Work

Characterizations of Products of IVIFSS-Subalgebras and Ideals in Sheffer Stroke Hilbert Algebras

Year: 2026

Type: article

Abstract: This paper develops a comprehensive framework for interval-valued intuitionistic fuzzy Sheffer stroke subsets (IVIFSS) within Sheffer stroke Hilbert algebras (SSHA).We introduce and characterize IVIFSS-subalgebras and IVIFSS-ideals, proving that these structures are closed under Cartesian products, intersections, and the operators ⊕ and ⊗.It is further shown that the product of two IVIFSS-subalgebras (or IVIFSS-ideals) preserves the corresponding algebraic properties in the product algebra.By employing level subset characterizations, we derive necessary and sufficient conditions for IVIFSS-filters and IVIFSSdeductive systems, demonstrating that both notions are equivalent.These results generalize classical theories of subalgebras, ideals, and filters in Hilbert algebras to the interval-valued intuitionistic fuzzy context, thereby enriching the study of fuzzy algebraic logic and providing a unified algebraic foundation for approximate reasoning frameworks.

Source: Asia Pacific Journal of Mathematics

DOI: 10.28924/apjm/13-57

Authors: Tahsin Oner, Arsham Borumand Saeid, Aiyared Iampan, Kannan Geetha, Neelamegarajan Rajesh

Institutions: Ege University, Shahid Bahonar University of Kerman, University of Phayao, Rajah Serfoji Government College (Autonomous)

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: University of Phayao, Thailand Science Research and Innovation

OpenAlex ID: W7160950520

FWCI:

Cites:

Cited by:

Related to: 10