A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory

Luca, Aldo de; Termini, Settimo

doi:10.1016/b978-1-4832-1450-4.50020-1

Cited by 261 publications

(400 citation statements)

References 4 publications

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“…As it is usually done, Campello takes the intersection of fuzzy binary relations as the t-norm of the membership degrees of the pairs, and he uses the sigma-count principle for defining the fuzzy set cardinality (see [6]). Thus, the coefficients a, b, c, d are obtained as follows:…”

Section: The Campello's Fuzzy Rand Indexmentioning

confidence: 99%

Lazy Induction of Descriptions Using Two Fuzzy Versions of the Rand Index

Armengol¹,

García-Cerdaña²

2010

Communications in Computer and Information Science

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Abstract. In this paper we introduce an extension of the lazy learning method called Lazy Induction of Descriptions (LID). This new version is able to deal with fuzzy cases, i.e., cases described by attributes taking continuous values represented as fuzzy sets. LID classifies new cases based on the relevance of the attributes describing them. This relevance is assessed using a distance measure that compares the correct partition (i.e., the correct classification of cases) with the partitions induced by each one of the attributes. The fuzzy version of LID introduced in this paper uses two fuzzy versions of the Rand index to compare fuzzy partitions: one proposed by Campello and another proposed by Hüllermeier and Rifqi. We experimented with both indexes on data sets from the UCI machine learning repository.

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Section: The Campello's Fuzzy Rand Indexmentioning

confidence: 99%

Lazy Induction of Descriptions Using Two Fuzzy Versions of the Rand Index

Armengol¹,

García-Cerdaña²

2010

Communications in Computer and Information Science

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“…It is therefore natural to ask for the degree of fuzziness of a set, or, to put it another way, the global difficulty of deciding which elements belongs to a set. The answer is given by the theory of "measures of fuzziness", firstly proposed in [4]. For a survey of this theory see [5].…”

Section: Measures Of Fuzzinessmentioning

confidence: 99%

A fuzzy methodology to alleviate information overload in eLearning

D’Asaro¹,

Perticone²,

Tabacchi³

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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Some aspects of eLearning experience can be enhanced in a very natural way by using the basic tools offered by fuzzy logic. As a matter of example, consider the uncontrolled growth of information produced in a collaborative-oriented context, in which each participant (e.g. students, teachers) is able to insert and share new contents (e.g. comments, texts) concerning a university course. All the incrementally added pieces of information can be evaluated in several ways: by the intervention of a "dictator" (e.g. the teacher), using a rating form, or even according to the frequency of access. As contents rapidly become unusable for the effects of information overload, basic tools of fuzzy logic such as membership functions and measures of fuzziness can help to distinguish between relevant and trivial content, without thereby canceling any contribution. This very same idea can of course also be applied to different contexts.

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“…De Luca and Termini (1972) introduced this definition and called it the power of a fuzzy set. It evaluates "how many" elements F contains.…”

Section: Scalar Characteristics Of a Fuzzy Setmentioning

confidence: 99%

“…-) The idea of uncertainty of membership decision leads to the entropic view of De Luca and Termini (1972):…”

Section: Scalar Characteristics Of a Fuzzy Setmentioning

confidence: 99%

Fuzzy Sets: History and Basic Notions

Dubois¹,

Ostasiewicz

Prade³

2000

The Handbooks of Fuzzy Sets Series

139

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Abstract. This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's works have cristalized and popularized a concern that has appeared in the first half of the century, mainly in philosophical circles. Another purpose of the paper is to scan the basic definitions in the field, that are required for a proper reading of the rest of the volume, as well as the other volumes of the Handbooks of Fuzzy Sets Series. This Chapter also contains a discussion on operational semantics of the generally too abstract notion of membership function. Lastly, a survey of variants of fuzzy sets and related matters is provided.

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A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory

Cited by 261 publications

References 4 publications

Lazy Induction of Descriptions Using Two Fuzzy Versions of the Rand Index

Lazy Induction of Descriptions Using Two Fuzzy Versions of the Rand Index

A fuzzy methodology to alleviate information overload in eLearning

Fuzzy Sets: History and Basic Notions

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