Gilles Mauris

Probability-Possibility Transformations, Triangular Fuzzy Sets, and Probabilistic Inequalities

A possibility measure can encode a family of probability measures. This fact is the basis for a transformation of a probability distribution into a possibility distribution that generalises the notion of best interval substitute to a probability distribution with prescribed confidence. This paper describes new properties of this transformation, by relating it with the well-known probability inequalities of Bienaymé-Chebychev and Camp-Meidel. The paper also provides a justification of symmetric triangular fuzzy numbers in the spirit of such inequalities. It shows that the cuts of such a triangular fuzzy number contains the “confidence intervals” of any symmetric probability distribution with the same mode and support. This result is also the basis of a fuzzy approach to the representation of uncertainty in measurement. It consists in representing measurements by a family of nested intervals with various confidence levels. From the operational point of view, the proposed representation is compatible with the recommendations of the ISO Guide for the expression of uncertainty in physical measurement.

A fuzzy approach for the expression of uncertainty in measurement

This paper deals with a fuzzy expression of uncertainty in measurement. The fuzzy approach proposed consists of representing measurements by a family of intervals of confidence stacked atop one another, that in fact define the upper bound of the probability distributions consistent with these intervals of confidence. This approach is compatible with the ISO Guide for the expression of uncertainty in measurement, and is particularly interesting because it allows both the handling of specificity and uncertainty of measurement. Moreover, fuzzy uncertainty propagation is available thanks to fuzzy arithmetic, which is a generalization of interval analysis, yielding both worst case results and best estimates at the same time. In order to simplify the propagation, a parameterized possibility distribution approximating the optimal one is proposed and compared with the probabilistic approaches.

Fuzzy fusion techniques for linear features detection in multitemporal SAR images

This paper is concerned with the automatic detection of linear features in SAR satellite data, with application to road network extraction. After a directional prefiltering step, a morphological line detector is presented. To improve the detection performances, the results obtained on multitemporal data are fused. Different fusion strategies involving different fusion operators are then presented. Since extensions of classical set union and intersection do not lead to satisfactory results (the corresponding operators are either too indulgent or too severe), the first strategy consists of fusing the data using a compromise operator. The second strategy consists of fusing the results computed with two operators that have opposite properties, in order to obtain a final intermediate result. Thanks to the wide range of properties they provide, fuzzy operators are used to test and compare these two fusion strategies on real ERS-1 multitemporal data.

Global vision and performance indicators for an industrial improvement approach

Abstract This article organizes reflections around the notion of industrial performance. If the latter has always justified all the actions carried out in an enterprise, these actions have evolved with the evolution of the context. From a brief review of the characteristics of this context where information technology plays an expanding role, two concepts inherent to today’s performance are deduced and then analyzed: the need to consider the enterprise through a global vision on the one hand, and the importance of a continuous improvement approach of the performance of the whole or parts of the enterprise on the other hand. Then, the study will focus more particularly on the performance indicator as a fundamental tool in an improvement approach.

Fuzzy symbolic sensors—From concept to applications

Abstract This paper deals with sensors which compute and report liguistic assessments of numerical acquired values. Such sensors, called symbolic sensors, are particularly adapted when working with control systems which use artificial intelligence techniques. After having reconsidered some elements of the measurement theory, this paper sets the foundations of the symbolic sensors by introducing the meaning of a lexical value and the description of a numeric measurement as two mappings that link the set of the subsets of the numerical domain with the set of the subsets of the lexical domain. It is then shown how the fuzzy subset theory provides a smart way for the treatment of symbol graduality, for measurement imprecisions and measurement validation, and for taking into account the measurement context. This approach leads to introducing a specific structure into the sensors, then called fuzzy symbolic sensors. As application, two specimens of fuzzy symbolic sensors have been successfully implemented. The first is an ultrasonic range finding sensor, which uses a procedure of management of errors and a procedure of creation of concepts by semantic relationships. The second is a colour matching sensor, which uses an interpolation method for creating the concepts by learning with a teacher.

