Vladik Kreinovich

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This report summarizes a variety of the most useful and commonly applied methods for obtaining Dempster-Shafer structures, and their mathematical kin probability boxes, from empirical information or theoretical knowledge. The report includes a review of the aggregation methods for handling agreement and conflict when multiple such objects are obtained from(More)
In many real-life situations, we are interested in the value of a physical quantity y that is diicult or impossible to measure directly. To estimate y, we nd some easier-to-measure quantities x 1 ; : : : ; x n which are related to y by a known relation y = f (x 1 ; : : : ; x n). Measurements are never 100% accurate; hence, the measured values e x i are(More)
One of the reasons why fuzzy methodology is successful is that fuzzy systems are universal approximators, i.e., that we can approximate an arbitrary continuous function within any given accuracy by a fuzzy system. In some practical applications (e.g., in control), it is desirable to approximate not only the original function, but also its derivatives (so(More)
Security games provide a framework for allocating limited security resources in adversarial domains, and are currently used in deployed systems for LAX, the Federal Air Marshals, and the U.S. Coast Guard. One of the major challenges in security games is finding solutions that are robust to uncertainty about the game model. Bayesian game models have been(More)
Traditional decision theory assumes that for every two alternatives, people always make the same (deterministic) choice. In practice, people’s choices are often probabilistic, especially for similar alternatives: the same decision maker can sometimes select one of them and sometimes the other one. In many practical situations, an adequate description of(More)
In the last several years, there have been several studies about the computational complexity of classical planning assuming that the planner has complete knowledge about the initial situation. Recently, there have been proposals to usèsensing' actions to plan in the presence of incompleteness. In this paper we study the complexity of planning in such(More)
Fuzzy control is a very successful way to transform the expert’s knowledge of the type “if the velocity is big and the distance from the object is small, hit the brakes and decelerate as fast as possible” into an actual control. To apply this transformation one must: 1) choose fuzzy variables corresponding to words like “small”, “big”; 2) choose operations(More)
When we have only interval ranges [<i>x<inf>i</inf>,</i> <i>x<inf>i</inf></i>] of sample values <i>x</i><inf>1</inf>,&#8230;, <i>x<inf>n</inf>,</i> what is the interval [<i>V, V</i>] of possible values for the variance <i>V</i> of these values? We prove that the problem of computing the upper bound <i>V</i> is NP-hard. We provide a feasible (quadratic time)(More)