Vague sets are intuitionistic fuzzy sets

Bustince, Humberto; Burillo, P.

doi:10.1016/0165-0114(95)00154-9

Cited by 784 publications

(292 citation statements)

References 14 publications

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“…A grey number could be represented as a set of intervals with gaps in between. For example, g ± ∈ { [5,6], [10,12]} is a grey number where its underlying white number may get its value from [5,6] or [10,12], but we know for sure that it will not get its value within (6,10). This is clearly different from an interval [5,12] where (6, 10) is a valid part for candidate values.…”

Section: Generalised Grey Numbersmentioning

confidence: 79%

Grey sets and greyness

Yang

John

2012

Information Sciences

109

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This paper discusses the application of grey numbers for uncertainty representation. It highlights the difference between grey sets and interval-valued fuzzy sets, and investigates the degree of greyness for grey sets. It facilitates the representation of uncertainty not only for elements of a set, but also the set itself as a whole. Our results show that a grey set could be specified for interval-valued fuzzy sets or rough sets under special conditions. With the notion of grey sets and their associated degrees of greyness, various set operations between grey sets are discussed.

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Section: Generalised Grey Numbersmentioning

confidence: 79%

Grey sets and greyness

Yang

John

2012

Information Sciences

109

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“…In 1993, Gau and Buehrer introduced the concept of vague sets [40]. Later, in 1996, it was proved that vague sets are in fact A-IFSs [41].…”

Section: Relation To Other Extensionsmentioning

confidence: 99%

A Survey of Interval‐Valued Fuzzy Sets

Bustince

Montero

Pagola

et al. 2008

Handbook of Granular Computing

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“…Yet other concepts equivalent to interval-valued fuzzy sets are grey sets of (Deng, 1989) and vague sets of Gau and Buehrer (1993). See Bustince and Burillo (1996) for a full discussion of these notions.…”

Section: Interval--valued Fuzzy Setsmentioning

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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Vague sets are intuitionistic fuzzy sets

Cited by 784 publications

References 14 publications

Grey sets and greyness

Grey sets and greyness

A Survey of Interval‐Valued Fuzzy Sets

Fuzzy Sets: History and Basic Notions

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