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Slope Stability Assessment Method Using the Arctangent and Tangent Similarity Measure of Neutrosophic Numbers
Slope is a typical disaster in open-pit mining. Then it is a kind of non-continuous and uncertain natural geological body. In this case, common assessment approaches cannot assess the slope stability problems with both certain and uncertain information. Then, a neutrosophic number (NN) can easily represent the certain and uncertain information. Unfortunately NNs have not been applied in slope stability analysis so far.
Expression and Analysis of Joint Roughness Coefficient Using Neutrosophic Number Functions
In nature, the mechanical properties of geological bodies are very complex, and its various mechanical parameters are vague, incomplete, imprecise, and indeterminate.
Neutrosophic Function for Assessing the Scale Effect of the Rock Joint Surface Roughness
A new investigation method is proposed for recording large-sized joint profiles and making statistical analyses of the joint roughness coefficient (JRC) values of the 10–300 cm sized profiles. )e mechanical hand profilograph is used for joint roughness measurement due to its advantage of easy operation and high accuracy in recording joint traces. Based on the proposed method, it provides sufficient samples from various positions on the large joint profile, which allows the statistical evaluation of JRC values. A neutrosophic number (NN) is employed for revealing determinate and/or indeterminate information as it consists of determinate and indeterminate parts. Due to the uncertainty of JRC in the real world, NN is chosen to represent the JRC value, which is not only random but also a fuzzy indefinite parameter. The neutrosophic function is used to analyze and express the scale effect of joint surface roughness, and its derivative is used to describe the changing trend of the scale effect.
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).
Expressions of Rock Joint Roughness Coefficient Using Neutrosophic Interval Statistical Numbers
In nature, the mechanical properties of geological bodies are very complex, and their various mechanical parameters are vague, incomplete, imprecise, and indeterminate. However, we cannot express them by the crisp values in classical probability and statistics. In geotechnical engineering, we need to try our best to approximate exact values in indeterminate environments because determining the joint roughness coefficient (JRC) effectively is a key parameter in the shear strength between rock joint surfaces. In this original study, we first propose neutrosophic interval probability (NIP) and define the confidence degree based on the cosine measure between NIP and the ideal NIP.
SIMPLIFIED NEUTROSOPHIC INDETERMINATE DECISION MAKING METHOD WITH DECISION MAKERS’ INDETERMINATE RANGES
There exists the indeterminate situations of truth, falsity, indeterminacy degrees due to the uncertainty and inconsistency of decision makers’ arguments in a complicated decision making (DM) problem. Then, existing neutrosophic set cannot describe the indeterminate information of truth, falsity, indeterminacy degrees. It is noted that the simplified neutrosophic set (SNS) is depicted by truth, falsity, indeterminacy degrees, while a neutrosophic number (NN) can be flexibly depicted by its determinate part and its indeterminate part.
Scale Effect and Anisotropy Analyzed for Neutrosophic Numbers of Rock Joint Roughness Coefficient Based on Neutrosophic Statistics
In rock mechanics, the study of shear strength on the structural surface is crucial to evaluating the stability of engineering rock mass. In order to determine the shear strength, a key parameter is the joint roughness coefficient (JRC). To express and analyze JRC values, Ye et al. have proposed JRC neutrosophic numbers (JRC-NNs) and fitting functions of JRC-NNs, which are obtained by the classical statistics and curve fitting in the current method.
Vector Similarity Measures between Refined Simplified Neutrosophic Sets and Their Multiple Attribute Decision-Making Method
A refined single-valued/interval neutrosophic set is very suitable for the expression and application of decision-making problems with both attributes and sub-attributes since it is described by its refined truth, indeterminacy, and falsity degrees.
Symmetry, vol. 9, issue 10 / 2007 - Special Issue: Neutrosophic Theories Applied in Engineering
This Special Issue presents original research papers that report on state-of-the-art and recent advancements in neutrosophic sets and logic in soft computing, artificial intelligence, big and small data mining, decision making problems, and practical achievements.
