Linear Diophantine fuzzy algebraic structures


KAMACI H.

JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING, vol.12, no.11, pp.10353-10373, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 11
  • Publication Date: 2021
  • Doi Number: 10.1007/s12652-020-02826-x
  • Journal Name: JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC
  • Page Numbers: pp.10353-10373
  • Keywords: Fuzzy set, Linear Diophantine fuzzy set, Group, Ring, Ideal, Field, Coding theory
  • Yozgat Bozok University Affiliated: Yes

Abstract

The main objective of this paper is to introduce some algebraic properties of finite linear Diophantine fuzzy subsets of group, ring and field. Relatedly, we define the concepts of linear Diophantine fuzzy subgroup and normal subgroup of a group, linear Diophantine fuzzy subring and ideal of a ring, and linear Diophantine fuzzy subfield of a field. We investigate their basic properties, relations and characterizations in detail. Furthermore, we establish the homomorphic images and preimages of the emerged linear Diophantine fuzzy algebraic structures. Finally, we describe linear Diophantine fuzzy code and investigate the relationships between this code and some linear Diophantine fuzzy algebraic structures.