Henri Prade

Bio: Henri Prade is an academic researcher from Paul Sabatier University. The author has contributed to research in topics: Possibility theory & Fuzzy set. The author has an hindex of 108, co-authored 917 publications receiving 54583 citations. Previous affiliations of Henri Prade include Centre national de la recherche scientifique & University of Toulouse.

Fuzzy Sets and Systems: Theory and Applications

Abstract: (1982). Fuzzy Sets and Systems — Theory and Applications. Journal of the Operational Research Society: Vol. 33, No. 2, pp. 198-198.

Rough fuzzy sets and fuzzy rough sets

Abstract: The notion of a rough set introduced by Pawlak has often been compared to that of a fuzzy set, sometimes with a view to prove that one is more general, or, more useful than the other. In this paper we argue that both notions aim to different purposes. Seen this way, it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems. First, one may think of deriving the upper and lower approximations of a fuzzy set, when a reference scale is coarsened by means of an equivalence relation. We then come close to Caianiello's C-calculus. Shafer's concept of coarsened belief functions also belongs to the same line of thought. Another idea is to turn the equivalence relation into a fuzzy similarity relation, for the modeling of coarseness, as already proposed by Farinas del Cerro and Prade. Instead of using a similarity relation, we can start with fuzzy granules which make a fuzzy partition of the reference scale. The main contribut...

