ALGEBRAIC SUM AND ALGEBRAIC PRODUCT OF SPHERICAL NEUTROSOPHIC SETS - Manimaran, A; Muthukumaran, V; Vijaykrishnaraj, R; Silambarasan, I (TWMS journal of applied and engineering mathematics, 2024)
The Spherical Neutrosophic Set is a generalization of Spherical Fuzzy Set. In this paper, we define Algebraic sum and Algebraic product of spherical neutrosophic sets (SNSs) and investigate their desirable properties. Further, we construct scalar multiplication (nA) and exponentiation ([A.sup.n]) operations of a spherical neutrosophic sets. Finally, define a new operation(@) on spherical neutrosophic sets and discuss distributive law in the case where the operations of [direct sum], [cross product], [conjunction] and [disjunction] are combined each other. Significant Statement: The important methodological problems of other analyzed theories were revealed and discussed. Many of the novel theories, such as Neutrosophic, Pythagorean, Spherical and Picture sets theories, were developed to solve interior problems of the Atanassov's intuitionistic fuzzy sets. Since the results obtained within the framework of these criticized novel theories appeared to be significantly worse than expected, in this paper, an alternative approach based on the extension of the Spherical fuzzy Sets in the framework of the Spherical Neutrosophic Sets theory is proposed. Our study is actually the study of an important type of advanced fuzzy algebraic structure. Keywords: Intuitionistic fuzzy set, Pythagorean fuzzy set, Picture fuzzy set. Spherical fuzzy set, Spherical Neutrosophic set, Algebraic sum, Algebraic product, Scalar multiplication, Exponentiation operations. AMS Subject Classification: 03B99, 08A72, 03E99.