Idealistic vague soft rings and vague soft ring homomorphism

Ganeshsree Selvachandran, Abdul Razak Salleh

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Soft set theory, proposed by Molodtsov has been regarded as an effective mathematical tool to deal with uncertainties. Vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of [0, 1]. Such a set is characterized by a truth-membership function and a falsemembership function. Thus, a vague set is actually a form of fuzzy set, albeit a more accurate form of fuzzy set. Hence the concept of vague soft sets were introduced as an extension to the notion of soft sets, as a means to overcome the problem of assigning a suitable value for the grade of membership of an element in a set since the exact grade of membership may be unknown. Hence using the concept of vague soft sets, we are able to ascertain that the grade of membership of an element lies within a certain closed interval which can help to overcome the problems faced when using ordinary soft sets or fuzzy soft sets. In this paper, we introduce the novel concept of idealistic vague soft rings and vague soft ring homomorphism in Rosenfeld's sense. The notion of idealistic vague soft rings is an extension to the concept of vague soft rings and vague soft ideals of a ring. The basic properties and structural characteristics of these concepts are also studied and discussed.

Original languageEnglish
Pages (from-to)1275-1290
Number of pages16
JournalInternational Journal of Mathematical Analysis
Volume6
Issue number25-28
Publication statusPublished - 2012

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Soft Set
Vague Set
Homomorphism
Ring
Fuzzy Sets
Closed interval
Set Theory
Membership Function
Concepts
Uncertainty
Unknown

Keywords

  • Idealistic vague soft rings
  • Vague soft ideals
  • Vague soft ring homomorphism
  • Vague soft rings
  • Vague soft sets

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Idealistic vague soft rings and vague soft ring homomorphism. / Selvachandran, Ganeshsree; Salleh, Abdul Razak.

In: International Journal of Mathematical Analysis, Vol. 6, No. 25-28, 2012, p. 1275-1290.

Research output: Contribution to journalArticle

Selvachandran, G & Salleh, AR 2012, 'Idealistic vague soft rings and vague soft ring homomorphism', International Journal of Mathematical Analysis, vol. 6, no. 25-28, pp. 1275-1290.
Selvachandran, Ganeshsree ; Salleh, Abdul Razak. / Idealistic vague soft rings and vague soft ring homomorphism. In: International Journal of Mathematical Analysis. 2012 ; Vol. 6, No. 25-28. pp. 1275-1290.
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