Plithogenic Cubic Sets

In this article, using the concepts of cubic set and plithogenic set, the ideas of plithogenic fuzzy cubic set, plithogenic intuitionistic fuzzy cubic set, plithogenic neutrosophic cubic set are introduced and its corresponding internal and external cubic sets are discussed with examples

More on R-Union and R-Intersection of Neutrosophic Soft Cubic Set

R-unions and R-intersections, R-OR, R-AND of Neutrosophic soft cubic sets are introduced and related properties are investigated. We show that the R-union (R-intersection) of internal neutrosophic soft cubic set is also an internal neutrosophic soft cubic set. We show that the R-union and the R-intersection T-external (I-external, F-external) neutrosophic soft cubic sets are also T-external ( I-external, F-external) neutrosophic soft cubic sets. The conditions for the R-intersection of two cubic soft sets to be both an external neutrosophic soft cubic set and an internal neutrosophic soft cubic set. Further we provide a condition for the R- intersection and R union of two T-internal (I-internal, F-internal) neutrosophic soft cubic sets are T-external (I-external, F-external) neutrosophic soft cubic sets

An extension of the ratio system approach of MOORA method for group decision-making based on interval-valued triangular fuzzy numbers

Decision-making in fuzzy environment is often a very complex, especially when related to predictions and assessments. The Ratio system approach of the MOORA method and Intervalvalued fuzzy numbers have already proved themselves as the effective tools for solving complex decision-making problems. Therefore, in this paper an extension of the Ratio system approach of the MOORA method, which allows a group decision-making as well as the use of interval-valued triangular fuzzy numbers, is proposed. Interval-fuzzy numbers are rather complex, and therefore, they are not practical for direct assigning performance ratings. For this reason, in this paper it has also been suggested the approach which allows the expression of individual performance ratings using crisp, interval or fuzzy numbers, and their further transformation into the group performance ratings, expressed in the form of interval-valued triangular fuzzy numbers, which provide greater flexibility and reality compared to the use of linguistic variables. Finally, in this paper the weighted averaging operator was proposed for defuzzification of interval-valued triangular fuzzy numbers. First published online: 21 Sep 201

Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets

AbstractWe begin the paper studying the axioms that the indicators of the grade of inclusion of a fuzzy set in another fuzzy set must satisfy. Next, we present an expression of such indicator, first for fuzzy sets and then for interval-valued fuzzy sets, analyzing in both cases their main properties. Then, we suggest an expression for the similarity measure between interval-valued fuzzy sets. Besides, we study two methods for inference in approximate reasoning based on interval-valued fuzzy sets, the inclusion grade indicator and the similarity measure. Afterwards, we expose some of the most important properties of the methods of inference presented and we compare these methods to Gorzalczany's. Lastly, we use the indicator of the grade of inclusion for interval-valued fuzzy sets as an element that selects from the different methods of inference studied, the one that will be executed in each case

Multi criteria risk analysis of a subsea BOP system

The Subsea blowout preventer (BOP) which is latched to a subsea wellhead is one of several barriers in the well to prevent kicks and blowouts and it is the most important and critical equipment, as it becomes the last line of protection against blowout. The BOP system used in Subsea drilling operations is considered a Safety – Critical System, with a high severity consequence following its failure. Following past offshore blowout incidents such as the most recent Macondo in the Gulf of Mexico, there have been investigations, research, and improvements sought for improved understanding of the BOP system and its operation. This informs the need for a systematic re-evaluation of the Subsea BOP system to understand its associated risk and reliability and identify critical areas/aspects/components. Different risk analysis techniques were surveyed and the Failure modes effect and criticality analysis (FMECA) selected to be used to drive the study in this thesis. This is due to it being a simple proven cost effective process that can add value to the understanding of the behaviours and properties of a system, component, software, function or other. The output of the FMECA can be used to inform or support other key engineering tasks such as redesigning, enhanced qualification and testing activity or maintenance for greater inherent reliability and reduced risk potential. This thesis underscores the application of the FMECA technique to critique associated risk of the Subsea BOP system. System Functional diagrams was developed with boundaries defined, a FMECA were carried out and an initial select list of critical component failure modes identified. The limitations surrounding the confidence of the FMECA failure modes ranking outcome based on Risk priority number (RPN) is presented and potential variations in risk interpretation are discussed. The main contribution in this thesis is an innovative framework utilising Multicriteria decision making (MCDA) analysis techniques with consideration of fuzzy interval data is applied to the Subsea BOP system critical failure modes from the FMECA analysis. It utilised nine criticality assessment criteria deduced from expert consultation to obtain a more reliable ranking of failure modes. The MCDA techniques applied includes the technique for order of Preference for similarity to the Ideal Solution (TOPSIS), Fuzzy TOPSIS, TOPSIS with interval data, and Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE). The outcome of the Multi-criteria analysis of the BOP system clearly shows failures of the Wellhead connector, LMRP hydraulic connector and Control system related failure as the Top 3 most critical failure with respect to a well control. The critical failure mode and components outcome from the analysis in this thesis is validated using failure data from industry database and a sensitivity analysis carried out. The importance of maintenance, testing and redundancy to the BOP system criticality was established by the sensitivity analysis. The potential for MCDA to be used for more specific analysis of criteria for a technology was demonstrated. Improper maintenance, inspection, testing (functional and pressure) are critical to the BOP system performance and sustenance of a high reliability level. Material selection and performance of components (seals, flanges, packers, bolts, mechanical body housings) relative to use environment and operational conditions is fundamental to avoiding failure mechanisms occurrence. Also worthy of notice is the contribution of personnel and organisations (by way of procedures to robustness and verification structure to ensure standard expected practices/rules are followed) to failures as seen in the root cause discussion. OEMs, operators and drilling contractors to periodically review operation scenarios relative to BOP system product design through the use of a Failure reporting analysis and corrective action system. This can improve design of monitoring systems, informs requirement for re-qualification of technology and/or next generation designs. Operations personnel are to correctly log in failures in these systems, and responsible Authority to ensure root cause analysis is done to uncover underlying issue initiating and driving failures

New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations

This Special Issue puts forward for discussion state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, neutrosophic symmetry, and their applications in the real world. This book leads to the further advancement of the neutrosophic and plithogenic theories of NeutroAlgebra and AntiAlgebra, NeutroGeometry and AntiGeometry, Neutrosophic n-SuperHyperGraph (the most general form of graph of today), Neutrosophic Statistics, Plithogenic Logic as a generalization of MultiVariate Logic, Plithogenic Probability and Plithogenic Statistics as a generalization of MultiVariate Probability and Statistics, respectively, and presents their countless applications in our every-day world