Home 9 Author: M. Palanikumar
M. Palanikumar
Open AccessArticle

On New Approach Towards Cubic Vague Subbisemirings in Bisemirings

Annals of Communications in Mathematics 2021

, 4 (3)

, 237-248

DOI: https://doi.org/10.62072/acm.2021.040303

AbstractFrom 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 operation such as intersection, cartesian product on them and use these to obtain some of its basic properties under CVSBS. Let L = hA¯L, VLi be the cubic vague subset of S. It is shown that L is a CVSBS if and only if all non empty level set L(α,β) (α, β ∈ D[0, 1]) is a SBS. Let L be the CVSBS and W be the strongest vague relation of S. We show that L is a CVSBS if and only if W is a CVSBS of S × 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.
Open AccessArticle

Generalized Spherical Fuzzy Soft Sets in Medical Diagnosis for a Decision

Annals of Communications in Mathematics 2021

, 4 (3)

, 261-277

DOI: https://doi.org/10.62072/acm.2021.040306

AbstractIn the present communication, we introduce the theory of generalized spherical fuzzy soft set and define some operations such as complement, union, intersection, AND and OR. Notably, we tend to showed De Morgan’s laws, associate laws and distributive laws that are holds in generalized spherical fuzzy soft set. Also, we advocate an algorithm to solve the decision making problem based on generalized soft set model. We introduce a similarity measure of two generalized spherical fuzzy soft sets and discuss its application in a medical diagnosis problem. Suppose that there are five patients P1, P2, P3, P4 and P5 in a hospital with certain symptoms of dengue hemorrhagic fever. Let the universal set contain only three elements. That is X = {x1 : severe, x2: mild, x3 : no}, the set of parameters E is the set of certain symptoms of dengue hemorrhagic fever is represented by E = {e1 : severe abdominal pain, e2: persistent vomiting, e3 : rapid breathing, e4 : bleeding gums, e5: restlessness and blood in vomit}. An illustrative examples are mentioned to show that they can be successfully used to solve problems with uncertainties.
Open AccessArticle

New approach towards A-ideals in ternary semirings

Annals of Communications in Mathematics 2021

, 4 (2)

, 114-125

DOI: https://doi.org/10.62072/acm.2021.040203

AbstractTo interact somebody with someone various almost ideals (shortly A -ideals), quasi A -ideals, bi quasi A -ideals, tri A -ideals and tri quasi A -ideals in ternary semiring and give some characterizations. We develop the implications ideal =⇒ quasi ideal =⇒ two sided bi quasi ideal =⇒ two sided tri quasi ideal =⇒ two sided tri quasi A -ideal =⇒ two sided bi quasi A -ideal =⇒ bi A -ideal =⇒ quasi A -ideal =⇒ A -ideal and reverse implications do not holds with examples. We show that the union of A -ideals (bi A -ideals, quasi A -ideals, bi quasi A -ideals) is a A -ideal (bi A -ideal, quasi A -ideal, bi quasi A -ideal) in ternary semiring.
Open AccessArticle

Different Types of Prime bi-ideals in Ternary Semirings

Annals of Communications in Mathematics 2021

, 4 (2)

, 141-148

DOI: https://doi.org/10.62072/acm.2021.040206

AbstractTo interact three different types of prime bi-ideals are introduce and the relation between them is obtain. Also we have define three different mb -systems. The bi-ideal P of a ternary semiring R is 2-prime if and only if RML ⊆ P, where R is a right ideal, M is a lateral ideal and L is a left ideal of R, implies R ⊆ P or M ⊆ P or L ⊆ P. If B is a bi-ideal of R, then HB is the unique largest two-sided ideal of R contained B. Let M be a mb 3 system and bi-ideal B of R with B ∩ M = φ. Then there exists a 3-prime P of R containing B with P ∩ M = φ.
Open AccessArticle

m-ideals and its generators of ternary semigroups

Annals of Communications in Mathematics 2021

, 4 (2)

, 164-171

DOI: https://doi.org/10.62072/acm.2021.040209

AbstractThe purpose of this paper is to introduce some new classes of m-bi ideals and m-quasi ideals in ternary semigroups and give some characterizations in terms of bi ideals and quasi ideals. Let U1 be the m-bi ideal of T and U2 be the m-bi ideal of U1 such that U3 2 = U2, shown that U2 is a m-bi ideal of T. Let U1, U2 and U3 be the three ternary subsemigroups of T, it has been shown that U1U2U3 is a t-bi ideal if at least one of U1, U2, U3 is l-RI or m-LATI or n-LI of T. Also we discuss m-bi ideal generated by B is < B > sub>m= B ∪ P finite
Open AccessArticle

On various almost ideals of semirings

Annals of Communications in Mathematics 2021

, 4 (1)

, 17-25

DOI: https://doi.org/10.62072/acm.2021.040103

AbstractIn this paper, we study various almost ideals (shortly A -ideals), quasi A – ideals, bi quasi A -ideals, tri A -ideals and tri quasi A -ideals in semiring and give some characterizations. Some relevant counter examples are also indicated. We develop the implications ideal =⇒ quasi ideal =⇒ bi quasi ideal =⇒ tri quasi ideal =⇒ tri quasi A -ideal =⇒ bi quasi A -ideal =⇒ bi A -ideal =⇒ quasi A -ideal =⇒ A -ideal and reverse implications do not holds with examples. We show that the union of A -ideals (bi A -ideals, quasi A -ideals, bi quasi A -ideals) is a A -ideal (bi A -ideal, quasi A -ideal, bi quasi A -ideal) in semiring.
Open AccessArticle

On Pythagorean normal subbisemiring of bisemiring

Annals of Communications in Mathematics 2021

, 4 (1)

, 63-72

DOI: https://doi.org/10.62072/acm.2021.040107

AbstractWe discuss the notion of Pythagorean subbisemiring, level sets of Pythagorean subbisemirings and Pythagorean normal subbisemiring of a bisemiring. Also, we investigate some of the properties related to subbisemirings. The fuzzy subset L = (πPL , ωPL ) is a Pythagorean subbisemiring if and only if all non-empty level set L(t,s) (t, s ∈ (0, 1]) is a subbisemiring. The cartesian product of two Pythagorean subbisemiring is also Pythagorean subbisemiring. The homomorphic image and preimage of Pythagorean subbisemiring is also Pythagorean subbisemiring. To illustrate our results and examples are given.