Neutrosophy A New Branch Of Philosophy

In this paper we present a new branch of philosophy, called Neutrosophy, which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophy is a generalization of dialectics. While the Dialectics means the dynamics of opposites ( and ), the Neutrosophy means the dynamics of opposites together with the neutrals between them: , , and . The Fundamental Thesis: Any idea is T% true, I% indeterminate, and F% false, where T, I, F are standard or non-standard subsets included in ]0-, 1+[. The Fundamental Theory: Every idea tends to be neutralized, diminished, balanced by ideas (not only , as Hegel asserted) - as a state of equilibrium. Neutrosophy is the base of neutrosophic logic, a multiple value logic that generalizes the fuzzy logic, of neutrosophic set that generalizes the fuzzy set, and of neutrosphic probability and neutrosophic statistics, which generalize the classical and imprecise probability and statistics respectively.

N-Norm and N-conorm are extended in Neutrosophic Logic/Set.

Examples of Neutrosophy used in Arabic philosophy:- While Avicenna promotes the idea that the world is contingent if it is necessitated by its causes, Averroes rejects it, and both of them are right from their point of view. Hence and have common parts.- Islamic dialectical theology (kalam) promoting creationism was connected by Avicenna in an extraordinary way with the opposite Aristotelian-Neoplatonic tradition.Much work by Avicenna is neutrosophic.- Averroes's religious judges (qadis) can be connected with atheists' believes.- al-Farabi's metaphysics and general theory of emanation vs. al-Ghazali's Sufi writings and mystical treatises [we may think about a coherence of al-Ghazali's "Incoherence of the Incoherence" book].- al-Kindi's combination of Koranic doctrines with Greek philosophy.- Islamic Neoplatonism + Western Neoplatonism. - Ibn ? Khaldun?s statements in his theory on the cyclic sequence of civilizations, says that: Luxury leads to the raising of civilization (because the people seek for comforts of life) but also Luxury leads to the decay of civilization (because its correlation with ethics corruption).- On the other hand, there?s the method of absent?by?present syllogism in jurisprudence, in which we find the same principles and laws of neutrosophy.- We can also function a lot of Arabic aphorisms, maxims, Koranic miracles (Ayat Al-Qur??n) and Sunna of the prophet, to support the theory of neutrosophy. Take the colloquial proverb that "The continuance of state is impossible" too, or "Everything, if it?s increased over its extreme, it will turn over to its opposite"!

This special issue reflects the impact of neutrosophic theory in Latin America, especially after creating the Latin American Association of Neutrosophic Sciences. Among the areas of publication most addressed in the region are found in the interrelation of social sciences and neutrosophy, presenting outstanding results in these research areas. The main objective of this special issue is to divulge the impact publication related to the Neutrosophic theory and explore new areas of research and application in the region. The SI reflects the influence of the neutrosophic publications in Latin America by opening new research areas mainly related to Neutrosophic Statistics, Plithogeny, and NeutroAlgebra. Furthermore, it is worth mentioning the incorporation of authors from new countries in the region, such as Paraguay, Uruguay, and Panama, to have authors in total from 15 countries, 12 of them from the Latin American region.

Papers on neutrosophic statistics, neutrosophic probability, plithogenic set, paradoxism, neutrosophic set, NeutroAlgebra, etc. and their applications.

The newly introduced theories, proposed as extensions of the fuzzy theory, such as the Neutrosophic, Pythagorean, Spherical, Picture, Cubic theories, and their numerous hybrid forms, are criticized by the authors of [1]. In this paper we respond to their critics with respect to the neutrosophic theories and show that the DST, that they want to replace the A-IFS with, has many flaws. Their misunderstanding, with respect to the partial and total independence of the neutrosophic components, is that in the framework of the neutrosophic theories we deal with a MultiVariate Truth-Value (truth upon many independent random variables) as in our real-life world, not with a UniVariate Truth-Value (truth upon only one random variable) as they believe. About the membership degrees outside of the interval [0, 1], which are now in the arXiv and HAL mainstream, it is normal that somebody who over-works (works overtime) to have an over-membership (i.e., membership degree above 1) to be distinguished from those who do not work overtime (whose membership degree is between 0 and 1). And, similarly, a negative employee (that who does only damages to the company) to have a negative membership (i.e., membership degree below 0) in order to distinguish him from the positive employees (those whose membership degree is above 0). There are elementary practical applications in this paper that allow us to think out of box (in this case the box is the interval [0, 1]).

In this volume, we present a set of research that was published in cooperation with a number of researchers and those interested in keeping pace with the great scientific development that our contemporary world is witnessing, and one of its products was neutrosophic science, which was founded by the American scientist and mathematical philosopher Florentin Smarandache in 1995. Through it, we present a new vision for some research methods. Operations research to the concepts of this science.

This book offers a comprehensive guide to the use of neutrosophic sets in multiple criteria decision making problems. It shows how neutrosophic sets, which have been developed as an extension of fuzzy and paraconsistent logic, can help in dealing with certain types of uncertainty that classical methods could not cope with. The chapters, written by well-known researchers, report on cutting-edge methodologies they have been developing and testing on a variety of engineering problems. The book is unique in its kind as it reports for the first time and in a comprehensive manner on the joint use of neutrosophic sets together with existing decision making methods to solve multi-criteria decision-making problems, as well as other engineering problems that are complex, hard to model and/or include incomplete and vague data. By providing new ideas, suggestions and directions for the solution of complex problems in engineering and decision making, it represents an excellent guide for researchers, lecturers and postgraduate students pursuing research on neutrosophic decision making, and more in general in the area of industrial and management engineering.