Narrow Results

Arithmetic circuits in general do not exactly match specifications, leading to different implementations within allowed imprecision. Starting from real-valued representation, such as Taylor series, we propose a new technique based on arithmetic transform (AT) to analyze simultaneous selection of multiple word lengths and even the function approximation schemes, and then derive a verification algorithm to check whether an implementation fits the error bound. To find optimized implementations which both satisfy a given error bound and constraints included interface input, delay and area. An optimization algorithm is derived to explore multiple precision parameters and get the optimized implementations by various constraints.

We study optimization problems for polyhedral terrains in the presence of data imprecision. An imprecise terrain is given by a triangulated point set where the height component of the vertices is specified by an interval of possible values. We restrict ourselves to terrains with a one-dimensional projection, usually referred to as 1.5-dimensional terrains, where an imprecise terrain is given by an x-monotone polyline, and the y-coordinate of each vertex is not fixed but only constrained to a given interval. Motivated mainly by applications in terrain analysis, in this paper we study five different optimization measures related to obtaining smooth terrains, for the 1.5-dimensional case. In particular, we present exact algorithms to minimize and maximize the total turning angle, as well as to minimize the maximum slope change. Furthermore, we also give approximation algorithms to minimize the largest turning angle and to maximize the smallest turning angle.

Priority analysis is one of the most important issues in the trade-off analysis of imprecise conflicting requirements whose elasticity is captured using fuzzy logic. Requirement analysts need to know not only the relative ordering of requirements based on their importance but also how much a requirement is more important than another requirement in order to achieve an effective trade-off. This paper presents a formal approach for reasoning about the relative priority by analyzing the customer’s trade-off preference among imprecise conflicting requirements. A possibilistic reasoning framework for inferring the lower bound of relative priority from case analysis under uncertainty is also developed. Consistency and nonredundancy criteria are established to facilitate the conversion of a possibilistic statement on a lower bound of relative priority into a relative priority. Finally, relative priorities are transformed into weights of importance so that they can be used in the aggregation of conflicting requirements to resolve conflicts.

In belief functions, there are two types of uncertainty which are due to lack of knowledge: randomness and non-specificity. In this paper, we present a non-specificity measure for convex sets of probability distributions that generalizes Dubois and Prade's non-specificity measure in the Dempster-Shafer theory of evidence.

In belief functions, there is a total measure of uncertainty that quantify the lack of knowledge and verifies a set of important properties. It is based on two measures: maximum of entropy and non-specificity. In this paper, we prove that the maximum of entropy verifies the same set of properties in a more general theory as credal sets and we present an algorithm that finds the probability distribution of maximum entropy for another interesting type of credal sets as probability intervals.

The special needs of the OLAP technology were the main cause of the use of a multidimensional view of the data. Crisp models are not suitable to model complex or non well defined domains. They also fail to integrate data from semi/non-structured sources (e.g. Internet) or with incompatibilities in their schemata. In these situations, as a result of the modelling and/or integration, imprecision appears. So, we need a model able to manage imprecision in the structures and data. If we want to use expert's knowledge in the analysis, we have to keep in mind that expert users are more comfortable when they use linguistic expressions instead of exact values. In this paper we present an extension of a fuzzy multidimensional model to support the use of linguistic labels in the definition of the hierarchies and the OLAP system that implements this model.

Relevant contributions of fuzzy logic to the logical models in information retrieval is studied. It makes it possible to grasp the graduality of some relevant concepts and to model both imprecision and uncertainty inherent to the retrieval process, still in the framework of the broadly meant logical approach. In this perspective we discuss various extensions to the basic Boolean model which are needed to attain such a greater expressivity. In particular, we show how the well-known semantics of keywords weights may be recovered in various fuzzy logic based information retrieval models.

