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

System Qualities Ontology, Tradespace and Affordability (SQOTA) Project – Phase 4

This task was proposed and established as a result of a pair of 2012 workshops sponsored by the DoD Engineered Resilient Systems technology priority area and by the SERC. The workshops focused on how best to strengthen DoD’s capabilities in dealing with its systems’ non-functional requirements, often also called system qualities, properties, levels of service, and –ilities. The term –ilities was often used during the workshops, and became the title of the resulting SERC research task: “ilities Tradespace and Affordability Project (iTAP).” As the project progressed, the term “ilities” often became a source of confusion, as in “Do your results include considerations of safety, security, resilience, etc., which don’t have “ility” in their names?” Also, as our ontology, methods, processes, and tools became of interest across the DoD and across international and standards communities, we found that the term “System Qualities” was most often used. As a result, we are changing the name of the project to “System Qualities Ontology, Tradespace, and Affordability (SQOTA).” Some of this year’s university reports still refer to the project as “iTAP.”This material is based upon work supported, in whole or in part, by the U.S. Department of Defense through the Office of the Assistant of Defense for Research and Engineering (ASD(R&E)) under Contract HQ0034-13-D-0004.This material is based upon work supported, in whole or in part, by the U.S. Department of Defense through the Office of the Assistant of Defense for Research and Engineering (ASD(R&E)) under Contract HQ0034-13-D-0004

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

Fuzzy multicriteria analysis and its applications for decision making under uncertainty

Multicriteria decision making refers to selecting or ranking alternatives from available alternatives with respect to multiple, usually conflicting criteria involving either a single decision maker or multiple decision makers. It often takes place in an environment where the information available is uncertain, subjective and imprecise. To adequately solve this decision problem, the application of fuzzy sets theory for adequately modelling the uncertainty and imprecision in multicriteria decision making has proven to be effective. Much research has been done on the development of various fuzzy multicriteria analysis approaches for effectively solving the multicriteria decision making problem, and numerous applications have been reported in the literature. In general, existing approaches can be categorized into (a) multicriteria decision making with a single decision maker and (b) multicriteria group decision making. Existing approaches, however, are not totally satisfactory due to various shortcomings that they suffer from including (a) the inability to adequately model the uncertainty and imprecision of human decision making, (b) the failure to effectively handle the requirements of decision maker(s), (c) the tedious mathematical computation required, and (d) cognitively very demanding on the decision maker(s). This research has developed four novel approaches for effectively solving the multicriteria decision making problem under uncertainty. To effectively reduce the cognitive demand on the decision maker, a pairwise comparison based approach is developed in Chapter 4 for solving the multicriteria problem under uncertainty. To adequately meet the interest of various stakeholders in the multicriteria decision making process, a decision support system (DSS) based approach is introduced in Chapter 5. In Chapter 6, a consensus oriented approach is presented in multicriteria group decision making on which a DSS is proposed for facilitating consensus building in solving the multicriteria group decision making problem. In Chapter 7, a risk-oriented approach is developed for adequately modelling the inherent risk in multicriteria group decision making with the use of the concept of ideal solutions so that the complex and unreliable process of comparing fuzzy utilities usually required in fuzzy multicriteria analysis is avoided. Empirical studies of four real fuzzy multicriteria decision making problems are presented for illustrating the applicability of the approaches developed in solving the multicriteria decision making problem. A hospital location selection problem is discussed in Chapter 8. An international distribution centre location problem is illustrated in Chapter 9. A supplier selection problem is presented in Chapter 10. A hotel location problem is discussed in Chapter 11. These studies have shown the distinct advantages of the approaches developed respectively in this research from different perspectives in solving the multicriteria decision making problem

Multi-Objective and Multi-Attribute Optimisation for Sustainable Development Decision Aiding

Optimization is considered as a decision-making process for getting the most out of available resources for the best attainable results. Many real-world problems are multi-objective or multi-attribute problems that naturally involve several competing objectives that need to be optimized simultaneously, while respecting some constraints or involving selection among feasible discrete alternatives. In this Reprint of the Special Issue, 19 research papers co-authored by 88 researchers from 14 different countries explore aspects of multi-objective or multi-attribute modeling and optimization in crisp or uncertain environments by suggesting multiple-attribute decision-making (MADM) and multi-objective decision-making (MODM) approaches. The papers elaborate upon the approaches of state-of-the-art case studies in selected areas of applications related to sustainable development decision aiding in engineering and management, including construction, transportation, infrastructure development, production, and organization management