the problem of design drift and corrosion. We propose runtime checks as a solution to mitigate this problem. The key idea of our approach is to translate design constraints written in a formal notation such as OCL into aspects that, when applied to …

On Chromatic Numbers Of Space-Times: Open Problems, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

A Paradox Of Altruism: How Caring About Future Generations Can Result In Poverty For Everyone (Game-Theoretic Analysis), Tanja Magoc, Vladik Kreinovich

Departmental Technical Reports (CS)

Political and social activists are rightfully concerned about future generations: whenever a country borrows money, or an environmental situation worsens, this means, in effect, that we impose an additional burdens on future generations. There is clearly a conflict between the present generation's actions and interests and the welfare of the future generations. There exists a mathematical toolbox that provides solutions to many well-defined conflict situations: namely, the toolbox of game theory. It therefore seems reasonable to apply game theory techniques to the conflict between the generations. In this paper, we show that we need to be very cautious about this …

Viability Of Travel-Time Sensitivity Testing For Estimating Uncertainty Of Tomographic Velocity Models: A Case Study, Matthew G. Averill, Kate C. Miller, Vladik Kreinovich, Aaron A. Velasco

Departmental Technical Reports (CS)

Seismic tomography is now a common approach to estimating velocity structure of the Earth, regardless of whether the data sources are earthquake recordings or controlled sources such as explosions, airguns or Vibroseis. Seismic tomography is convenient to implement because it requires little to no a priori knowledge of Earth structure and is much less time consuming than forward modeling schemes. Despite its convenience, the method still lacks satisfactory quantitative assessments of model reliability. Here we explore the viability of applying travel-time sensitivity testing that uses a modified Cauchy distribution as its statistical foundation to assessing the uncertainty in velocity models …

Asymmetric Information Measures: How To Extract Knowledge From An Expert So That The Expert's Effort Is Minimal, Hung T. Nguyen, Vladik Kreinovich, Elizabeth N. Kamoroff

Departmental Technical Reports (CS)

Knowledge acquisition is when we ask experts questions, and put the answers into the computer system. Since this is a very time-consuming task, it is desirable to minimize the effort of an expert.

As a crude estimate for this effort, we can take a number of binary (yes-no) questions that we ask. The procedure that minimizes this number is binary search.

This approach does not take into account that people often feel more comfortable answering "yes" than answering "no". So, to make our estimates more realistic, we will take into consideration that for a negative answer the effort is bigger. …

Current Financial Crisis And Inadequate Uncertainty Processing: A Comment, Tanja Magoc, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Computational Methods For Investment Portfolio: The Use Of Fuzzy Measures And Constraint Programming For Risk Management, Tanja Magoc, Francois Modave, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Computational intelligence techniques are very useful tools for solving problems that involve understanding, modeling, and analysis of large data sets. One of the numerous fields where computational intelligence has found an extremely important role is finance. More precisely, optimization issues of one's financial investments, to guarantee a given return, at a minimal risk, have been solved using intelligent techniques such as genetic algorithm, rule-based expert system, neural network, and support-vector machine. Even though these methods provide good and usually fast approximation of the best investment strategy, they suffer some common drawbacks including the neglect of the dependence among among criteria …

Maximum Entropy In Support Of Semantically Annotated Datasets, Paulo Pinheiro Da Silva, Vladik Kreinovich, Christian Servin

Departmental Technical Reports (CS)

One of the important problems of semantic web is checking whether two datasets describe the same quantity. The existing solution to this problem is to use these datasets' ontologies to deduce that these datasets indeed represent the same quantity. However, even when ontologies seem to confirm the identify of the two corresponding quantities, it is still possible that in reality, we deal with somewhat different quantities. A natural way to check the identity is to compare the numerical values of the measurement results: if they are close (within measurement errors), then most probably we deal with the same quantity, else …

Trustmap: Towards Trust Recommendations For Maps, Paulo Pinheiro Da Silva, Nicholas Ricky Del Rio, Vladik Kreinovich, Alejandro Castaneda

Departmental Technical Reports (CS)

The web is a rich environment for exchanging spatial information. When spatial information is shared in the form of images, i.e., maps, these images almost never come with meta-information about how they were generated. This kind of meta-information is often called knowledge provenance. Access to knowledge provenance may facilitate users to make informed decisions about the quality of maps. In this paper, we propose TrustMap, a new approach for enhancing maps with trust recommendations. For a given map, TrustMap can generate recommendations from the knowledge provenance and a network of trust relations between sources of information used to derive the …

Additional Information About American And Arab Perceptions Of An Arabic Turn-Taking Cue, Nigel Ward, Yaffa Al Bayyari

Departmental Technical Reports (CS)

This technical report is a supplement to "American and Arab perceptions of an Arabic turn-taking cue", a paper submitted to the Journal of Cross-Cultural Psychology. It provides additional details, discussion, figures, tables, and references relating to the main finding, that English speakers tend to misinterpret the prosodic pattern used in Arabic to cue back-channel responses, perceiving it as an expression of negative affect. It also describes an experimental demonstration that being able to detect and respond to this prosodic pattern in dialog can increase native-speaker perceptions of the social effectiveness of learners.

