Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment

Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment
Author: Harish Garg
Publisher: Infinite Study
Total Pages: 25
Release:
Genre: Mathematics
ISBN:

The aim of this paper is to introduce some new operators for aggregating single-valued neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making (MCDM) problems. Single-valued neutrosophic set, as an extension and generalization of an intuitionistic fuzzy set, is a powerful tool to describe the fuzziness and uncertainty, and Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. In order to make full use of the advantages of both, we introduce two new prioritized MM aggregation operators, such as the SVN prioritized MM (SVNPMM) and SVN prioritized dual MM (SVNPDMM) under SVN set environment. In addition, some properties of these new aggregation operators are investigated and some special cases are discussed. Furthermore, we propose a new method based on these operators for solving the MCDM problems. Finally, an illustrative example is presented to testify the efficiency and superiority of the proposed method by comparing it with the existing method.

Linguistic neutrosophic Hamacher aggregation operators and the application in evaluating land reclamation schemes for mines

Linguistic neutrosophic Hamacher aggregation operators and the application in evaluating land reclamation schemes for mines
Author: Weizhang Liang
Publisher: Infinite Study
Total Pages: 29
Release:
Genre: Business & Economics
ISBN:

Land reclamation has become a significant way for the improvement of ecological environment in mining areas. When selecting the optimal land reclamation scheme, LNNs (linguistic neutrosophic numbers) are suitable to describe the complex fuzzy evaluation information through linguistic truth, indeterminacy and falsity membership degrees. Furthermore, the Hamacher aggregation operators are good tools to handle multi-criteria decision making problems. Accordingly, the aim of this paper is to extend Hamacher aggregation operators with LNNs and then build a decision making framework for evaluating land reclamation schemes in mining areas.

Logarithmic Hybrid Aggregation Operators Based on Single Valued Neutrosophic Sets and Their Applications in Decision Support Systems

Logarithmic Hybrid Aggregation Operators Based on Single Valued Neutrosophic Sets and Their Applications in Decision Support Systems
Author: Shahzaib Ashraf
Publisher: Infinite Study
Total Pages: 23
Release:
Genre: Mathematics
ISBN:

The purpose of this paper is to introduce new aggregation operators based on logarithmic operations and to develop a multi-criteria decision-making approach to study the interaction between the input argument under the single valued neutrosophic (SVN) environment. The main advantage of the proposed operator is that it can deal with the situations of the positive interaction, negative interaction or non-interaction among the criteria, during decision-making process.

The Generalized Neutrosophic Cubic Aggregation Operators and Their Application to Multi-Expert Decision-Making Method

The Generalized Neutrosophic Cubic Aggregation Operators and Their Application to Multi-Expert Decision-Making Method
Author: Majid Khan
Publisher: Infinite Study
Total Pages: 17
Release:
Genre: Mathematics
ISBN:

In the modern world, the computation of vague data is a challenging job. Different theories are presented to deal with such situations. Amongst them, fuzzy set theory and its extensions produced remarkable results. Smarandache extended the theory to a new horizon with the neutrosophic set (NS), which was further extended to interval neutrosophic set (INS).

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

New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications

New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications
Author: Florentin Smarandache
Publisher: MDPI
Total Pages: 714
Release: 2019-11-27
Genre: Technology & Engineering
ISBN: 3039219383

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.

Linguistic neutrosophic power Muirhead mean operators for safety evaluation of mines

Linguistic neutrosophic power Muirhead mean operators for safety evaluation of mines
Author: Suizhi Luo
Publisher: Infinite Study
Total Pages: 21
Release:
Genre: Mathematics
ISBN:

Safety is the fundamental guarantee for the sustainable development of mining enterprises. As the safety evaluation of mines is a complex system engineering project, consistent and inconsistent, even hesitant evaluation information may be contained simultaneously. Linguistic neutrosophic numbers (LNNs), as the extensions of linguistic terms, are effective means to entirely and qualitatively convey such evaluation information with three independent linguistic membership functions. The aim of our work is to investigate several mean operators so that the safety evaluation issues of mines are addressed under linguistic neutrosophic environment.

Neutrosophic Operational Research

Neutrosophic Operational Research
Author: Florentin Smarandache
Publisher: Springer Nature
Total Pages: 628
Release: 2021-09-09
Genre: Business & Economics
ISBN: 3030571971

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.

Strategic Fuzzy Extensions and Decision-making Techniques

Strategic Fuzzy Extensions and Decision-making Techniques
Author: Kamal Kumar
Publisher: CRC Press
Total Pages: 177
Release: 2024-07-31
Genre: Technology & Engineering
ISBN: 1040088694

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.