Single-valued neutrosophic hesitant fuzzy set is a merged form of single-valued neutrosophic sets and hesitant fuzzy sets. This set is a useful tool to handle imprecise, incomplete and inconsistent information existing in multi-attribute decision making problems. In multi-attribute decision making, distance measures play an important role to take a decision regarding alternatives.
This paper aims at developing new methods for multi-attribute decision making (MADM) under a single-valued neutrosophic hesitant fuzzy environment, in which each element has sets of possible values designed by truth, indeterminacy, and falsity membership hesitant functions.
In this study, a multiobjective nonlinear programming problem (MO-NLPP) has been formulated in the manufacturing system. A new algorithm, neutrosophic hesitant fuzzy programming approach (NHFPA), based on single valued neutrosophic hesitant fuzzy decision set has been proposed which contains the concept of indeterminacy hesitant degree along with truth and falsity hesitant degrees of different objectives.
With respect to a combination of hesitant sets, and single-valued neutrosophic sets which are a special case of neutrosophic sets, the single valued neutrosophic hesitant sets (SVNHFS) have been proposed as a new theory set that allows the truth-membership degree, indeterminacy membership degree and falsity-membership degree including a collection of crisp values between zero and one, respectively.
Single-valued neutrosophic hesitant fuzzy set (SVNHFS) is a combination of single-valued neutrosophic set and hesitant fuzzy set, and its aggregation tools play an important role in the multiple criteria decision-making (MCDM) process.
In this paper, the hesitant neutrosophic linguistic set is first defined by extending a hesitant fuzzy set to accommodate linguistic terms and neutrosophic fuzzy values. Some operational laws are defined for hesitant neutrosophic linguistic fuzzy information.
Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus the hesitant information needs to be considered in measures. Then, it can effectively avoid the loss of fuzzy information.
Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus the hesitant information needs to be considered in measures. Then, it can effectively avoid the loss of fuzzy information. However, regarding fuzzy information, it only reflects the subjective factor. Obviously, this is a shortcoming thatwill result in an inaccurate decision conclusion. Thus, based on the definition of a probabilistic neutrosophic hesitant fuzzy set (PNHFS), as an extended theory of fuzzy set, the basic definition of distance, similarity and entropy measures of PNHFS are established. Next, the interconnection among the distance, similarity and entropy measures are studied. Simultaneously, a novel measure model is established based on the PNHFSs. In addition, the new measure model is compared by some existed measures. Finally, we display their applicability concerning the investment problems, which can be utilized to avoid redundant evaluation processes.
The uncertainty and concurrence of randomness are considered when many practical problems are dealt with. To describe the aleatory uncertainty and imprecision in a neutrosophic environment and prevent the obliteration of more data, the concept of the probabilistic single-valued (interval) neutrosophic hesitant fuzzy set is introduced. By definition, we know that the probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS) is a special case of the probabilistic interval neutrosophic hesitant fuzzy set (PINHFS). PSVNHFSs can satisfy all the properties of PINHFSs.
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.
