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74
Fuzzy mathematical morphologies: A comparative study
 Pattern Recognition
, 1995
"... AbstractFuzzy set theory has found a promising field of application i the domain of digital image processing, since fuzziness i an intrinsic property of images. For dealing with spatial information i this framework from the signal evel to the highest decision level, several attempts have been made ..."
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Cited by 58 (5 self)
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AbstractFuzzy set theory has found a promising field of application i the domain of digital image processing, since fuzziness i an intrinsic property of images. For dealing with spatial information i this framework from the signal evel to the highest decision level, several attempts have been made to define mathematical morphology on fuzzy sets. The purpose of this paper is to present and discuss the different ways to build a fuzzy mathematical morphology. We will compare their properties with respect o mathematical morphology and to fuzzy sets and interpret them in terms of logic and decision theory. Fuzzy sets Mathematical morphology Fuzzy mathematical morphology Dilation Erosion Opening Closing Fuzzification Triangular norms and conorms Stochastic geometry Approximate r asoning Decision making Uncertain and imprecise spatial information Data fusion I.
What Are Fuzzy Rules and How to Use Them
 Fuzzy Sets and Systems
, 1996
"... Fuzzy rules have been advocated as a key tool for expressing pieces of knowledge in "fuzzy logic". However, there does not exist a unique kind of fuzzy rules, nor is there only one type of "fuzzy logic". This diversity has caused many a misunderstanding in the literature of fuzzy ..."
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Cited by 57 (14 self)
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Fuzzy rules have been advocated as a key tool for expressing pieces of knowledge in "fuzzy logic". However, there does not exist a unique kind of fuzzy rules, nor is there only one type of "fuzzy logic". This diversity has caused many a misunderstanding in the literature of fuzzy control. The paper is a survey of different possible semantics for a fuzzy rule and shows how they can be captured in the framework of fuzzy set and possibility theory. It is pointed out that the interpretation of fuzzy rules dictates the way the fuzzy rules should be combined. The various kinds of fuzzy rules considered in the paper (gradual rules, certainty rules, possibility rules, and others) have different inference behaviors and correspond to various intended uses and applications. The representation of fuzzy unlessrules is briefly investigated on the basis of their intended meaning. The problem of defining and checking the coherence of a block of parallel fuzzy rules is also briefly addressed. This iss...
A Logic Programming Framework for Possibilistic Argumentation with Vague Knowledge
 In Proc. of the Intl. Conf. in Uncertainty in Art. Intelligence. (UAI
, 2004
"... Defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning from incomplete and potentially inconsistent knowledge. Defeasible Logic Programming (DeLP) is a defeasible argumentation formalism based on an extension of logic programm ..."
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Cited by 33 (19 self)
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Defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning from incomplete and potentially inconsistent knowledge. Defeasible Logic Programming (DeLP) is a defeasible argumentation formalism based on an extension of logic programming.
FUZZY AGGREGATION OF NUMERICAL PREFERENCES
"... The problem of aggregating numerical values is addressed in this chapter. The first part deals with the aggregation of criteria into a single one. Properties which are suitable for this case are presented, together with the most common aggregation operators. A special section is devoted to ordered ..."
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Cited by 27 (6 self)
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The problem of aggregating numerical values is addressed in this chapter. The first part deals with the aggregation of criteria into a single one. Properties which are suitable for this case are presented, together with the most common aggregation operators. A special section is devoted to ordered weighted averaging (OWA) operators, and fuzzy integrals. Then, relation between properties, links between operators, characterization of some operators are presented. An important section is devoted to the behavioral analysis of OWA operators and fuzzy integrals, linking values of parameters with the attitude of the decision maker. The last section of this first part is concerned with the problem of identification of operators in a practical problem, a key issue in every application. The second part is devoted to special aspects in aggregation of preferences, in a multiattribute context. The Pareto principle is explained, and then the agreementdiscordance principle, which is the basis of ELECTRE III and IV, is addressed.
Equality Relations as a Basis for Fuzzy Control
 Fuzzy Sets and Systems
, 1994
"... : The aim of this paper is to introduce a fuzzy control model with wellfounded semantics in order to explain the concepts applied in fuzzy control. Assuming that the domains of the input and output variables for the process are endowed with equality relations, that reflect the indistinguishabili ..."
