Annals of Communications in Mathematics

ABSTRACT.From the nature of subbisemiring, we develop a new generalized hybrid structure of vague subbisemiring known as cubic vague subbisemiring (shortly CVSBS). We talk about the CVSBS and level sets CVSBS of bisemiring. At first we define some basic operations such as intersection and Cartesian product on them and use these to obtain some of its basic properties under CVSBS. Let \[\tilde{\mathcal{L}} = \langle \tilde{\mathcal{A}}_{c}, \, V_{c} \rangle\]be the cubic vague subset of \( S \). It is shown that \( \tilde{\mathcal{L}} \) is a CVSBS if and only if all non-empty level sets \[\tilde{\mathcal{L}}_{(\alpha,\beta)} \, (\alpha,\beta \in D[0,1])\]is a SBS. Let \( \tilde{\mathcal{L}} \) be the CVSBS and \( W \) be the strongest vague relation of \( S \). We show that \( \tilde{\mathcal{L}} \) is a CVSBS if and only if \( W \) is a CVSBS of \( S \times S \). After we define homomorphic image and preimage of bisemiring, it will be shown that the homomorphic image and preimage of CVSBS is a CVSBS. To strengthen our results with examples are indicated.

AbstractThe aim of this paper is to introduce and study the concept of somewhat fuzzy completely e-irresolute mapping and somewhat fuzzy irresolute e-open mapping. Further, some interesting properties of those mappings are given and some comparative results discussed.

ABSTRACT.We discuss the notion of Pythagorean subbisemiring, level sets of Pythagorean subbisemirings and Pythagorean normal subbisemiring of a bisemiring and investigate some of the properties related to subbisemirings. The fuzzy subset \[L = (\mu_{S}^{P}, \, \omega_{S}^{P})\]is a Pythagorean subbisemiring if and only if all non-empty level set \[L_{(\alpha,\beta)} \, (\alpha,\beta \in (0,1])\]is a subbisemiring. The Cartesian product of two Pythagorean subbisemirings is also Pythagorean subbisemiring. The homomorphic image and preimage of Pythagorean subbisemiring is also Pythagorean subbisemiring. To illustrate our results and examples are given.