In this book, we introduce for the first time the notions of neutrosophic measure and neutrosophic integral, and we develop the 1995 notion of neutrosophic probability. We present many practical examples. It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Neutrosophics study the indeterminacy. Indeterminacy is different from randomness. It can be caused by physical space materials and type of construction, by items involved in the space, etc.

This volume is a collection of ten papers, written by different authors and co-authors (listed in the order of the papers): F. Smarandache, Jun Ye, M. Shabir, M. Ali, M. Naz, F. Yuhua, A. A. Salama, S. Vladutescu, Y. Guo, A. Sengur, S. Broumi, P. Chi, and P. Liu. In first paper, the author proposed Neutrosophic Measure and neutrosophic Integral. Another Form of Correlation Coefficient between Single Valued Neutrosophic Sets and Multiple Attribute Decision-Making Method is proposed in the second paper. Soft Neutrosophic Group is studied in third paper. In fourth paper Neutrosophic Example in Physics is discussed. Similarly in fifth paper Filters via Neutrosophic Crisp Sets are discussed. In paper six, Commnication vs. Information, an Axiomatic Neutrosophic Solution is presented by the authors. A Novel Image Segmentation Algorithm Based on Neutrosophic Filtering and Level Set is given in seventh paper. Paper eight is about to Neutrosophic Crisp Points and Neutrosophic Crisp Ideals. In the next paper Several Similarity Measures of Neutrosophic Sets are discussed. The authors introduced An Extended TOPSIS Method for the Multiple Attribute Decision Making Problems Based on Interval Neutrosophic Sets in the last paper.

Neutrosophic Statistics means statistical analysis of population or sample that has indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data. For example, the population or sample size might not be exactly determinate because of some individuals that partially belong to the population or sample, and partially they do not belong, or individuals whose appurtenance is completely unknown. Also, there are population or sample individuals whose data could be indeterminate. In this book, we develop the 1995 notion of neutrosophic statistics. We present various practical examples. It is possible to define the neutrosophic statistics in many ways, because there are various types of indeterminacies, depending on the problem to solve.

Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of indeterminate change. The Neutrosophic Precalculus and Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the methods used to deal with such indeterminacy. In this book, the author presents a few examples of indeterminacies and several methods to deal with these specific indeterminacies, but many other indeterminacies there exist in our everyday life, and they have to be studied and resolved using similar of different methods. Therefore, more research should to be done in the field of neutrosophics. The author introduces for the first time the notions of neutrosophic mereo-limit, neutrosophic mereo-continuity (in a different way from the classical semi-continuity), neutrosophic mereo-derivative and neutrosophic mereo-integral (both in different ways from the fractional calculus), besides the classical definitions of limit, continuity, derivative, and integral respectively. Future research may be done in the neutrosophic fractional calculus. It means that in neutrosophic calculus there are limits, continuity, derivatives, and integrals that are not complete, i.e. there are neutrosophic functions that at a given point may have a degree of a limit (not 100%) called mereo-limit, or may be continuous in a certain degree (not 100%) called mereo-continuity, or may be differentiable or integrable in a certain degree (not 100%) called mereo-derivatives and respectively mereo-integrals. These occur because of indeterminacies...

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

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

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.