### 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 language | English |
---|---|

Pages (from-to) | 3561-3573 |

Number of pages | 13 |

Journal | Applied Mathematical Sciences |

Volume | 5 |

Issue number | 69-72 |

Publication status | Published - 2011 |

### Fingerprint

### Keywords

- Soft multiset
- Soft set

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Applied Mathematical Sciences*,

*5*(69-72), 3561-3573.

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

Research output: Contribution to journal › Article

*Applied Mathematical Sciences*, vol. 5, no. 69-72, pp. 3561-3573.

}

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 -