Systematic review of decision making algorithms in extended neutrosophic sets

The Neutrosophic set (NS) has grasped concentration by its ability for handling indeterminate, uncertain, incomplete, and inconsistent information encountered in daily life. Recently, there have been various extensions of the NS, such as single valued neutrosophic sets (SVNSs), Interval neutrosophic sets (INSs), bipolar neutrosophic sets (BNSs), Refined Neutrosophic Sets (RNSs), and triangular fuzzy number neutrosophic set (TFNNs). This paper contains an extended overview of the concept of NS as well as several instances and extensions of this model that have been introduced in the last decade, and have had a significant impact in literature. Theoretical and mathematical properties of NS and their counterparts are discussed in this paper as well. Neutrosophic-set-driven decision making algorithms are also overviewed in detail

Neutrosophic state feedback design method for SISO neutrosophic linear systems

The indeterminacy of parameters in actual control systems is inherent property because some parameters in actual control systems are changeable rather than constants in some cases, such as manufacturing tolerances, aging of main components, and environmental changes, which present an uncertain threat to actual control systems

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. Regarding the indeterminate situations of truth, falsity, indeterminacy degrees in indeterminate DM problems, this study first presents a simplified neutrosophic indeterminate set (SNIS) to express the hybrid information of SNS and NN and defines the score, accuracy, and certainty functions of simplified neutrosophic indeterminate elements (SNIEs) with indeterminate ranges to compare SNIEs. Then, we introduce a SNIE weighted arithmetic averaging (SNIEWAA) operator and a SNIE weighted geometric averaging (SNIEWGA) operator to aggregate simplified neutrosophic indeterminate information. Next, a multi-attribute DM approach with decision makers’ indeterminate ranges is established regarding the SNIEWAA and SNIEWGA operators in SNIS setting. Finally, the proposed DM approach is applied in a DM example on choosing a suitable slope design scheme to indicate the applicability and suitability of the proposed approach

The Encyclopedia of Neutrosophic Researchers - vol. 1

This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc