Soft multisets theory

Shawkat Alkhazaleh, Abdul Razak Salleh, Nasruddin Hassan

Research output: Contribution to journalArticle

66 Citations (Scopus)

Abstract

In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. The solutions of such problems involve the use of mathematical principles based on uncertainty and imprecision. In this paper we recall the definition of a soft set, its properties and its operations. As a generalization of Molodtsov's soft set we introduce the definitions of a soft multiset, its basic operations such as complement, union and intersection. We give examples for these concepts. Basic properties of the operations are also given.

Original languageEnglish
Pages (from-to)3561-3573
Number of pages13
JournalApplied Mathematical Sciences
Volume5
Issue number69-72
Publication statusPublished - 2011

Fingerprint

Soft Set
Multiset
Set theory
Uncertainty
Imprecision
Set Theory
Union
Complement
Intersection
Concepts

Keywords

  • Soft multiset
  • Soft set

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Alkhazaleh, S., Salleh, A. R., & Hassan, N. (2011). Soft multisets theory. Applied Mathematical Sciences, 5(69-72), 3561-3573.

Soft multisets theory. / Alkhazaleh, Shawkat; Salleh, Abdul Razak; Hassan, Nasruddin.

In: Applied Mathematical Sciences, Vol. 5, No. 69-72, 2011, p. 3561-3573.

Research output: Contribution to journalArticle

Alkhazaleh, S, Salleh, AR & Hassan, N 2011, 'Soft multisets theory', Applied Mathematical Sciences, vol. 5, no. 69-72, pp. 3561-3573.
Alkhazaleh S, Salleh AR, Hassan N. Soft multisets theory. Applied Mathematical Sciences. 2011;5(69-72):3561-3573.
Alkhazaleh, Shawkat ; Salleh, Abdul Razak ; Hassan, Nasruddin. / Soft multisets theory. In: Applied Mathematical Sciences. 2011 ; Vol. 5, No. 69-72. pp. 3561-3573.
@article{0f906fd16bc647238aa3c46a63d52e12,
title = "Soft multisets theory",
abstract = "In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. The solutions of such problems involve the use of mathematical principles based on uncertainty and imprecision. In this paper we recall the definition of a soft set, its properties and its operations. As a generalization of Molodtsov's soft set we introduce the definitions of a soft multiset, its basic operations such as complement, union and intersection. We give examples for these concepts. Basic properties of the operations are also given.",
keywords = "Soft multiset, Soft set",
author = "Shawkat Alkhazaleh and Salleh, {Abdul Razak} and Nasruddin Hassan",
year = "2011",
language = "English",
volume = "5",
pages = "3561--3573",
journal = "Applied Mathematical Sciences",
issn = "1312-885X",
publisher = "Hikari Ltd.",
number = "69-72",

}

TY - JOUR

T1 - Soft multisets theory

AU - Alkhazaleh, Shawkat

AU - Salleh, Abdul Razak

AU - Hassan, Nasruddin

PY - 2011

Y1 - 2011

N2 - In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. The solutions of such problems involve the use of mathematical principles based on uncertainty and imprecision. In this paper we recall the definition of a soft set, its properties and its operations. As a generalization of Molodtsov's soft set we introduce the definitions of a soft multiset, its basic operations such as complement, union and intersection. We give examples for these concepts. Basic properties of the operations are also given.

AB - In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. The solutions of such problems involve the use of mathematical principles based on uncertainty and imprecision. In this paper we recall the definition of a soft set, its properties and its operations. As a generalization of Molodtsov's soft set we introduce the definitions of a soft multiset, its basic operations such as complement, union and intersection. We give examples for these concepts. Basic properties of the operations are also given.

KW - Soft multiset

KW - Soft set

UR - http://www.scopus.com/inward/record.url?scp=81555225802&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=81555225802&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:81555225802

VL - 5

SP - 3561

EP - 3573

JO - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

SN - 1312-885X

IS - 69-72

ER -