Multi-attribute decision-making problems under the trapezoidal fuzzy neutrosophic numbers environment are complex, particularly when the attribute value data are incomplete, and the attribute weight is completely unknown. As a solution, this study proposes a decision-making method based on information entropy and grey theory.

This paper proposes a methodology for the assessment of the sustainability among three different structural design alternatives for a single-family home. The response associated with each alternative has been measured using 43 indicators considering all stages of the life cycle. A decision-making model is carried out on the basis of a neutrosophic group analytical hierarchy process (NAHP-G) capturing the maximum information in terms of credibility, inconsistency and indetermination.

Studies to neutrosophic graphs happens to be not only innovative and interesting, but gives a new dimension to graph theory. The classic coloring of edge problem happens to give various results. Neutrosophic tree will certainly find lots of applications in data mining when certain levels of indeterminacy is involved in the problem. Several open problems are suggested.

This book presents the proceedings of the 13th International Conference on Application of Fuzzy Systems and Soft Computing (ICAFS 2018), held in Warsaw, Poland on August 27–28, 2018. It includes contributions from diverse areas of soft computing such as uncertain computation, Z-information processing, neuro-fuzzy approaches, evolutionary computing and others. The topics of the papers include theory of uncertainty computation; theory and application of soft computing; decision theory with imperfect information; neuro-fuzzy technology; image processing with soft computing; intelligent control; machine learning; fuzzy logic in data analytics and data mining; evolutionary computing; chaotic systems; soft computing in business, economics and finance; fuzzy logic and soft computing in the earth sciences; fuzzy logic and soft computing in engineering; soft computing in medicine, biomedical engineering and the pharmaceutical sciences; and probabilistic and statistical reasoning in the social and educational sciences. The book covers new ideas from theoretical and practical perspectives in economics, business, industry, education, medicine, the earth sciences and other fields. In addition to promoting the development and application of soft computing methods in various real-life fields, it offers a useful guide for academics, practitioners, and graduates in fuzzy logic and soft computing fields.

This book addresses new concepts, methods, algorithms, modeling, and applications of green supply chain, inventory control problems, assignment problems, transportation problem, linear problems and new information related to optimization for the topic from the theoretical and applied viewpoints of neutrosophic sets and logic. The book is an innovatory of new tools and procedures, such as: Neutrosophic Statistical Tests and Dependent State Samplings, Neutrosophic Probabilistic Expert Systems, Neutrosophic HyperSoft Set, Quadripartitioned Neutrosophic Cross-Entropy, Octagonal and Spherical and Cubic Neutrosophic Numbers used in machine learning. It highlights the process of neutrosofication {which means to split the universe into three parts, two opposite ones (Truth and Falsehood), and an Indeterminate or neutral one (I) in between them}. It explains Three-Ways Decision, how the universe set is split into three different distinct areas, in regard to the decision process, representing: Acceptance, Noncommitment, and Rejection, respectively. The Three-Way Decision is used in the Neutrosophic Linguistic Rough Set, which has never been done before.

This book presents a collection of recent research on topics related to Pythagorean fuzzy set, dealing with dynamic and complex decision-making problems. It discusses a wide range of theoretical and practical information to the latest research on Pythagorean fuzzy sets, allowing readers to gain an extensive understanding of both fundamentals and applications. It aims at solving various decision-making problems such as medical diagnosis, pattern recognition, construction problems, technology selection, and more, under the Pythagorean fuzzy environment, making it of much value to students, researchers, and professionals associated with the field.

The book offers a comprehensive survey of interval-valued intuitionistic fuzzy sets. It reports on cutting-edge research carried out by the founder of the intuitionistic fuzzy sets, Prof. Krassimir Atanassov, giving a special emphasis to the practical applications of this extension. A few interesting case studies, such as in the area of data mining, decision making and pattern recognition, among others, are discussed in detail. The book offers the first comprehensive guide on interval-valued intuitionistic fuzzy sets. By providing the readers with a thorough survey and important practical details, it is expected to support them in carrying out applied research and to encourage them to test the theory behind the sets for new advanced applications. The book is a valuable reference resource for graduate students and researchers alike.

Digital systems that bring together the computing capacity for processing large bodies of information with the human cognitive capability are called intelligent systems. Building these systems has become one of the great goals of modem technology. This goal has both intellectual and economic incentives. The need for such intelligent systems has become more intense in the face of the global connectivity of the internet. There has become an almost insatiable requirement for instantaneous information and decision brought about by this confluence of computing and communication. This requirement can only be satisfied by the construction of innovative intelligent systems. A second and perhaps an even more significant development is the great advances being made in genetics and related areas of biotechnology. Future developments in biotechnology may open the possibility for the development of a true human-silicon interaction at the micro level, neural and cellular, bringing about a need for "intelligent" systems. What is needed to further the development of intelligent systems are tools to enable the representation of human cognition in a manner that allows formal manipulation. The idea of developing such an algebra goes back to Leibniz in the 17th century with his dream of a calculus ratiocinator. It wasn't until two hundred years later beginning with the work of Boole, Cantor and Frege that a formal mathematical logic for modeling human reasoning was developed. The introduction of the modem digital computer during the Second World War by von Neumann and others was a culmination of this intellectual trend.

Entropy is a measure of uncertainty and often used in information theory to determine the precise testimonials about unclear situations. Different entropy measures available in the literature are based on the exact form of the observations and lacks in dealing with the interval-valued data. The interval-valued data often arises from the situations having ambiguity, imprecise, unclear, indefinite, or vague states of the experiment and is called neutrosophic data. In this research modified forms of different entropy measures for normal probability distribution have been proposed by considering the neutrosophic form data. The performance of the proposed neutrosophic entropies for normal distribution has been assessed via a simulation study. Moreover, the proposed measures are also applied to two real data sets for their wide applicability.