New Fuzzy Algebraic Structure Consists of Homomorphism via Multi-Fuzzy Set Applied to Cubic Vague Subbisemirings Over Bisemirings

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DOI: https://doi.org/10.28924/2291-8639-23-2025-281
Published: Nov 5, 2025
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D. Mahendar, M. Palanikumar, Aiyared Iampan, M. S. Malchijah Raj, New Fuzzy Algebraic Structure Consists of Homomorphism via Multi-Fuzzy Set Applied to Cubic Vague Subbisemirings Over Bisemirings, Int. J. Anal. Appl., 23 (2025), 281.

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D. Mahendar, M. Palanikumar, Aiyared Iampan, M. S. Malchijah Raj

Abstract

We discussed that the concept of multi-fuzzy cubic vague subbisemiring (MFCVSBS) is a novel generalized hybrid structure of vague subbisemiring. The MFCVSBS and level sets using MFCVSBS of bisemirings are discussed. We define some simple operations on them, including intersection and Cartesian product, to discuss some of their basic properties under MFCVSBS. It is assumed that \(\mathcal{Z}= \langle \coprod_{i}\circ\bar{\aleph}_{\mathcal{Z}}, \coprod_{i}\circ\beth_{\mathcal{Z}} \rangle\) is the multi-fuzzy cubic vague subset of k. Assuming that any non-empty level set \(\mathcal{Z}_{(\zeta,\sigma)} (\zeta,\sigma \in D[0, 1])\) is an SBS, it can be demonstrated that \(\mathcal{Z}\) is an MFCVSBS. It will be demonstrated that MFCVSBS is both its homomorphic image and pre-image. Examples are given to illustrate our conclusions.

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