Possibility Theory: An Approach to Computerized Processing of Uncertainty

Abstract: 1. Measures of Possibility and Fuzzy Sets.- 1.1. Imprecision and Uncertainty.- 1.2. Traditional Models of Imprecision and Uncertainty.- 1.3. Confidence Measures.- 1.3.1. Measures of Possibility and of Necessity.- 1.3.2. Possibility and Probability.- 1.4. Fuzzy Sets.- 1.5. Elementary Fuzzy Set Operations.- 1.6. Practical Methods for Determining Membership Functions.- 1.6.1. Vague Categories as Perceived by an Individual.- 1.6.2. Fuzzy Sets Constructed from Statistical Data.- 1.6.3. Remarks on the Set of Degrees of Membership.- 1.7. Confidence Measures for a Fuzzy Event.- 1.8. Fuzzy Relations and Cartesian Products of Fuzzy Sets.- References.- 2. The Calculus of Fuzzy Quantities.- 2.1. Definitions and a Fundamental Principle.- 2.1.1. Fuzzy Quantities, Fuzzy Intervals, Fuzzy Numbers.- 2.1.2. The Extension Principle.- 2.2. Calculus of Fuzzy Quantities with Noninteractive Variables.- 2.2.1. Fundamental Result.- 2.2.2. Relation to Interval Analysis.- 2.2.3. Application to Standard Operations.- 2.2.4. The Problem of Equivalent Representations of a Function.- 2.3. Practical Calculation with Fuzzy Intervals.- 2.3.1. Parametric Representation of a Fuzzy Interval.- 2.3.2. Exact Practical Calculation with the Four Arithmetic Operations.- 2.3.3. Approximate Calculation of Functions of Fuzzy Intervals.- 2.4. Further Calculi of Fuzzy Quantities.- 2.4.1. "Pessimistic" Calculus of Fuzzy Quantities with Interactive Variables.- 2.4.2. "Optimistic" Calculus of Fuzzy Quantities with Noninteractive Variables.- 2.5. Illustrative Examples.- 2.5.1. Estimation of Resources in a Budget.- 2.5.2. Calculation of a PERT Analysis with Fuzzy Duration Estimates.- 2.5.3. A Problem in the Control of a Machine Tool.- Appendix: Computer Programs.- References.- 3. The Use of Fuzzy Sets for the Evaluation and Ranking of Objects.- 3.1. A Quantitative Approach to Multiaspect Choice.- 3.1.1. Basic Principles of the Approach.- 3.1.2. Fuzzy Set-Theoretic Operations.- 3.1.3. Application to the Combination of Criteria.- 3.1.4. Identification of Operators.- 3.1.5. Example.- 3.2. Comparison of Imprecise Evaluations.- 3.2.1. Comparison of a Real Number and a Fuzzy Interval.- 3.2.2. Comparison of Two Fuzzy Intervals.- 3.2.3. Ordering of n Fuzzy Intervals.- 3.2.4. Computer Implementation.- 3.2.5. Example.- Appendix: Computer Programs.- References.- 4. Models for Approximate Reasoning in Expert Systems.- 4.1. Remarks on Modeling Imprecision and Uncertainty.- 4.1.1. Credibility and Plausibility.- 4.1.2. Decomposable Measures.- 4.1.3. Vague Propositions.- 4.1.4. Evaluating the Truth Value of a Proposition.- 4.2. Reasoning from Uncertain Premises.- 4.2.1. Deductive Inference with Uncertain Premises.- 4.2.2. Complex Premises.- 4.2.3. Combining Degrees of Uncertainty Relative to the Same Proposition.- 4.3. Inference from Vague or Fuzzy Premises.- 4.3.1. Representation of the Rule "if X is A, then Y is B".- 4.3.2. "Generalized" Modus Ponens.- 4.3.3. Complex Premises.- 4.3.4. Combining Possibility Distributions.- 4.4. Brief Summary of Current Work and Systems.- 4.5. Example.- Appendix A..- Appendix B: Computer Programs.- References.- 5. Heuristic Search in an Imprecise Environment, and Fuzzy Programming.- 5.1. Heuristic Search in an Imprecise Environment.- 5.1.1. A and A* Algorithms.- 5.1.2. The Classical Traveling Salesman Problem (Reminder).- 5.1.3. Heuristic Search with Imprecise Evaluations.- 5.1.4. Heuristic Search with Fuzzy Values.- 5.2. An Example of Fuzzy Programming: Tracing the Execution of an Itinerary Specified in Imprecise Terms.- 5.2.1. Execution and Chaining of Instructions.- 5.2.2. Illustrative Example.- 5.2.3. Problems Arising in Fuzzy Programming.- 5.2.4. Concluding Remarks.- Appendix: Computer Programs.- A.1. Selection of "the Smallest" of N Fuzzy Numbers.- A.2. Tracing Imprecisely Specified Itineraries.- References.- 6. Handling of Incomplete or Uncertain Data and Vague Queries in Database Applications.- 6.1. Representation of Incomplete or Uncertain Data.- 6.1.1. Representing Data by Means of Possibility Distributions.- 6.1.2. Differences and Similarities with Other Fuzzy Approaches.- 6.1.3. Dependencies and Possibilistic Information.- 6.2. The Extended Relational Algebra and the Corresponding Query Language.- 6.2.1. Generalization of ?-Selection.- 6.2.2. Cartesian Product, ?-Join, and Projection.- 6.2.3. Union and Intersection-Redundancy.- 6.2.4. Queries Employing Other Operations.- 6.3. Example.- 6.3.1. Representation of Data.- 6.3.2. Examples of Queries.- 6.4. Conclusion.- Appendix: Computer Program.- A.1. Data Structures.- A.2. Representation of Queries.- A.3. Description of Implemeted Procedures.- References.

Operations on fuzzy numbers

Abstract: A fuzzy number is a fuzzy subset of the real line whose highest membership values are clustered around a given real number called the mean value ; the membership function is monotonia on both sides of this mean value. In this paper, the usual algebraic operations on real numbers are extended to fuzzy numbers by the use of a fuzzification principle. The practical use of fuzzified operations is shown to be easy, requiring no more computation than when dealing with error intervals in classic tolerance analysis. The field of applications of this approach seems to be large, since it allows many known algorithms to be fitted to fuzzy data.

Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference

Abstract: From the Publisher: Probabilistic Reasoning in Intelligent Systems is a complete andaccessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertainty—and offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognition—in short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information. Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

ANFIS: adaptive-network-based fuzzy inference system

Abstract: The architecture and learning procedure underlying ANFIS (adaptive-network-based fuzzy inference system) is presented, which is a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping based on both human knowledge (in the form of fuzzy if-then rules) and stipulated input-output data pairs. In the simulation, the ANFIS architecture is employed to model nonlinear functions, identify nonlinear components on-line in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificial neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. >

Machine learning

Abstract: Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Fuzzy Set Theory - and Its Applications

Abstract: Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.