Verified Methods For Computing Pareto Sets: General Algorithmic Analysis, Boglarka G.-Toth, Vladik Kreinovich

Departmental Technical Reports (CS)

In many engineering problems, we face multi-objective optimization, with several objective functions f1,...,fn. We want to provide the user with the Pareto set -- set of all possible solutions x which cannot be improved in all categories (i.e., for which fj(x')>=f_j(x) for all j and fj(x')>fj(x) for some j is impossible). The user should be able to select an appropriate trade-off between, say, cost and durability. We extend the general results about the (verified) algorithmic computability of maxima locations to show that Pareto sets can also computed.

Hypothesis Testing With Interval Data: Case Of Regulatory Constraints, Sa-Aat Niwitpong, Hung T. Nguyen, Ingo Neumann, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, there exist regulatory thresholds: e.g., a concentration of certain chemicals in the car exhaust cannot exceed a certain level, etc. If we know the exact value of the corresponding quantity, then we can immediately tell whether, e.g., a car design resulting in this value is acceptable (below the threshold) or not acceptable (above the threshold). In practice, however, the value of the desired quantity comes from measurements or from expert estimates; in both cases, the resulting estimates are not 100% accurate. It is therefore necessary to make an accept/reject decision based on this estimate, i.e., based …

Computing Degrees Of Subsethood And Similarity For Interval-Valued Fuzzy Sets: Fast Algorithms, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

We propose fast algorithms for computing degrees of subsethood and similarity for interval-valued fuzzy sets.

Towards A More Adequate Use Of Interval-Valued Fuzzy Techniques In Intelligent Control: A Fuzzy Analogue Of Unimodality, Van Nam Huynh, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that interval-valued fuzzy sets provide a more adequate description of expert uncertainty than the more traditional "type-1" (number-valued) fuzzy techniques. In the current approaches for using interval-valued fuzzy techniques, it is usually assumed that all fuzzy sets m(x) from the interval [l(x),u(x)] are possible. In this paper, we show that it is reasonable to restrict ourselves only to fuzzy numbers m(x), i.e., "unimodal" fuzzy sets. We also describe feasible algorithms for implementing thus modified intelligent control.

Towards A Combination Of Interval And Ellipsoid Uncertainty, Vladik Kreinovich, Arnold Neumaier, Gang Xiang

Departmental Technical Reports (CS)

In many real-life situations, we do not know the probability distribution of measurement errors but only upper bounds on these errors. In such situations, once we know the measurement results, we can only conclude that the actual (unknown) values of a quantity belongs to some interval. Based on this interval uncertainty, we want to find the range of possible values of a desired function of the uncertain quantities. In general, computing this range is an NP-hard problem, but in a linear approximation, valid for small uncertainties, there is a linear time algorithm for computing the range. In other situations, we …

Intermediate Degrees Are Needed For The World To Be Cognizable: Towards A New Justification For Fuzzy Logic Ideas, Hung T. Nguyen, Vladik Kreinovich, J. Esteban Gamez, Francois Modave, Olga Kosheleva

Departmental Technical Reports (CS)

Most traditional examples of fuzziness come from the analysis of commonsense reasoning. When we reason, we use words from natural language like "young", "well". In many practical situations, these words do not have a precise true-or-false meaning, they are fuzzy. One may therefore be left with an impression that fuzziness is a subjective characteristic, it is caused by the specific way our brains work.

However, the fact that that we are the result of billions of years of successful adjusting-to-the-environment evolution makes us conclude that everything about us humans is not accidental. In particular, the way we reason is not …

Choquet Integrals And Owa Criteria As A Natural (And Optimal) Next Step After Linear Aggregation: A New General Justification, Francois Modave, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In multi-criteria decision making, it is necessary to aggregate (combine) utility values corresponding to several criteria (parameters). The simplest way to combine these values is to use linear aggregation. In many practical situations, however, linear aggregation does not fully adequately describe the actual decision making process, so non-linear aggregation is needed.

