Degrees of Membership \u3e 1 and \u3c 0 of the Elements with Respect to a Neutrosophic OffSet

We have defined the Neutrosophic Over- /Under-/Off-Set and -Logic for the first time in 1995 and published in 2007. During 1995-2016 we presented them to various national and international conferences and seminars ([16]-[37]) and did more publishing during 2007-2016 ([1]-[15]). These new notions are totally different from other sets/logics/probabilities. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is \u3e 1}, to Neutrosophic Underset {when some neutrosophic component is \u3c 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component \u3e 1 and other neutrosophic component \u3c 0}. This is no surprise since our real-world has numerous examples and applications of over-/under-/off-neutrosophic components

Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset. Similarly for Neutrosophic Over-/Under-/Off- Logic, Probability, and Statistics

Neutrosophic Over-/Under-/Off-Set and -Logic were defined by the author in 1995 and published for the first time in 2007. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is over 1}, Neutrosophic Underset {when some neutrosophic component is below 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component over 1 and other neutrosophic component below 0}. This is no surprise with respect to the classical fuzzy set/logic, intuitionistic fuzzy set/logic, or classical/imprecise probability, where the values are not allowed outside the interval [0, 1], since our real-world has numerous examples and applications of over-/under-/off-neutrosophic components. For example, person working overtime deserves a membership degree over 1, while a person producing more damage than benefit to a company deserves a membership below 0. Then, similarly, the Neutrosophic Logic/Measure/Probability/Statistics etc. were extended to respectively Neutrosophic Over-/Under-/Off-Logic, -Measure, -Probability, -Statistics etc. [Smarandache, 2007].Comment: 170 page

Single Valued Neutrosophic Signedgraphs

Motivated by the notion of single valued neutrosophic graphs defined by Broumi, Talea, Bakali and Smarandache[2] and notion of intuitionistic fuzzy signed graphs defined by Mishra and Pal[8], we introduce the concept of single valued neutrosophic signed graphs and examine the properties of this new concept and examples

A Bipolar Single Valued Neutrosophic Isolated Graphs: Revisited

In this research paper, the graph of the bipolar single-valued neutrosophic set model (BSVNS) is proposed. The graphs of single valued neutrosophic set models is generalized by this graph. For the BSVNS model, several results have been proved on complete and isolated graphs. Adding, an important and suitable condition for the graphs of the BSVNS model to become an isolated graph of the BSVNS model has been demonstrated

n-Refined Neutrosophic Modules

This paper introduces the concept of n-refined neutrosophic module as a new generalization of neutrosophic modules and refined neutrosophic modules respectively and as a new algebraic application of n-refined neutrosophic set. It studies elementary properties of these modules. Also, This work discusses some corresponding concepts such as weak/strong n-refined neutrosophic modules, n-refined neutrosophic homomorphisms, and kernels

Nidus idearum. Scilogs, III: Viva la Neutrosophia!

Welcome into my scientific lab! My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings ground , opinion , expectation ), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this third book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. Feel free to budge in or just use the scilogs as open source for your own ideas! * Neutrosophy is a new branch of philosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. I coined the words “neutrosophy” and “neutrosophic” in my 1998 book: Florentin Smarandache, Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998; http://fs.gallup.unm.edu/eBook-neutrosophics6.pdf (last edition online)

Neutrosophic Statistics is an extension of Interval Statistics, while Plithogenic Statistics is the most general form of statistics (second version)

In this paper, we prove that Neutrosophic Statistics is more general than Interval Statistics, since it may deal with all types of indeterminacies (with respect to the data, inferential procedures, probability distributions, graphical representations, etc.), it allows the reduction of indeterminacy, and it uses the neutrosophic probability that is more general than imprecise and classical probabilities and has more detailed corresponding probability density functions. While Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments by Woodall et al. [1]. We show that not all indeterminacies (uncertainties) may be represented by intervals. Also, in some cases, we should better use hesitant sets (that have less indeterminacy) instead of intervals. We redirect the authors to the Plithogenic Probability and Plithogenic Statistics which are the most general forms of MultiVariate Probability and Multivariate Statistics respectively (including, of course, the Imprecise Probability and Interval Statistics as subclasses)