Mathematics and Statistics Vol. 10(5), pp. 1121 - 1126
DOI: 10.13189/ms.2022.100523
Reprint (PDF) (212Kb)

Anti-hesitant Fuzzy Subalgebras, Ideals and Deductive Systems of Hilbert Algebras

Aiyared Iampan ^1,*, S. Yamunadevi ², P. Maragatha Meenakshi ³, N. Rajesh ^4
1 Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand
² Department of Mathematics, Vivekanandha College of Arts and Science for Women, Tiruchengode-637205, Tamilnadu, India
³ Department of Mathematics, Periyar E.V.R College, Tiruchirappalli (affiliated to Bharathidasan University), Tiruchirappalli 620023, Tamilnadu, India
⁴ Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamilnadu, India

ABSTRACT

The Hilbert algebra, one of several algebraic structures, was first described by Diego in 1966 [7] and has since been extensively studied by other mathematicians. Torra [18] was the first to suggest the idea of hesitant fuzzy sets (HFSs) in 2010, which is a generalization of the fuzzy sets defined by Zadeh [20] in 1965 as a function from a reference set to a power set of the unit interval. The significance of the ideas of hesitant fuzzy subalgebras, ideals, and filters in the study of the different logical algebras aroused our interest in applying these concepts to Hilbert algebras. In this paper, the concepts of HFSs to subalgebras (SAs), ideals (IDs), and deductive systems (DSs) of Hilbert algebras are introduced in terms of anti-types. We call them anti-hesitant fuzzy subalgebras (AHFSAs), anti-hesitant fuzzy ideals (AHFIDs), and anti-hesitant fuzzy deductive systems (AHFDSs). The relationships between AHFSAs, AHFIDs, and AHFDSs and their lower and strong level subsets are provided. As a result of the study, we found their generalization as follows: every AHFID of a Hilbert algebra Ω is an AHFSA and an AHFDS of Ω. We also study and find the conditions for the complement of an HFS to be an AHFSA, an AHFID, and an AHFDS. In addition, the relationships between the complements of AHFSAs, AHFIDs, and AHFDSs and their upper and strong level subsets are also provided.

KEYWORDS
Hilbert Algebra, Anti-hesitant Fuzzy Subalgebra, Anti-hesitant Fuzzy Ideal and Anti-hesitant Fuzzy Deductive System

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Aiyared Iampan , S. Yamunadevi , P. Maragatha Meenakshi , N. Rajesh , "Anti-hesitant Fuzzy Subalgebras, Ideals and Deductive Systems of Hilbert Algebras," Mathematics and Statistics, Vol. 10, No. 5, pp. 1121 - 1126, 2022. DOI: 10.13189/ms.2022.100523.

(b). APA Format:
Aiyared Iampan , S. Yamunadevi , P. Maragatha Meenakshi , N. Rajesh (2022). Anti-hesitant Fuzzy Subalgebras, Ideals and Deductive Systems of Hilbert Algebras. Mathematics and Statistics, 10(5), 1121 - 1126. DOI: 10.13189/ms.2022.100523.