Abstract
In this study, for the first time, we study some basic definitions of soft neutrosophic modules in algebra being generalized and its several related properties, structural characteristics are investigated with suitable examples. In this paper, we utilized neutrosophic soft sets and neutrosophic modules. As a result, we defined soft neutrosophic modules. After weak soft neutrosophic modules and strong soft neutrosophic modules are described and illustrated by examples. Finally soft neutrosophic module homomorphism is defined and soft neutrosophic module isomorphism is explained.
Highlights
In 1980, Florentin Smarandanche characterized the notion of neutrosophy as a new branch of philosophy
Neutrosophic set is a power general formal structure which generalizes the concept of the intuitionistic fuzzy set, interval valued fuzzy set, fuzzy set, classic set etc
Struggle with uncertainties is a big problem in many areas like medical science, environment, economics, social sciences, etc. These kinds of problems cannot be overcome by classical methods, because there are inherent difficulties in the classical methods
Summary
In 1980, Florentin Smarandanche characterized the notion of neutrosophy as a new branch of philosophy. “It is a branch of philosophy which studies the nature, scope and origin of neutralities, as well as their interactions with different ideational spectra” It is the base of neutrosophic logic that is an extension fuzzy logic in that indeterminacy is inclusive. Some authors [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] have studied neutrosophic algebraic structures and nowadays, researchers are still interested in this subject.
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