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Cited by 17 (2 self)
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: The aim of this paper is to introduce a fuzzy control model with wellfounded semantics in order to explain the concepts applied in fuzzy control. Assuming that the domains of the input and output variables for the process are endowed with equality relations, that reflect the indistinguishability of values lying closely together, the use of triangular and trapezoidal membership functions can be justified and maxu inference where u is a tnorm turns out to be a consequence of our model. Distinguishing between a functional and a relational view of the control rules it is possible to explain when defuzzification strategies like MOM or COA are appropriate or lead to undesired results. Keywords: Fuzzy control; equality relation 1 Introduction The basic techniques of fuzzy control were already known in 1974 [18, 21], but due to the large number of successful applications of fuzzy controllers in recent years, especially in Japan, the interest of both practitioners and theorists in f...
Semantics of Quotient Operators in Fuzzy Relational Databases
 Fuzzy Sets and Systems
, 1996
"... The quotient operator plays an important role for query evaluation in relational databases. Its extension to fuzzy databases raises the question of the intended interpretation of the intermediary degrees attached to the items in the fuzzy relations. This note points out that the fuzzy quotient opera ..."
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Cited by 17 (6 self)
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The quotient operator plays an important role for query evaluation in relational databases. Its extension to fuzzy databases raises the question of the intended interpretation of the intermediary degrees attached to the items in the fuzzy relations. This note points out that the fuzzy quotient operator should be defined in slightly different ways depending on the possible interpretations of the degrees: levels of satisfaction of a gradual property, levels of importance of a required property, uncertainty pertaining to the membership of an element to a subset. (*) This short paper is a revised and slightly expanded version of a note entitled "Quotient operators in fuzzy relational databases" presented at the Second European Congress on Intelligent Techniques and Soft Computing (EUFIT'94), Aachen, Germany, September 2024, 1994 and which appears pp. 357360 in the Proceedings. 2 1. Introduction Quotient operations aim at finding out the subrelation R S of a relation R, containing ...
Timed Possibilistic Logic
 Handbook of logic in Artificial Intelligence and logic programming
, 1991
"... . This paper is an attempt to cast both uncertainty and time in a logical framework. It generalizes possibilistic logic, previously developed by the authors, where each classical formula is associated with a weight which obeys the laws of possibility theory. In the possibilistic temporal logic we pr ..."
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Cited by 17 (4 self)
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. This paper is an attempt to cast both uncertainty and time in a logical framework. It generalizes possibilistic logic, previously developed by the authors, where each classical formula is associated with a weight which obeys the laws of possibility theory. In the possibilistic temporal logic we present here, each formula is associated with a time set (a fuzzy set in the more general case) which represents the set of instants where the formula is certainly true (more or less certainly true in the general case). When a particular instant is fixed we recover possibilistic logic. Timed possibilistic logic generalizes possibilistic logic also in the sense that we substitute the lattice structure of the set of the (fuzzy) subsets of the temporal scale to the lattice structure underlying the certainty weights in possibilistic logic. Thus many results from possibilistic logic can be straightforwardly generalized to timed possibilistic logic. Illustrative examples are given. 1. Introduction ...
Graphical Models
 In Proceedings of International School for the Synthesis of Expert Knowledge (ISSEK’98
, 2002
"... Graphical modeling is an important method to efficiently represent and analyze uncertain information in knowledgebased systems. Its most prominent representatives are Bayesian networks and Markov networks for probabilistic reasoning, which have been wellknown for over ten years now. However, they ..."
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Cited by 17 (0 self)
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Graphical modeling is an important method to efficiently represent and analyze uncertain information in knowledgebased systems. Its most prominent representatives are Bayesian networks and Markov networks for probabilistic reasoning, which have been wellknown 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 setvalued 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. 1
Fuzzy Control on the Basis of Equality Relations  with an Example from Idle Speed Control
 IEEE Transactions on Fuzzy Systems
, 1995
"... The way engineers use fuzzy control in real world applications is often not coherent with an understanding of the control rules as logical statements or implications. In most cases fuzzy control can be seen as an interpolation of a partially specified control function in a vague environment, which r ..."
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Cited by 15 (3 self)
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The way engineers use fuzzy control in real world applications is often not coherent with an understanding of the control rules as logical statements or implications. In most cases fuzzy control can be seen as an interpolation of a partially specified control function in a vague environment, which reflects the indistinguishability of measurements or control values. In this paper we show that equality relations turn out to be the natural way to represent such vague environments and we develop suitable interpolation methods to obtain a control function. As a special case of our approach we obtain Mamdani's model and can justify the inference mechanism in this model and the use of triangular membership functions not only for the reason of simplified computations, and we can explain why typical fuzzy partitions are preferred. We also obtain a criterion for reasonable defuzzification strategies. The fuzzy control methodology introduced in this paper has been applied successfully in a case s...