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Neutrosophic cubic sets (NCSs) can express complex multi-attribute decision-making (MADM) problems with its interval and single-valued neutrosophic numbers simultaneously. The weighted arithmetic average (WAA) and geometric average (WGA) operators are common aggregation operators for handling MADM problems. However, the neutrosophic cubic weighted arithmetic average (NCWAA) and neutrosophic cubic geometric weighted average (NCWGA) operators may result in some unreasonable aggregated values in some cases. In order to overcome the drawbacks of the NCWAA and NCWGA, this paper developed a new neutrosophic cubic hybrid weighted arithmetic and geometric aggregation (NCHWAGA) operator and investigates its suitability and effectiveness. Then, we established a MADM method based on the NCHWAGA operator. Finally, a MADM problem with neutrosophic cubic information was provided to illustrate the application and effectiveness of the proposed method.
This book contains 37 papers by 73 renowned experts from 13 countries around the world, on following topics: neutrosophic set; neutrosophic rings; neutrosophic quadruple rings; idempotents; neutrosophic extended triplet group; hypergroup; semihypergroup; neutrosophic extended triplet group; neutrosophic extended triplet semihypergroup and hypergroup; neutrosophic offset; uninorm; neutrosophic offuninorm and offnorm; neutrosophic offconorm; implicator; prospector; n-person cooperative game; ordinary single-valued neutrosophic (co)topology; ordinary single-valued neutrosophic subspace; α-level; ordinary single-valued neutrosophic neighborhood system; ordinary single-valued neutrosophic base and subbase; fuzzy numbers; neutrosophic numbers; neutrosophic symmetric scenarios; performance indicators; financial assets; neutrosophic extended triplet group; neutrosophic quadruple numbers; refined neutrosophic numbers; refined neutrosophic quadruple numbers; multigranulation neutrosophic rough set; nondual; two universes; multiattribute group decision making; nonstandard analysis; extended nonstandard analysis; monad; binad; left monad closed to the right; right monad closed to the left; pierced binad; unpierced binad; nonstandard neutrosophic mobinad set; neutrosophic topology; nonstandard neutrosophic topology; visual tracking; neutrosophic weight; objectness; weighted multiple instance learning; neutrosophic triangular norms; residuated lattices; representable neutrosophic t-norms; De Morgan neutrosophic triples; neutrosophic residual implications; infinitely ∨-distributive; probabilistic neutrosophic hesitant fuzzy set; decision-making; Choquet integral; e-marketing; Internet of Things; neutrosophic set; multicriteria decision making techniques; uncertainty modeling; neutrosophic goal programming approach; shale gas water management system.
The application of a novel correlation coefficient of linguistic intuitionistic fuzzy sets to medical diagnosis problems provides the topic for Strategic Fuzzy Extensions and Decision-making Techniques. It further explains neutrosophic cubic set-based aggregation operators for library ranking systems, and techniques for order performance by similarity to ideal solution. The text also introduces the new aggregation operators, similarity measures, and distance measures for the fuzzy sets and their extensions. This book: Introduces the new aggregation operators, similarity measures, and distance measures for the fuzzy sets and their extensions. Covers recent studies in the field of fuzzy optimization and decision making such as advanced decision-making algorithms. Highlights the application in the field of image processing and pattern recognition. Presents a technique for order performance by similarity to an ideal solution and VIKOR method for decision-making. Explores the limitations of existing fuzzy decision-making approaches such as the malfunctioning of existing formulations. It is primarily written for senior undergraduate, graduate students, and academic researchers in fields including industrial engineering, manufacturing engineering, production engineering, mechanical engineering, and engineering mathematics.
