A novel concept of (m, n)-ary subhypermodules in the framework of fuzzy sets


Kazanci O., Davvaz B., Yilmaz S.

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, vol.32, no.3, pp.2437-2446, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.3233/jifs-16419
  • Journal Name: JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2437-2446
  • Keywords: (m,n)-ary hypermodules, (is an element of, is an element of boolean OR q(k))- fuzzy (m, n)-ary subhypermodules, ((is an element of)over-bar, (is an element of)over-bar boolean OR (q(k))over-bar)-fuzzy (m, n)-ary subhypermodules, fuzzy (m, n)-ary subhypermodules with thresholds, N-ARY HYPERGROUPS, MANY-VALUED IMPLICATIONS, KRASNER (M, N)-HYPERRINGS, HYPERRINGS, PRIME, HYPERMODULES, SUBMODULES, SUBGROUP
  • Karadeniz Technical University Affiliated: Yes

Abstract

This paper provides a continuation of ideas presented by Davvaz and Corsini in [20]. We introduce the concepts of (is an element of, is an element of boolean OR q(k))- fuzzy (m, n)-ary subhypermodules and ((is an element of) over bar, (is an element of) over bar boolean OR (q) over bar (k))-fuzzy (m, n)-ary subhypermodules in an (m, n)-ary hypermodule, which are generalization of the concepts as given in [20]. Different classes of (m, n)-ary hypermodules are characterized by the properties of these fuzzy (m, n)-ary subhypermodules. Using the notion of fuzzy (m, n)-ary subhypermodule with thresholds, characterization of fuzzy (m, n)-ary subhypermodules, (is an element of, is an element of boolean OR q(k))-fuzzy (m, n)-ary subhypermodules and ((is an element of) over bar, (is an element of) over bar boolean OR (q) over bar (k))-fuzzy (m, n)-ary subhypermodules are discussed.