Interval valued L-fuzzy prime ideals, triangular norms and partially ordered groups
- 144 Downloads
We introduce interval valued equiprime, 3-prime and c-prime L-fuzzy ideals of a nearring N by using interval valued t-norms and interval valued t-conorms. We characterize interval valued prime L-fuzzy ideals in terms of their level subsets. We define interval valued equisemiprime, 3-semiprime and c-semiprime L-fuzzy ideals of nearrings and study their properties. We find interrelations among different interval valued prime L-fuzzy ideals. We study these concepts further in a partially ordered group and define implications based on interval valued L-fuzzy ideals.
KeywordsLattice t-norm t-conorm Ideal Equiprime 3-prime c-prime
We thank the anonymous referees and the editor for their constructive comments and suggestions which improved this paper. All authors acknowledge Manipal University for their encouragement. The third author acknowledges St Joseph Engineering College, Mangaluru, India, for their encouragement.
Compliance with ethical standards
Conflicts of interest
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
- Goguen JA (1967) L-fuzzy sets. J Math Anal Appl 18(1):145–174Google Scholar
- Kazanc O, Yamak S (2008) Generalized fuzzy bi-ideals of semigroups. Soft Comput 12:1119–1124Google Scholar
- Kedukodi BS, Jagadeesha B, Kuncham SP (2016) Automorphisms, t-norms and t-conorms on a lattice, CommunicatedGoogle Scholar
- Kedukodi BS, Jagadeesha B, Kuncham SP, Juglal S (2017) Different prime graphs of a nearring with respect to an ideal. In: Nearrings, nearfields and related topics. World Scientific, Singapore, pp 185 -203. doi: 10.1142/9789813207363_0018
- Pilz G (1983) Near-rings. Revised edition. North Hollond, AmsterdamGoogle Scholar
- Wang GJ, Li XP (1996) TH interval valued fuzzy subgroups. J Lanzhou Univ 32:96–99Google Scholar