Spanish primary and secondary school curricula comprise several contents, learning outcomes and assessment criteria directly related with probability and approximate calculus. Some of them refer to situations modeled by the students, which entail not only uncertainty but also imprecision. For this reason, different techniques including fuzzy logic and fuzzy sets theory could be applied when dealing with this kind of situations in the classroom. Several teaching situations handling imprecise concepts in primary and secondary schools are suggested from a theoretical point of view. These more exible ways of reasoning could be combined with the traditional probability approach, allowing to tackle more general problems and not only those involving exact calculations or specific numerical assignments. Moreover, this type of approaches will provide the students with tools to manage imprecision as a mathematical tool in their personal life.

Occupancy grids are common tools used in robotics to represent the robot environment, and that may be used to plan trajectories, select additional measurements to acquire, etc. However, deriving information about those occupancy grids from sensor measurements often induce a lot of uncertainty, especially for grid elements that correspond to occluded or far away area from the robot. This means that occupancy information may be quite uncertain and imprecise at some places, while being very accurate at others. Modelling finely this occupancy information is essential to decide the optimal action the robot should take, but a refined modelling of uncertainty often implies a higher computational cost, a prohibitive feature for real-time applications. In this paper, we introduce the notion of credal occupancy grids, using the very general theory of imprecise probabilities to model occupancy uncertainty. We also show how one can perform efficient, real-time inferences with such a model, and show a use-case applying the model to an autonomous vehicle trajectory planning problem.

Within the many-valued approach for approximate reasoning, the aim of this paper is two-fold. First, to extend truth-values lattices to cope with the imprecision due to possible incompleteness of the available information. This is done by considering two bilattices of truth-value intervals corresponding to the so-called weak and strong truth orderings. Based on the use of interval bilattices, the second aim is to introduce what we call partial many-valued logics. The (partial) models of such logics may assign intervals of truth-values to formulas, and so they stand for representations of incomplete states of knowledge. Finally, the relation between partial and complete semantical entailment is studied, and it is provedtheir equivalence for a family of formulas, including the so-called free well formed formulas.

Elasticity in an imprecise requirement needs to be captured to enable the trade-off analysis of conflicting requirements. One of the most important issues in the trade-off analysis of conflicting requirements is to understand their priorities. Requirement analysts need to know not only the relative ordering of requirements based on their importance but also how much a requirement is more important than another requirement in order to achieve an effective trade-off between conflicting requirements. Existing formal methods for requirement engineering are limited in addressing these issues. This paper presents a formal methodology for reasoning about their priority by analyzing the customer’s trade-off preference among imprecise conflicting requirements. The elasticity in imprecise requirements is captured using fuzzy logic. Conflicting and cooperative relationships are classified to detect the conflicts between requirements. Multiple requirements are combined based fuzzy multi-criteria decision making techniques. We have also developed a possibilistic reasoning framework for inferring the lower bound of relative priority from case analysis. Consistency and nonredundancy criteria are established to facilitate the aggregation of possibilistic statement on the lower bounds of relative priority. Finally, we describe a process for transforming the lower bounds of relative priority into weights of importance so that they can be used in the aggregation of conflicting requirements to resolve conflicts.

Sonar sensors are widely used in mobile robots applications such as navigation, map building, and localization. The performance of these sensors is affected by the environmental phenomena, sensor design, and target characteristics. Therefore, the readings obtained from these sensors are uncertain. This uncertainity is often modeled by using Probability Theory. However, the probablistic approach is valid when the available knowledge is precise which is not the case in sonar readings. In this paper, the behavior of sonar readings reflected from walls and corners are studied, then new models of angular uncertainty and radial imprecision for sonar readings obtained from corners and walls are proposed. These models are represented by using Possibility Theory, mainly possibility distributions.

Learning Classifier Systems (LCSs) are a kind of evolutionary machine learning algorithms that provide highly adaptive components to deal with real world problems. They have been widely used in resolving complex problems such as decision making and classification. LCSs are flexible algorithms that are able to construct, incrementally, a set of rules and evolve them through the Evolutionary Algorithm (EA). Despite their efficiency, LCSs are not capable of handling imperfect information, which may lead to reduced performance in terms of classification accuracy. We propose a new accuracy-based Michigan-style LCS that integrates the belief function theory in the supervised classifier system. The belief function or evidence theory represents an efficient framework for treating imperfect information. The new approach shows promising results in real world classification problems.