Representations and constructions of similarity-based fuzzy orderings

Bodenhofer, Ulrich

doi:10.1016/s0165-0114(02)00436-0

Cited by 93 publications

(55 citation statements)

References 14 publications

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“…Conventions of usual outranking relations are retrieved when restricting to Boolean values. The expression of antisymmetry must be handled with care in connection to the underlying similarity relation on the preference scale, as shown by Bodenhofer [36]. The above type of fuzzy relations presupposes that objects to be compared are known precisely enough to allow for a precise quantification of preference intensity.…”

Section: The Two Meanings Of Fuzzy Preference Relationsmentioning

confidence: 99%

The role of fuzzy sets in decision sciences: Old techniques and new directions

Dubois

2011

Fuzzy Sets and Systems

269

118

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We try to provide a tentative assessment of the role of fuzzy sets in decision analysis. We discuss membership functions, aggregation operations, linguistic variables, fuzzy intervals and the valued preference relations they induce. The importance of the notion of bipolarity and the potential of qualitative evaluation methods are also pointed out. We take a critical standpoint on where we stand, in order to highlight the actual achievements and question what is often considered debatable by decision scientists observing the fuzzy decision analysis literature.

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Section: The Two Meanings Of Fuzzy Preference Relationsmentioning

confidence: 99%

The role of fuzzy sets in decision sciences: Old techniques and new directions

Dubois

2011

Fuzzy Sets and Systems

269

118

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“…(2) [31,2] Let F ⊆ I X be a family of fuzzy subsets in X and * (F) be the Valverde order determined by F, i.e.,…”

Section: Example 39mentioning

confidence: 99%

“…pseudo-metrics) on X for special triangular norms on [0, 1], see, e.g. [2,7,9,12,19]. And, since a fuzzy equivalence R on a set X can also be viewed as a generalized metric on X, it generates a topology on X in a natural way [15,9].…”

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confidence: 99%

Fuzzy preorder and fuzzy topology

Lai

Zhang

2006

Fuzzy Sets and Systems

196

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“…Bodenhofer and Klawonn [6] propose a fuzzy extension of the gamma coefficient based on concepts of fuzzy orderings and -equivalence relations, where denotes a t-norm [4]. A fuzzy relation E : U × U → [0, 1] is called fuzzy equivalence with respect to a t-norm , for brevity -equivalence, if it is reflexive (E(u, u) = 1),…”

Section: Fuzzy Equivalence and Order Relationsmentioning

confidence: 99%

Fuzzy Rules in Data Mining: From Fuzzy Associations to Gradual Dependencies

Hüllermeier

2012

Combining Experimentation and Theory

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Fuzzy rules, doubtlessly one of the most powerful tools of fuzzy logic, have not only been used successfully in established application areas like control engineering and approximate reasoning, but more recently also in the field of data mining. In this chapter, we provide a synthesis of different approaches to fuzzy association analysis, that is, the data-driven extraction of interesting patterns expressed in the form of fuzzy rules. In this regard, we highlight a specific advantage of a fuzzy in comparison to a conventional approach, namely an increased expressiveness that allows for representing patterns of interest in a more distinctive way. Therefore, we specifically focus on the modeling of a less common type of pattern, namely gradual dependencies between attributes in a data set.

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Representations and constructions of similarity-based fuzzy orderings

Cited by 93 publications

References 14 publications

The role of fuzzy sets in decision sciences: Old techniques and new directions

The role of fuzzy sets in decision sciences: Old techniques and new directions

Fuzzy preorder and fuzzy topology

Fuzzy Rules in Data Mining: From Fuzzy Associations to Gradual Dependencies

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