Fuzzy shadows

Chakrabarty, Kankana; Biswas, Ranjit; Nanda, Sudarsan

doi:10.1016/s0165-0114(97)00109-7

Cited by 20 publications

(8 citation statements)

References 10 publications

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“…Chakrabarty et al 21 consider the concept of shadow bags introduced by Blizard and the theory of fuzzy bags developed by Yager 5 to generalize the concept of fuzzy bags. However, we have shown 11,12 that Yager's propositions suffer from a serious drawback: although crisp bags are considered as special cases of fuzzy bags, fuzzy sets are not always special cases of fuzzy bags.…”

Section: Blizardmentioning

confidence: 99%

The set of fuzzy relative integers and fuzzy bags

RocacherDaniel

BoscPatrick

2009

Int. J. Intell. Syst.

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A characterization of fuzzy bags with conjunctive fuzzy integers (N f ) provides a general framework in which sets, bags, fuzzy sets, and fuzzy bags are treated in a uniform way. In this context, the difference between two fuzzy bags does not always exist and, in such cases, only approximations of the difference have been defined. The problem comes from the fact that the fuzzy bag model considered so far is based on positive fuzzy integers. In this paper, we construct the set of fuzzy relative integers (Z f ) where the existence of negative multiplicities allows us to define exact complementations. Then we define fuzzy bags on Z f , which offer a well-founded framework in which the difference of two fuzzy bags is always defined. C 2009 Wiley Periodicals, Inc.

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Section: Blizardmentioning

confidence: 99%

The set of fuzzy relative integers and fuzzy bags

RocacherDaniel

BoscPatrick

2009

Int. J. Intell. Syst.

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“…On the contrary, a bag is a type of collection in which redundancy of objects is not only allowed, but it also plays a key role in determining the behaviour of the objects [9], [7], [15], [12], [2], [8], [4]. Some algebraic structures like the group, semigroup, abelian group, etc.…”

Section: Introductionmentioning

confidence: 99%

On B-groups

Chakrabarty

2013

2013 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)

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The notion of bags play an essential role in dealing with knowledge representation problems where object classes allow repeated occurrence of elements. Sometimes bags with some special conditions can be drawn from a given set. Under these situations, is possible to define some algebraic structures on the given set.The present paper considers the situation when some bags with special conditions are drawn from a set, which, under a given operation, forms a group. Consequently, it demonstrates how an existing group structure defined on a given set can induce special structures on some bags drawn from this set. Hence, the notions of induced B-groups, induced abelian B-groups, and induced semi B-groups are introduced and discussed. Further, some characteristics of B-groups, abelian B-groups, and semi BGroups are studied.

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“…8 for additional references). Bags have been extended to fuzzy bags in several different ways, 1,5,9 with similar applications.…”

Section: Introductionmentioning

confidence: 99%

An extended characterization of fuzzy bags

DelgadoMiguel

Martín-BautistaMaría-José

SánchezDaniel

et al. 2009

Int. J. Intell. Syst.

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The algebraic structures known as bags were introduced by R. Yager as set-like algebraic structures where elements are allowed to be repeated. Since the original papers by Yager, different definitions of the concept of fuzzy bag, and the corresponding operators, are available in the literature, as well as some extensions of the union, intersection and difference operators of sets, and new algebraic operators.In general, the current definitions of bag pose very interesting issues related to the ontological aspects and practical use of bags. In this paper, we introduce a characterization of bags viewing them as the result of a count operation on the basis of a mathematical correspondence. We also discuss on the extension of our alternative characterization of bags to the fuzzy case. On these basis, we introduce some operators on bags and fuzzy bags, and we compare them to existing approaches. Finally, we deal with the case where no information about the correspondence is available, and only bounds can be provided for the count of elements of the result of algebraic operators. For this purpose, the notion of IC-bag (Chakrabarty, in: Proc.

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Fuzzy shadows

Cited by 20 publications

References 10 publications

The set of fuzzy relative integers and fuzzy bags

The set of fuzzy relative integers and fuzzy bags

On B-groups

An extended characterization of fuzzy bags

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