The concept of SVNS is an extension of the concept of FS. A SVNS, say A, in the universe U is defined as A = {(x,T(x),I(x),F(x)): x ? U, T(x),I(x),F(x) ? [0,1], 0 =T(x)+I(x)+F(x)= 3}, where T(x), I(x), F(x) are the degrees of truth (or membership), indeterminacy (or neutrality) and falsity (or non-membership) of x in A respectively, called the neutrosophic components of x. When the sum T(x) + I(x) + F(x) <1, then x leaves room for incomplete information, when is equal to 1 for complete information and when is greater than 1 for paraconsistent (i.e. contradiction tolerant) information. A SVNS may contain simultaneously elements leaving room to all the previous types of information.
Published in Chapter:
Use of Soft and Neutrosophic Sets for a Mathematical Representation of the Ethical Rules
Copyright: © 2023
|Pages: 19
DOI: 10.4018/978-1-6684-4740-6.ch005
Abstract
Soft and neutrosophic sets are used in this chapter as tools for introducing a multi-valued logic for ethics. The introduction of a multi-valued logic in ethics is not a new idea, but there is not any integrated proposal about this reported in the literature until now. The target is not to add another theory about ethics, but instead to create a new basis enabling a modern approach to the subject. The chapter starts by examining the role of human logic and statistical thinking for the creation and evolution of ethics. A brief historical account of the development of ethics follows with emphasis to the moral dilemmas, the existence of which motivates the application of a multi-valued logic. The basic information about fuzzy sets, fuzzy logic, soft sets, and neutrosophic sets, needed for the understanding of the rest of the chapter, are also presented before using soft and neutrosophic sets for a mathematical representation of the ethical rules and in extension of the moral theories.