Abstract
A simplified neutrosophic set is characterized by a truth-membership function, an indeterminacy-membership function, and a falsity-membership function, which is a subclass of the neutrosophic set and contains the concepts of an interval neutrosophic set and a single valued neutrosophic set. It is a powerful structure in expressing indeterminate and inconsistent information. However, there has only been one paper until now—to the best of my knowledge—on the subtraction and division operators in the basic operational laws of neutrosophic single-valued numbers defined in existing literature. Therefore, this paper proposes subtraction operation and division operation for simplified neutrosophic sets, including single valued neutrosophic sets and interval neutrosophic sets respectively, under some constrained conditions to form the integral theoretical framework of simplified neutrosophic sets. In addition, we give numerical examples to illustrate the defined operations. The subtraction and division operations are very important in many practical applications, such as decision making and image processing.
Highlights
IntroductionImprecise, incomplete, and inconsistent information, Smarandache [1]
To handle uncertainty, imprecise, incomplete, and inconsistent information, Smarandache [1]proposed the concept of a neutrosophic set from philosophical viewpoint, which is a powerful general formal framework and generalizes the concepts of the classic set, fuzzy set [2], intuitionistic fuzzy set (IFS) [3], interval-valued intuitionistic fuzzy set (IVIFS) [4]
Proposed the concept of a neutrosophic set from philosophical viewpoint, which is a powerful general formal framework and generalizes the concepts of the classic set, fuzzy set [2], intuitionistic fuzzy set (IFS) [3], interval-valued intuitionistic fuzzy set (IVIFS) [4]
Summary
Imprecise, incomplete, and inconsistent information, Smarandache [1]. The defined range of ρ(x), σ(x), and τ(x) in a neutrosophic set is the non-standard unit interval ]− 0, 1+ [, the neutrosophic set is merely used for philosophical applications, while its engineering applications are difficult. Ye [7] introduced a simplified neutrosophic set (SNS), which is a subclass of the neutrosophic set and contains a SVNS and an INS, and defined some basic operational laws over SNSs, such as addition and multiplication. Motivated by the subtraction and division operations for IFSs and IVIFSs, this paper will try to develop the two new subtraction and division operations for SNSs to form the integral theoretical framework of SNSs. The remainder of this paper is arranged as follows.
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