Jean-Marc Tacnet

Fusion of sources of evidence with different importances and reliabilities

This paper presents a new approach for combining sources of evidences with different importances and reliabilities. Usually, the combination of sources of evidences with different reliabilities is done by the classical Shafers discounting approach. Therefore, to consider unequal importances of sources, if any, a similar reliability discounting process is generally used, making no difference between the notion of importance and reliability. In fact, in multicriteria decision context, these notions should be clearly distinguished. This paper shows how this can be done and we provide simple examples to show the differences between both solutions for managing importances and reliabilities of sources. We also discuss the possibility for mixing them in a global fusion process.

How to manage natural risks in mountain areas in a context of imperfect information? New frameworks and paradigms for expert assessments and decision-making

In mountain areas, natural phenomena such as snow avalanches, debris flows and rock-falls, put people and objects at risk with sometimes dramatic consequences. Risk is classically considered as a combination of hazard, the combination of the intensity and frequency of the phenomenon, and vulnerability which corresponds to the consequences of the phenomenon on exposed people and material assets. Risk management consists in identifying the risk level as well as choosing the best strategies for risk prevention, i.e. mitigation. In the context of natural phenomena in mountainous areas, technical and scientific knowledge is often lacking. Risk management decisions are therefore based on imperfect information. This information comes from more or less reliable sources ranging from historical data, expert assessments, numerical simulations etc. Finally, risk management decisions are the result of complex knowledge management and reasoning processes. Tracing the information and propagating information quality from data acquisition to decisions are therefore important steps in the decision-making process. In this paper, a global integrated framework is proposed to improve the risk management process in a context of information imperfection provided by more or less reliable sources. It includes uncertainty as well as imprecision, inconsistency and incompleteness. It is original in the methods used and their association: sequential decision context description, development of specific decision-making methods, imperfection propagation in numerical modelling and information fusion. This framework not only assists in decision-making but also traces the process and evaluates the impact of information quality on decision-making.

Hierarchical Proportional Redistribution for bba Approximation

Dempsters rule of combination is commonly used in the field of infor- mation fusion when dealing with belief functions. However, it generally requires a high computational cost. To reduce it, a basic belief assignment (bba) approxima- tion is needed. In this paper we present a new bba approximation approach called hierarchical proportional redistribution (HPR) allowing to approximate a bba at any given level of non-specificity. Two examples are given to show how our new HPR works.

Decision-Making with Belief Interval Distance

In this paper we propose a new general method for decision-making under uncertainty based on the belief interval distance. We show through several simple illustrative examples how this method works and its ability to provide reasonable results.

Sigmoidal Model for Belief Function- Based Electre Tri Method

Main decision-making problems can be described into choice, ranking or sorting of a set of alternatives or solutions. The principle of Electre TRI (ET) method is to sort alternatives ai according to criteria g j into categories C h whose lower and upper limits are respectively b h and b h + 1. The sorting procedure is based on the evaluations of outranking relations based firstly on calculation of partial concordance and discordance indexes and secondly on global concordance and credibility indexes. In this paper, we propose to replace the calculation of the original concordance and discordance indexes of ET method by a more effective sigmoidal model. Such model is part of a new Belief Function ET (BF-ET) method under development and allows a comprehensive, elegant and continuous mathematical representation of degree of concordance, discordance and the uncertainty level which is not directly taken into account explicitly in the classical Electre Tri.

Multi-Criteria Decision-Making with imprecise scores and BF-TOPSIS

In 2016 we developed a new approach for Multi-Criteria Decision-Making (MCDM) inspired by the technique for order preference by similarity to ideal solution (TOPSIS) and based on belief functions (BF). Our BF-TOPSIS (Belief Function based TOPSIS) approach assumes that the input score of each hypothesis for each criterion was a real precise number which is a quite restrictive assumption. In this paper we extend our BF-TOPSIS to deal with imprecise score values (intervals of real numbers) and we call it Imp-BF-TOPSIS. This new approach follows main ideas of BF-TOPSIS but extends its applicability for more realistic MCDM problems where the scores are given with a finite precision. Imp-BF-TOPSIS is based on Interval Arithmetic (IA), new probabilistic order relations between intervals and belief functions. We also present results of Imp-BF-TOPSIS for simple examples for illustrating its effectiveness.

The BF-TOPSIS Approach for Solving Non-classical MCDM Problems

In this paper we show how the Belief-Function based Technique for Order Preference by Similarity to Ideal Solution (BF-TOPSIS) approach can be used for solving non-classical multi-criteria decision-making (MCDM) problems. We give simple examples to illustrate our presentation.

Applying ER-MCDA and BF-TOPSIS to Decide on Effectiveness of Torrent Protection

Experts take into account several criteria to assess the effectiveness of torrential flood protection systems. In practice, scoring each criterion is imperfect. Each system is assessed choosing a qualitative class of effectiveness among several such classes (high, medium, low, no). Evidential Reasoning for Multi-Criteria Decision-Analysis (ER-MCDA) approach can help formalize this Multi-Criteria Decision-Making (MCDM) problem but only provides a coarse ranking of all systems. The recent Belief Function-based Technique for Order Preference by Similarity to Ideal Solution (BF-TOPSIS) methods give a finer ranking but are limited to perfect scoring of criteria. Our objective is to provide a coarse and a finer ranking of systems according to their effectiveness given the imperfect scoring of criteria. Therefore we propose to couple the two methods using an intermediary decision and a quantification transformation step. Given an actual MCDM problem, we apply the ER-MCDA and its coupling with BF-TOPSIS, showing that the final fine ranking is consistent with a previous coarse ranking in this case.

Hierarchical proportional redistribution principle for uncertainty reduction and BBA approximation

Dempster-Shafer evidence theory is very important in the fields of information fusion and decision making. However, it always brings high computational cost when the frames of discernments to deal with become large. To reduce the heavy computational load involved in many rules of combinations, the approximation of a general belief function is needed. In this paper we present a new general principle for uncertainty reduction based on hierarchical proportional redistribution (HPR) method which allows to approximate any general basic belief assignment (bba) at a given level of non-specificity, up to the ultimate level 1 corresponding to a Bayesian bba. The level of non-specificity can be adjusted by the users. Some experiments are provided to illustrate our proposed HPR method.

Resilience of Critical Infrastructures: Review and Analysis of Current Approaches: Resilience of Critical Infrastructures

In crisis situations, systems, organizations, and people must react and deal with events that are inherently unpredictable before they occur: vital societal functions and thus infrastructures must be restored or adapted as quickly as possible. This capacity refers to resilience. Progress concerning its conceptualization has been made but it remains difficult to assess and apply in practice. The results of this article stem from a literature review allowing the analysis of current advances in the development of proposals to improve the management of infrastructure resilience. The article: (i) identifies different dimensions of resilience; (ii) highlights current limits of assessing and controlling resilience; and (iii) proposes several directions for future research that could go beyond the current limits of resilience management, but subject to compliance with a number of constraints. These constraints are taking into account different hazards, cascade effects, and uncertain conditions, dealing with technical, organizational, economical, and human domains, and integrating temporal and spatial aspects.