Logic Connectives for Soft Sets and Fuzzy Soft Sets

Author

Ali, Muhammad Irfan ; Shabir, Muhammad

Author_Institution

Dept. of Math., Islamabad Model Coll. for Boys, Islamabad, Pakistan

Volume

22

Issue

6

fYear

2014

fDate

Dec. 2014

Firstpage

1431

Lastpage

1442

Abstract

Collections of soft sets and fuzzy soft sets are complete modular lattices with respect to certain binary operations. Therefore, logic connectives such as Triangular norms, Triangular conorms, and implications may be studied for them. A major hurdle in this study is that soft sets and fuzzy soft sets are not sets and fuzzy sets, respectively. Actually, they are parameterized collections of subsets and fuzzy subsets of a set. While studying logic connective for soft sets and fuzzy soft sets, one has to consider not only the subsets or fuzzy subsets but the parameters involved as well. In this paper, techniques have been devised to study logic connectives for soft sets and fuzzy soft sets.

Keywords

fuzzy set theory; binary operations; fuzzy soft sets; fuzzy subset; implications; logic connectives; modular lattices; triangular conorm; triangular norm; Fuzzy logic; Fuzzy set theory; Fuzzy sets; Lattices; Single photon emission computed tomography; $t$-conorms; $t$-norms; Fuzzy soft sets; implications; soft sets;

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/TFUZZ.2013.2294182

Filename

6678757