The posterity of Zadeh's 50-year-old paper: A retrospective in 101 Easy Pieces – and a Few More

International audienceThis article was commissioned by the 22nd IEEE International Conference of Fuzzy Systems (FUZZ-IEEE) to celebrate the 50th Anniversary of Lotfi Zadeh's seminal 1965 paper on fuzzy sets. In addition to Lotfi's original paper, this note itemizes 100 citations of books and papers deemed “important (significant, seminal, etc.)” by 20 of the 21 living IEEE CIS Fuzzy Systems pioneers. Each of the 20 contributors supplied 5 citations, and Lotfi's paper makes the overall list a tidy 101, as in “Fuzzy Sets 101”. This note is not a survey in any real sense of the word, but the contributors did offer short remarks to indicate the reason for inclusion (e.g., historical, topical, seminal, etc.) of each citation. Citation statistics are easy to find and notoriously erroneous, so we refrain from reporting them - almost. The exception is that according to Google scholar on April 9, 2015, Lotfi's 1965 paper has been cited 55,479 times

The Basic Principles of Uncertain Information Fusion. An organized review of merging rules in different representation frameworks

We propose and advocate basic principles for the fusion of incomplete or uncertain information items, that should apply regardless of the formalism adopted for representing pieces of information coming from several sources. This formalism can be based on sets, logic, partial orders, possibility theory, belief functions or imprecise probabilities. We propose a general notion of information item representing incomplete or uncertain information about the values of an entity of interest. It is supposed to rank such values in terms of relative plausibility, and explicitly point out impossible values. Basic issues affecting the results of the fusion process, such as relative information content and consistency of information items, as well as their mutual consistency, are discussed. For each representation setting, we present fusion rules that obey our principles, and compare them to postulates specific to the representation proposed in the past. In the crudest (Boolean) representation setting (using a set of possible values), we show that the understanding of the set in terms of most plausible values, or in terms of non-impossible ones matters for choosing a relevant fusion rule. Especially, in the latter case our principles justify the method of maximal consistent subsets, while the former is related to the fusion of logical bases. Then we consider several formal settings for incomplete or uncertain information items, where our postulates are instantiated: plausibility orderings, qualitative and quantitative possibility distributions, belief functions and convex sets of probabilities. The aim of this paper is to provide a unified picture of fusion rules across various uncertainty representation settings

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Second CLIPS Conference Proceedings, volume 1

Topics covered at the 2nd CLIPS Conference held at the Johnson Space Center, September 23-25, 1991 are given. Topics include rule groupings, fault detection using expert systems, decision making using expert systems, knowledge representation, computer aided design and debugging expert systems

Multi-attribute decision making with weighted description logics

We introduce a decision-theoretic framework based on Description Logics (DLs), which can be used to encode and solve single stage multi-attribute decision problems. In particular, we consider the background knowledge as a DL knowledge base where each attribute is represented by a concept, weighted by a utility value which is asserted by the user. This yields a compact representation of preferences over attributes. Moreover, we represent choices as knowledge base individuals, and induce a ranking via the aggregation of attributes that they satisfy. We discuss the benefits of the approach from a decision theory point of view. Furthermore, we introduce an implementation of the framework as a Protégé plugin called uDecide. The plugin takes as input an ontology as background knowledge, and returns the choices consistent with the user’s (the knowledge base) preferences. We describe a use case with data from DBpedia. We also provide empirical results for its performance in the size of the ontology using the reasoner Konclude