Fuzzy modeling of measurement data acquired from physical sensors

The measurement uncertainty in physical sensors is often represented by a probabilistic approach, but such a representation is not always adapted to new intelligent systems. Therefore, a fuzzy representation, based on the possibility theory, can sometimes be preferred. We previously proposed a truncated triangular probability-possibility transformation to be applied to any unimodal and symmetric probability distribution which can be assimilated to one of the four most encountered probability laws (Gaussian, double-exponential, triangular, uniform). In this paper, we propose to build a fuzzy model of data acquired from physical sensors by applying this transformation. For this purpose, a minimum of knowledge about the probabilistic modeling of sensors is required. Three main situations are considered and for each situation, an adapted fuzzy modeling is proposed. Examples of these three situations are based on FM-chirped ultrasonic sensors.

The aggregation of complementary information via fuzzy sensors

Abstract This paper focuses on the acquisition of high-level information, i.e. information that is related to many conventional physical quantities in a non-analytical way. In these complex cases, we proposed to use fuzzy sensors which compute and report linguistic assessments of numerically acquired values. Two methods are proposed to realized the aggregation from basic measurements. The first one performs a combination of the relevant features by means of a rule-based description of the relations between them. With the second, the aggregation is realized through an interpolation mechanism that creates a fuzzy partition of the numeric multi-dimensional space of the basic features. The two methods will be applied to a linguistic description of comfort deduced from temperature and humidity measurements. Finally, these two methods will be compared in terms of their efficiency and material implementation.

Information aggregation in industrial performance measurement: rationales, issues and definitions

Industrial performance can be defined in terms of numerous criteria to be synthesized for global control purposes, many of them being of a complex nature, i.e. not related to one elementary physical measure. In this context, determining a global performance expression raises the issue of performance expression aggregation. To address such an aggregation issue, so-called performance measurement systems need to be implemented. The analysis of the corresponding literature leads to the conclusion that the majority of the proposed approaches either do not provide explicit aggregation mechanisms or propose overly simplistic methods really to cope with the complexity of the situations at hand. Only a few consider explicit adequate aggregation methods. Therefore, a thorough characterization of performance expression aggregation based on four stages, namely extraction, representation, combination and interpretation, as proposed by the information aggregation community is presented. The contribution deals with the definition of a performance expression combination based on two kinds of performance expressions commonly encountered (physical measures and performance evaluations, i.e. objective satisfaction degrees). Methodological guidelines for performance expression aggregation are proposed as well as associated mathematical tools, especially the fuzzy Choquet integral for taking criteria interactions into account. An industrial case study is used as an illustration, and some concluding remarks and emerging problems to be considered in the future, such as temporal aggregation, are finally pointed out.

A statistical overview of recent literature in information fusion

The objective of this paper is to make a picture of the recent articles published on information fusion. Indeed, a great number of documents dealing with this technique are available in the literature. A classification scheme including application fields, fusion goals, fusion system architecture and mathematical tools is proposed. This overview of the last three years allows one to compute the article distribution in each class. Finally, some elements of a preliminary analysis of this classification are drawn.

Statistical and fuzzy models of ambulatory systolic blood pressure for hypertension diagnosis

A solution to reduce Ambulatory Systolic Blood Pressure (ASBP) variability during the analysis of a 24-h profile is studied and presented in this article. It consists of equipping the portable ASBP recorder device with other sensors, a three-axes accelerometer and a heart rate recorder, so as to enable an analysis of the tensional profile in the light of these concomitant data. A database has been collected, and two models linking ASBP variations with body acceleration and heart rate measurements are developed: a regression one, based on a priori knowledge of ASBP variations, and a fuzzy one, automatically built from experimental data. Their performances are tested in prediction and compared. Then, the results are compared to those obtained with one of the solutions currently used by the physicians to deal with ASBP variability. The results obtained on 16 young subjects from the database are significantly improved and thus, encouraging.