A Study of (a, b)-Fuzzy Sublattices and (a, b)-Fuzzy Ideals of Distributive Lattices

Santosh R. Mitkari; Avinash M. Pawar; Avinash M. Deshmukh; Tushar R. Shinde; Manoj Tarambale; Sheetal S. Patil

doi:10.54105/ijam.A1259.07010427

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Published: 30-10-2026

DOI: https://doi.org/10.54105/ijam.A1259.07010427

Keywords:

Fuzzy Mathematics, Fuzzy Logic, Algebraic Structures, Distributive Lattice, Fuzzy Ideals, Fuzzy Sublattices, Generalised Fuzzy Algebra

Santosh R. Mitkari

Department of Engineering Science and Allied Engineering, Bharati Vidyapeeth's College of Engineering for Women, Pune (Maharashtra), India.

https://orcid.org/0000-0002-4689-5044

Avinash M. Pawar

Department of Mechanical Engineering, Bharati Vidyapeeth's College of Engineering for Women, Pune (Maharashtra), India.

https://orcid.org/0000-0002-5075-0032

Avinash M. Deshmukh

Department of Basic Science and Engineering, SCTR's Pune Institute of Computer Technology, Pune (Maharashtra), India.

https://orcid.org/0000-0002-7359-057X

Tushar R. Shinde

Department of Engineering Sciences, Keystone School of Engineering, Pune (Maharashtra), India.

https://orcid.org/0009-0007-9154-8774

Manoj Tarambale

Professor, Department of Electrical Engineering, PVG’s College of Engineering, Technology and Management, Pune (Maharashtra), India.

https://orcid.org/0000-0002-9428-8708

Sheetal S. Patil

Department of Computer Science & Business Systems, Bharati Vidyapeeth (Deemed to be University) College of Engineering, Pune (Maharashtra), India.

https://orcid.org/0000-0003-4381-1228

Abstract

The framework of fuzzy algebraic structures is extended to distributive lattices through the introduction and investigation of (a, b)-fuzzy sublattices and (a, b)-fuzzy ideals. Building on foundational work by Zadeh, Rosenfeld, Liu, Sharma, Yuan, Wu, and S. K. Nimbhorkar, this study generalises the perception of (a, b)-fuzzy subrings and (a, b)-fuzzy ideals from ring theory to lattice theory. The paper recalls key definitions and properties of fuzzy subsets in distributive lattices with least and greatest elements to provide the necessary preliminaries. Subsequently, (a, b)-fuzzy sublattices and (a, b)-fuzzy ideals are formally defined, their fundamental properties are investigated, and their relationships with classical fuzzy sublattices and fuzzy ideals are explored. This generalisation offers new perspectives and analytical tools for studying fuzziness in lattice-theoretic contexts.

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Vol. 6 No. 2 (2026): Volume-6 Issue-2, October 2026

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How to Cite

[1]

Santosh R. Mitkari, Avinash M. Pawar, Avinash M. Deshmukh, Tushar R. Shinde, Manoj Tarambale, and Sheetal S. Patil , Trans., “A Study of (a, b)-Fuzzy Sublattices and (a, b)-Fuzzy Ideals of Distributive Lattices”, IJAM, vol. 6, no. 2, pp. 56–59, Oct. 2026, doi: 10.54105/ijam.A1259.07010427.

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