Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributions

Dubois, Didier; Prade, Henri

doi:10.1016/0165-0114(91)90050-z

Cited by 687 publications

(136 citation statements)

References 119 publications

Supporting

Mentioning

133

Contrasting

Unclassified

Order By: Relevance

“…A fairly general approach to reasoning under uncertainty in so-called valuation-based networks has been proposed in [46,48,47]. It can be applied, for example, to upper and lower probabilities [52], Dempster-Shafer theory of evidence [12,13,42,43,49], and possibility theory [56,15,16], and has been implemented in the software tool PULCINELLA [41].…”

Section: Evidence Propagationmentioning

confidence: 99%

“…Thus, similar to the probabilistic case where logical, empirical, and subjective interpretations of probability can be distinguished, there is a large variety of suggestions for semantics of a degree of possibility. Among them are the view of possibility distributions as epistemic interpretations of fuzzy sets [56], the axiomatic approach to possibility theory based on possibility measures [15,16], and the approach that bases possibility theory on likelihoods [14]. In connection to Dempster-Shafer theory, possibility distributions are seen as contour functions of consonant belief functions [42], and in the framework of set-valued statistics, they are interpreted as falling shadows [53].…”

Section: Possibilistic Networkmentioning

confidence: 99%

See 1 more Smart Citation

Possibilistic Graphical Models

Borgelt

Gebhardt

Kruse

2000

Computational Intelligence in Data Mining

View full text Add to dashboard Cite

Graphical modeling is an important method to efficiently represent and analyze uncertain information in knowledge-based systems. Its most prominent representatives are Bayesian networks and Markov networks for probabilistic reasoning, which have been well-known for over ten years now. However, they suffer from certain deficiencies, if imprecise information has to be taken into account. Therefore possibilistic graphical modeling has recently emerged as a promising new area of research. Possibilistic networks are a noteworthy alternative to probabilistic networks whenever it is necessary to model both uncertainty and imprecision. Imprecision, understood as set-valued data, has often to be considered in situations in which information is obtained from human observers or imprecise measuring instruments. In this paper we provide an overview on the state of the art of possibilistic networks w.r.t. to propagation and learning algorithms.

show abstract

Section: Evidence Propagationmentioning

confidence: 99%

Section: Possibilistic Networkmentioning

confidence: 99%

Possibilistic Graphical Models

Borgelt

Gebhardt

Kruse

2000

Computational Intelligence in Data Mining

View full text Add to dashboard Cite

show abstract

“…It can be proven [7], that the results of the FATI method are a subset of those obtained using the FITA procedure:…”

Section: Approximate Reasoning With Knowledge Basementioning

confidence: 99%

Introduction to Fuzzy Systems

Czabański

Jeżewski

Łęski

2017

Studies in Fuzziness and Soft Computing

View full text Add to dashboard Cite

The following chapter describes the basic concepts of fuzzy systems and approximate reasoning. The study focuses mainly on fuzzy models based on Zadeh's compositional rule of inference. The presentation begins with an introduction of fundamental ideas of fuzzy conditional (if-then) rules. A collection of fuzzy if-then rules formulates the so-called knowledge base, which formally represents the knowledge to be processed during approximate reasoning. The subsequent sections present formal definitions related to the compositional rule of inference and approximate reasoning using a knowledge base. Theoretical considerations are supplemented with practical examples of fuzzy systems as the foundation of many modern structures. The description includes fuzzy systems proposed by Mamdani and Assilan, Takagi, Sugeno and Kang, and Tsukamoto. IntroductionThe main inspiration behind the introduction of fuzzy sets theory was the necessity for modeling real-world phenomena, which are inherently vague and ambiguous. Human knowledge about complex problems can be successfully represented using the imprecise terms of natural language. The theories of fuzzy sets and fuzzy logic provide formal tools for mathematical representation and efficient processing of such information.The term "system" is usually understood as a set of interacting components with well-defined structure and organized as an intricate whole that can be distinguished from the "external" environment. A system communicates with the environment 2.1 The typical structure of a fuzzy system through so-called inputs and outputs. Fuzzy systems are structures based on fuzzy techniques oriented towards information processing, where the usage of classical sets theory and binary logic is impossible or difficult. In the literature, terms such as fuzzy system, fuzzy model, system based on fuzzy rules, fuzzy controller, or fuzzy associative memory are used interchangeably depending on the application type [16]. Their main characteristic involves symbolic knowledge representation in a form of fuzzy conditional (if-then) rules.The typical structure of a fuzzy system (Fig. 2.1) consists of four functional blocks: the fuzzifier, the fuzzy inference engine, the knowledge base, and the defuzzifier. Both linguistic values (defined by fuzzy sets) and crisp (numerical) data can be used as inputs for a fuzzy system. If crisp data are applied, then the inference process is preceded by fuzzification, which assigns the appropriate fuzzy set to the nonfuzzy input. The values of input variables are mapped into linguistic values of the output variable by means of the appropriate method of approximate reasoning (inference engine) using expert knowledge, which is represented as a collection of fuzzy conditional rules (knowledge base). In addition to the linguistic values, the numerical data may be required as the fuzzy system output. In such cases defuzzification methods are used, which assign the representative crisp data to the resultant output fuzzy set.Practical applications of fuz...

show abstract

“…It has been successfully used in a variety of fields such as control theory (Lee, 1990), artificial intelligence (Dubois & Prade, 1991) and expert system (Zadeh, 1983). Compared with standard crisp logic in which the values are either "true" or "false", fuzzy logic evaluates the logic values in the form of the degree of truth (DoT) ranging from 0 to 1.…”

Section: Reconstruction-based Fuzzy Logic Of the Signs Of Nodesmentioning

confidence: 99%