Application of Soft Sets and Neutrosophic Sets for Introducing a Multi-valued Logic in Ethics

The use of a multi-valued logic in ethics is not a new idea, but, to the best of our knowledge, there is not any integrated proposal for its application reported in the literature until now. In this work soft and neutrosophic sets are used as tools for introducing a multi-valued logic in ethics. Our target is not to add, in the already existing long catalogue, another theory about ethics, but instead to create a new basis enabling a modern approach to the subject. The paper starts by examining the role of human logic and statistical thinking to 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 to ethics. The basic information about fuzzy sets, fuzzy logic soft sets and neutrosophic sets, needed for the understanding of the rest of the paper, is also presented, before using the soft and neutrosophic sets for a mathematical representation of the ethical rules, and in extension of the moral theories. The final conclusions of all this discussion are summarized at the end of the paper.