This book comprises select peer-reviewed articles submitted for the proceedings of the International Conference on Mathematics and Computing (ICMC 2022), held by the School of Advanced Sciences, Vellore Institute of Technology, Vellore, India, in association with Ramanujan Mathematical Society, India, Cryptology Research Society of India and Society for Electronic Transactions and Security, India, from 6–8 January 2022. With an aim to identify the existing challenges in the areas of mathematics and computing, the book emphasizes the importance of establishing new methods and algorithms to address these challenges. The book includes topics on diverse applications of cryptology, network security, cyber security, block chain, IoT, mobile network, data analytics, applied algebra, mathematical analysis, mathematical modelling, fluid dynamics, fractional calculus, multi-optimization, integral equations, dynamical systems, numerical analysis and scientific computing. Divided into five major parts—applied algebra and analysis, fractional calculus and integral equations, mathematical modelling and fluid dynamics, numerical analysis, and computer science and applications—the book is a useful resource for students, researchers and faculty as well as practitioners.
Information management is a common paradigm in modern decision-making. A wide range of decision-making techniques have been proposed in the literature to model complex business and engineering processes. In this Special Issue, 16 selected and peer-reviewed original research articles contribute to business information management in various current real-world problems by proposing crisp or uncertain multiple-criteria decision-making (MCDM) models and techniques, mostly including multi-attribute decision-making (MADM) approaches, in addition to a single paper proposing an interactive multi-objective decision-making (MODM) approach. Particular attention is devoted to information aggregation operators—65% of papers dealt with this item. The topics of this Special Issue gained attention in Europe and Asia. A total of 48 authors from seven countries contributed to this Issue. The papers are mainly concentrated in three application areas: supplier selection and rational order allocation, the evaluation and selection of goods or facilities, and personnel selection/partner selection. A number of new approaches are proposed that are expected to attract great interest from the research community.
Employing the concept and function of tangency with similarity measures and counterpart distances for reliable medical consultations has been extensively studied in the past decades and results in lots of isomorphic measures for application. We compared the majority of such isomorphic measures proposed by various researchers and classified them into (a) maximum norm and (b) one-norm categories. Moreover, we found that previous researchers used monotonic functions to transform an identity function and resulted in complicated expressions. In this study, we provide a theoretical foundation to explain the isomorphic nature of a newer measure proposed by the following research paper against its studied existing one in deriving the same pattern recognition results. Specifically, this study initially proposes two similarity measures using maximum norm, arithmetic mean, and aggregation operators and followed by a detailed discussion on their mathematical characteristics. Subsequently, a simplified version of such measures is presented for easy application. This study completely covers two previous methods to point out that the complex approaches used were unnecessary. The findings will help physicians, patients, and their family members to obtain a proper medical diagnosis during multiple examinations.
Yager [1988] developed the ordered weighted averaging (OWA) operator and applied in decision making problems. Xu & Yager [2006] developed some geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy hybrid geometric (IFHG) operator and gave an application of the IFHG operator to multiple attribute group decision making with intuitionistic fuzzy information.
Linguistic neutrosophic numbers (LNNs) can easily describe the incomplete and indeterminate information by the truth, indeterminacy, and falsity linguistic variables (LVs), and the Hamy mean (HM) operator is a good tool to deal with multiple attribute group decision making (MAGDM) problems because it can capture the interrelationship among the multi-input arguments.
This article introduces the concept of Heronian mean operators, geometric Heronian mean operators, neutrosophic cubic number–improved generalized weighted Heronian mean operators, neutrosophic cubic number–improved generalized weighted geometric Heronian mean operators. These operators actually generalize the operators of fuzzy sets, cubic sets, and neutrosophic sets. We investigate the average weighted operator on neutrosophic cubic sets and weighted geometric operator on neutrosophic cubic sets to aggregate the neutrosophic cubic information. After this, based on average weighted and geometric weighted and cosine similarity function in neutrosophic cubic sets, we developed a multiple attribute group decision-making method. Finally, we give a mathematical example to illustrate the usefulness and application of the proposed method.
To comprehensively describe uncertain/interval linguistic arguments and confident linguistic arguments in the decision making process by a linguistic form, this study first presents the concept of a single-valued linguistic neutrosophic interval linguistic number (SVLN-ILN), which is comprehensively composed of its uncertain/interval linguistic number (determinate linguistic argument part) and its single-valued linguistic neutrosophic number (confident linguistic argument part), and its basic operations.