Abstract
The purpose of the article is to study about spherical cubic sets and spherical cubic bi-idealsof Gamma near-ring \(\mathcal R\). We define spherical internal and external cubic sets and their properties. We discuss P-order and \(\mathcal R\)-order, P-union, P-intersection, \(\mathcal R\)-union and \(\mathcal R\)-intersection of spherical cubic sets. We define spherical cubic bi-ideals of gamma near-ring \(\mathcal R\) and prove that P-union, P-intersection, \(\mathcal R\)-union and \(\mathcal R\)-intersection of spherical cubic bi-ideals of Gamma near-ring \(\mathcal R\) are also spherical cubic bi-ideals of Gamma near-ring \(\mathcal R\).
Highlights
The notion of fuzzy set was introduced by Zadeh [16] in 1965
Many extensions and generalizations of fuzzy set was conceived by a number of researchers and a large number of real-life applications were developed in a variety of areas
Parallel analysis of the classical results of many branches of Mathematics were carried out in the fuzzy settings. It was initiated by Rosenfeld [13], who coined the idea of fuzzy subgroup of a group in 1971 and studied some basic properties of this structure.Properties of fuzzy ideals in near-rings was studied by Hong et al [5]
Summary
The notion of fuzzy set was introduced by Zadeh [16] in 1965. It is identified as a better tool for the scientific study of uncertainty, and came as a boost to the researchers working in the field of uncertainty. Parallel analysis of the classical results of many branches of Mathematics were carried out in the fuzzy settings It was initiated by Rosenfeld [13], who coined the idea of fuzzy subgroup of a group in 1971 and studied some basic properties of this structure.Properties of fuzzy ideals in near-rings was studied by Hong et al [5]. Chinnadurai et al [2, 3] discussed spherical fuzzy and spherical interval-valued fuzzy bi-ideals of gamma near-rings. We introduce the notion of spherical cubic bi-ideal of Gamma near-ring R, establish some of its properties and study the relationship between bi-ideal and spherical cubic bi-ideal of Gamma near-ring R
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