Cognitive Maps

undefine

Transformation of graphical models to support knowledge transfer

Menschliche Experten verfügen über die Fähigkeit, ihr Entscheidungsverhalten flexibel auf die jeweilige Situation abzustimmen. Diese Fähigkeit zahlt sich insbesondere dann aus, wenn Entscheidungen unter beschränkten Ressourcen wie Zeitrestriktionen getroffen werden müssen. In solchen Situationen ist es besonders vorteilhaft, die Repräsentation des zugrunde liegenden Wissens anpassen und Entscheidungsmodelle auf unterschiedlichen Abstraktionsebenen verwenden zu können. Weiterhin zeichnen sich menschliche Experten durch die Fähigkeit aus, neben unsicheren Informationen auch unscharfe Wahrnehmungen in die Entscheidungsfindung einzubeziehen. Klassische entscheidungstheoretische Modelle basieren auf dem Konzept der Rationalität, wobei in jeder Situation die nutzenmaximale Entscheidung einer Entscheidungsfunktion zugeordnet wird. Neuere graphbasierte Modelle wie Bayes\u27sche Netze oder Entscheidungsnetze machen entscheidungstheoretische Methoden unter dem Aspekt der Modellbildung interessant. Als Hauptnachteil lässt sich die Komplexität nennen, wobei Inferenz in Entscheidungsnetzen NP-hart ist. Zielsetzung dieser Dissertation ist die Transformation entscheidungstheoretischer Modelle in Fuzzy-Regelbasen als Zielsprache. Fuzzy-Regelbasen lassen sich effizient auswerten, eignen sich zur Approximation nichtlinearer funktionaler Beziehungen und garantieren die Interpretierbarkeit des resultierenden Handlungsmodells. Die Übersetzung eines Entscheidungsmodells in eine Fuzzy-Regelbasis wird durch einen neuen Transformationsprozess unterstützt. Ein Agent kann zunächst ein Bayes\u27sches Netz durch Anwendung eines in dieser Arbeit neu vorgestellten parametrisierten Strukturlernalgorithmus generieren lassen. Anschließend lässt sich durch Anwendung von Präferenzlernverfahren und durch Präzisierung der Wahrscheinlichkeitsinformation ein entscheidungstheoretisches Modell erstellen. Ein Transformationsalgorithmus kompiliert daraus eine Regelbasis, wobei ein Approximationsmaß den erwarteten Nutzenverlust als Gütekriterium berechnet. Anhand eines Beispiels zur Zustandsüberwachung einer Rotationsspindel wird die Praxistauglichkeit des Konzeptes gezeigt.Human experts are able to flexible adjust their decision behaviour with regard to the respective situation. This capability pays in situations under limited resources like time restrictions. It is particularly advantageous to adapt the underlying knowledge representation and to make use of decision models at different levels of abstraction. Furthermore human experts have the ability to include uncertain information and vague perceptions in decision making. Classical decision-theoretic models are based directly on the concept of rationality, whereby the decision behaviour prescribed by the principle of maximum expected utility. For each observation some optimal decision function prescribes an action that maximizes expected utility. Modern graph-based methods like Bayesian networks or influence diagrams make use of modelling. One disadvantage of decision-theoretic methods concerns the issue of complexity. Finding an optimal decision might become very expensive. Inference in decision networks is known to be NP-hard. This dissertation aimed at combining the advantages of decision-theoretic models with rule-based systems by transforming a decision-theoretic model into a fuzzy rule-based system. Fuzzy rule bases are an efficient implementation from a computational point of view, they can approximate non-linear functional dependencies and they are also intelligible. There was a need for establishing a new transformation process to generate rule-based representations from decision models, which provide an efficient implementation architecture and represent knowledge in an explicit, intelligible way. At first, an agent can apply the new parameterized structure learning algorithm to identify the structure of the Bayesian network. The use of learning approaches to determine preferences and the specification of probability information subsequently enables to model decision and utility nodes and to generate a consolidated decision-theoretic model. Hence, a transformation process compiled a rule base by measuring the utility loss as approximation measure. The transformation process concept has been successfully applied to the problem of representing condition monitoring results for a rotation spindle

Second CLIPS Conference Proceedings, volume 2

Papers presented at the 2nd C Language Integrated Production System (CLIPS) Conference held at the Lyndon B. Johnson Space Center (JSC) on 23-25 September 1991 are documented in these proceedings. CLIPS is an expert system tool developed by the Software Technology Branch at NASA JSC and is used at over 4000 sites by government, industry, and business. During the three days of the conference, over 40 papers were presented by experts from NASA, Department of Defense, other government agencies, universities, and industry

Uncertainty and indistinguishability. Application to modelling with words.

