A Study of (a, b)-Fuzzy Sublattices and (a, b)-Fuzzy Ideals of Distributive Lattices
Santosh R. Mitkari1, Avinash M. Pawar*2, Avinash M. Deshmukh3, Tushar R. Shinde4, Manoj Tarambale5, Sheetal S. Patil6
1Dr. Santosh R. Mitkari, Department of Engineering Science and Allied Engineering, Bharati Vidyapeeth’s College of Engineering for Women, Pune (Maharashtra), India.
2Dr. Avinash M. Pawar, Department of Mechanical Engineering, Bharati Vidyapeeth’s College of Engineering for Women, Pune (Maharashtra), India.
3Dr. Avinash M. Deshmukh, Department of Basic Science and Engineering, SCTR’s Pune Institute of Computer Technology, Pune (Maharashtra), India.
4Dr. Tushar R. Shinde, Department of Engineering Sciences, Keystone School of Engineering, Pune (Maharashtra), India.
5Dr. Manoj Tarambale, Professor, Department of Electrical Engineering, PVG’s College of Engineering, Technology and Management, Pune (Maharashtra), India.
6Dr. Sheetal S. Patil, Department of Computer Science & Business Systems, Bharati Vidyapeeth (Deemed to be University) College of Engineering, Pune (Maharashtra), India.
Manuscript received on 05 September 2026 | First Revised Manuscript received on 14 September 2026 | Second Revised Manuscript received on 08 October 2026 | Manuscript Accepted on 15 October 2026 | Manuscript published on 30 October 2026 | PP: 56-59 | Volume-6 Issue-2, October 2026 | Retrieval Number: 100.1/ijam.A125907010427 | DOI: 10.54105/ijam.A1259.07010427
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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.
Keywords: Fuzzy Mathematics, Fuzzy Logic, Algebraic Structures, Distributive Lattice, Fuzzy Ideals, Fuzzy Sublattices, Generalised Fuzzy Algebra.
Scope of the Article: Mathematical Logic and Set Theory