From the purely mathematical viewpoint, the next natural step after linear functions is the use of quadratic functions. However, in decision making, a different type of non-linearities are usually more adequate than quadratic ones: non-linearities like OWA or Choquet integral that use min and max in addition to linear …

Extracting Trust Network Information From Scientific Web Portals, Alejandro Castaneda, Paulo Pinheiro Da Silva

Departmental Technical Reports (CS)

An increased exchange of (scientific) information across organizations and disciplines is one of the long-term goals of the semantic web. In any such exchange of information, it is not difficult to identify one or more (scientific) communities responsible for the measurement, gathering and processing of scientific information. More challenging, however, is to understand the trust relations between members of these communities, whether the members are organizations or people. With a better understanding of trust relations, one may be able to compute trust recommendations for scientific information exchange, increasing in this way the acceptance of information by scientists. In this paper, …

Testing The Value Of A Time-Based Language Model For Speech Recognition, Nisha Kiran, Nigel Ward

Departmental Technical Reports (CS)

Speech recognition relies on the language model in order to decode an utterance, and in general a better language model improves the performance of a speech recognizer. We have recently found that a time-based language model can improve on a standard trigram language model in terms of perplexity. This technical report presents the evaluation of this new language model in the context of speech recognition. First, a basic speech recognizer was built using the HTK tool. Then the recognizer was run using the standard language model and using the time-based one. On a testset of 39,147 words from the Switchboard …

Toward Formalizing Non-Monotonic Reasoning In Physics: The Use Of Kolmogorov Complexity, Vladik Kreinovich

Departmental Technical Reports (CS)

When a physicist writes down equations, or formulates a theory in any other terms, he usually means not only that these equations are true for the real world, but also that the model corresponding to the real world is "typical" among all the solutions of these equations. This type of argument is used when physicists conclude that some property is true by showing that it is true for "almost all" cases. There are formalisms that partially capture this type of reasoning, e.g., techniques based on the Kolmogorov-Martin-Lof definition of a random sequence. The existing formalisms, however, have difficulty formalizing, e.g., …

Trade-Off Between Sample Size And Accuracy: Case Of Measurements Under Interval Uncertainty, Hung T. Nguyen, Olga Kosheleva, Vladik Kreinovich, Scott Ferson

Departmental Technical Reports (CS)

In many practical situations, we are not satisfied with the accuracy of the existing measurements. There are two possible ways to improve the measurement accuracy:

first, instead of a single measurement, we can make repeated measurements; the additional information coming from these additional measurements can improve the accuracy of the result of this series of measurements;

second, we can replace the current measuring instrument with a more accurate one; correspondingly, we can use a more accurate (and more expensive) measurement procedure provided by a measuring lab -- e.g., a procedure that includes the use of a higher quality reagent.

In …

Application-Motivated Combinations Of Fuzzy, Interval, And Probability Approaches, And Their Use In Geoinformatics, Bioinformatics, And Engineering, Vladik Kreinovich

Departmental Technical Reports (CS)

Most data processing techniques traditionally used in scientific and engineering practice are statistical. These techniques are based on the assumption that we know the probability distributions of measurement errors etc. In practice, often, we do not know the distributions, we only know the bound D on the measurement accuracy - hence, after the get the measurement result X, the only information that we have about the actual (unknown) value x of the measured quantity is that x belongs to the interval [X - D, X + D]. Techniques for data processing under such interval uncertainty are called interval computations; these …

Program Synthesis From Workflow-Driven Ontologies, Leonardo Salayandia, Steve Roach, Ann Q. Gates

Departmental Technical Reports (CS)

An approach that results in the development of Workflow-Driven Ontologies (WDO) (called the WDO approach) allows domain scientists to capture process knowledge in the form of concepts as well as relations between concepts. Program synthesis techniques can be employed to generate algorithmic solutions by transforming the process knowledge expressed in the WDO as concepts and relations to variables and functions and computing unknown variables from known ones based on the process knowledge documented by the domain scientist. Furthermore, the algorithmic solutions that are generated by program synthesis potentially can support the composition of services, which result in the creation of …

Sloth-Nfs And The Possibility Of Using Fuzzy Control To Optimize Cache Management, Ryan C. Spring, Eric Freudenthal

Departmental Technical Reports (CS)

Modern software systems are complex and increasingly vulnerable to malicious attack. In order to apply bug fixes and protect against security weaknesses, workstation administrators must continuously patch operating system and application program installations. To simplify this process, administrators generally configure systems into clusters with common installations of operating systems and application programs in a manner that patches and other routine maintenance can be applied en masse. Two widely used approaches offer complementary advantages: Installations and updates are particularly convenient when all data including operating system and programs is served by traditional centralized network-connected file servers (networked file systems) because administrators …

Asymmetric Paternalism: Description Of The Phenomenon, Explanation Based On Decisions Under Uncertainty, And Possible Applications To Education, Olga Kosheleva, Francois Modave

Departmental Technical Reports (CS)

In general, human being are rational decision makers, but in many situations, they exhibit unexplained "inertia", reluctance to switch to a better decision. In this paper, we show that this seemingly irrational behavior can be explained if we take uncertainty into account; we also explain how this phenomenon can be utilized in education.