Neutrosophic and Modal Components of Relations in Complex Systems

In this work, we are going to deal with a very special type of complex systems: Deontical Impure Systems (Nescolarde-Selva et al, 2012; Nescolarde-Selva and Usó-Doménech, 2012; Nescolarde-Selva and UsóDoménech, 2013; Usó-Doménech and NescolardeSelva, 2012; Usó-Doménech and Nescolarde-Selva, 2013). They are Systems because there are objects and relations among them. They are Impure because these objects are formed by material and/or energy beings. They are Deontical because between its relations it has, at least, one that fulfills at least one of the deontical modalities: obligation, permission, prohibition, and faculty. We are talking about the human societies. Not a particular society, but to any human society, at any time and place. 1. A system is an organization of the knowledge on the part of the subject S that fulfils the following conditions (Nescolarde-Selva and Usó-Doménech, 2013): a. The subjective condition. b. The condition of rationality. c. The external condition. d. S knows what there is a system. The vision of a system interpreted by the set formed by different subjects within the system is determined by the belief system (Nescolarde-Selva and Usó-Doménech, 2013; Nescolarde-Selva, Usó-Doménech am Gash, 2014; Usó-Doménech and. Nescolarde-Selva, 2012; UsóDoménech and Nescolarde-Selva, 2013) that the subjects conceived as true, about themselves, the system and its environment. 2. An impure set is whose referential elements (absolute beings) are not counted as abstract objects and have the following conditions: a. They are real (material or energetic absolute beings). b. They exist independently of Subject. c. Subject develops perceptual significances d. True things can be said about them. e. Subject can know these true things about them. f. They have properties that support a robust notion of mathematical truth. 3. An impure system is one whose set of elements is an impure set. 4. A deontical system is an organization of the knowledge on the part of the subject S that fulfils aforementioned conditions and the following others: