Use of Soft and Neutrosophic Sets for a Mathematical Representation of the Ethical Rules

Introduction

The terms ethics and morality are frequently used interchangeably, loosely meaning a framework of rules and behaviors about “good” and “bad” or “right” and “wrong” conduct. The etymology of the word ethics is connected to the Greek word “ήθος” which means character (with the wide sense of the word), whereas the root of the word morality comes from the Latin word “mores” which means customs. Many people, however, think of morality as something which is personal and ethics as the standards of “good” and “bad” or “right” and “wrong” distinguished by a certain community or social setting.

For example, assume that your local community considers that sex before marriage is immoral, but you have no strong feelings about it. In this case your personal morality contradicts the ethics of your community. Ethics also has the meaning of a deontological code for those working in medicine, business or law, whereas morality is connected to Christianity for many people, since moral theology is prominent in the church. In general, the distinction between the two terms is not so clear.

The arising question, in any case, is what is “good” and “bad” or “wrong” and “right”. The several answers given through the centuries to this question, which played a very important role in the formation of human behavior and history, are in most cases inconsistent or even contradictory to each other and differ from time to time and from society to society. In fact, the humans are characterized by deep differences among each other, the result of which is the lack of unity and the absence of a universal will (Koestler, 1979). The development, therefore, of a universal system of principles, rules and laws for the right human behavior, or in other words of a universally acceptable theory of ethics, seems to be impossible or, at least, very difficult.

The previous problem becomes even harder due to the fact that the various theories about an ideal system of ethics, developed from the ancient years until nowadays, are based on the principles of the classical bivalent logic (BL), of Aristotle (384-322 BC). As a result, every human action or behavior is characterized only as “good” or “bad”, without taking into account how good or bad it is. This creates frequent moral dilemmas and impasses, which will be discussed later in this paper. A possible solution to this problem is the introduction of a multi-valued logic in ethics, where degrees of truth are used. This is not actually a new idea, but as far as we know, apart from some general suggestions (e.g. Kosko, 1993) or specific examples (e.g. Papaioannou, 2013), nobody has attempted until now to propose a concrete and general way to materialize it in practice.

In this chapter we propose the use of soft sets (SSs) and neutrosophic sets (NSs), introduced by Molodstov (1999) and Smarandache (1995) respectively, as tools for the introduction of a multi-valued logic in ethics. It must be emphasized, however, that our target is not to add, in the already existing long catalogue, a new theory about ethics, but simply to propose a new basis that enables a modern approach to the subject.

The rest of the chapter is formulated as follows: In the next section the influence of human logic for the creation and evolution of ethics is examined. The third section is devoted to a brief historical account of the development of ethics with emphasis on the moral dilemmas that motivate the application of a multi-valued logic to ethics. In the fourth section basic information about fuzzy sets (FSs), fuzzy logic (FL), NSs and SSs, which is needed for the understanding of the rest of the paper, is presented. The use of SSs and NSs for a mathematical representation of the ethical rules, and in extension of the ethical theories, is attempted in the fifth section and the chapter closes with some hints for further research and the final conclusions, presented in its last two sections.