El concepte d'igualtat és fonamental en qualsevol teoria donat que és una noció essencial a l'hora de discernir entre els elements objecte del seu estudi i possibilitar la definició de mecanismes de classificació.Quan totes les propietats són perfectament precises (absència d'incertesa), hom obtè la igualtat clàssica a on dos objectes són considerats iguals si i només si comparteixen el mateix conjunt de propietats. Però, què passa quan considerem l'aparició d'incertesa, com en el cas a on els objectes compleixen una determinada propietat només fins a un cert grau?. Llavors, donat que alguns objectes seran més similars entre si que d'altres, sorgeix la necessitat de una noció gradual del concepte d'igualtat.Aquestes consideracions refermen la idea de que certs contextos requereixen una definició més flexible, que superi la rigidesa de la noció clàssica d'igualtat. Els operadors de T-indistingibilitat semblen bons candidats per aquest nou tipus d'igualtat que cerquem.D'altra banda, La Teoria de l'Evidència de Dempster-Shafer, com a marc pel tractament d'evidències, defineix implícitament una noció d'indistingibilitat entre els elements del domini de discurs basada en la seva compatibilitat relativa amb l'evidència considerada. El capítol segon analitza diferents mètodes per definir l'operador de T-indistingibilitat associat a una evidència donada.En el capítol tercer, després de presentar un exhaustiu estat de l'art en mesures d'incertesa, ens centrem en la qüestió del còmput de l'entropia quan sobre els elements del domini s'ha definit una relació d'indistingibilitat. Llavors, l'entropia hauria de ser mesurada no en funció de l'ocurrència d'events diferents, sinó d'acord amb la variabilitat percebuda per un observador equipat amb la relació d'indistingibilitat considerada. Aquesta interpretació suggereix el "paradigma de l'observador" que ens porta a la introducció del concepte d'entropia observacional.La incertesa és un fenomen present al món real. El desenvolupament de tècniques que en permetin el tractament és doncs, una necessitat. La 'computació amb paraules' ('computing with words') pretén assolir aquest objectiu mitjançant un formalisme basat en etiquetes lingüístiques, en contrast amb els mètodes numèrics tradicionals. L'ús d'aquestes etiquetes millora la comprensibilitat del llenguatge de representació delconeixement, a l'hora que requereix una adaptació de les tècniques inductives tradicionals.En el quart capítol s'introdueix un nou tipus d'arbre de decisió que incorpora les indistingibilitats entre elements del domini a l'hora de calcular la impuresa dels nodes. Hem anomenat arbres de decisió observacionals a aquests nou tipus, donat que es basen en la incorporació de l'entropia observacional en la funció heurística de selecció d'atributs. A més, presentem un algorisme capaç d'induir regles lingüístiques mitjançant un tractament adient de la incertesa present a les etiquetes lingüístiques o a les dades mateixes. La definició de l'algorisme s'acompanya d'una comparació formal amb altres algorismes estàndards.The concept of equality is a fundamental notion in any theory since it is essential to the ability of discerning the objects to whom it concerns, ability which in turn is a requirement for any classification mechanism that might be defined. When all the properties involved are entirely precise, what we obtain is the classical equality, where two individuals are considered equal if and only if they share the same set of properties. What happens, however, when imprecision arises as in the case of properties which are fulfilled only up to a degree? Then, because certain individuals will be more similar than others, the need for a gradual notion of equality arises.These considerations show that certain contexts that are pervaded with uncertainty require a more flexible concept of equality that goes beyond the rigidity of the classic concept of equality. T-indistinguishability operators seem to be good candidates for this more flexible and general version of the concept of equality that we are searching for.On the other hand, Dempster-Shafer Theory of Evidence, as a framework for representing and managing general evidences, implicitly conveys the notion of indistinguishability between the elements of the domain of discourse based on their relative compatibility with the evidence at hand. In chapter two we are concerned with providing definitions for the T-indistinguishability operator associated to a given body of evidence.In chapter three, after providing a comprehensive summary of the state of the art on measures of uncertainty, we tackle the problem of computing entropy when an indistinguishability relation has been defined over the elements of the domain. Entropy should then be measured not according to the occurrence of different events, but according to the variability perceived by an observer equipped with indistinguishability abilities as defined by the indistinguishability relation considered. This idea naturally leads to the introduction of the concept of observational entropy.Real data is often pervaded with uncertainty so that devising techniques intended to induce knowledge in the presence of uncertainty seems entirely advisable.The paradigm of computing with words follows this line in order to provide a computation formalism based on linguistic labels in contrast to traditional numerical-based methods.The use of linguistic labels enriches the understandability of the representation language, although it also requires adapting the classical inductive learning procedures to cope with such labels.In chapter four, a novel approach to building decision trees is introduced, addressing the case when uncertainty arises as a consequence of considering a more realistic setting in which decision maker's discernment abilities are taken into account when computing node's impurity measures. This novel paradigm results in what have been called --observational decision trees' since the main idea stems from the notion of observational entropy in order to incorporate indistinguishability concerns. In addition, we present an algorithm intended to induce linguistic rules from data by properly managing the uncertainty present either in the set of describing labels or in the data itself. A formal comparison with standard algorithms is also provided