There are two kinds of tutorial articles: those that provide a primer on an established topic and those that let us in on the ground floor of something of emerging importance. The first type of tutorial can have a noted expert who has been gracious (and brave) enough to write a field guide about a particular topic. The other sort of tutorial typically involves researchers who have each been laboring on a topic for some years. Both sorts of tutorial articles are very much desired. But we, as an editorial board for both Systems and Transactions, know that there has been no logical place for them in the AESS until this series was started several years ago. With these tutorials, we hope to continue to give them a home, a welcome, and provide a service to our membership. We do not intend to publish tutorials on a regular basis, but we hope to deliver them once or twice per year. We need and welcome good, useful tutorial articles (both kinds) in relevant AESS areas. If you, the reader, can offer a topic of interest and an author to write about it, please contact us. Self-nominations are welcome, and even more ideal is a suggestion of an article that the editor(s) can solicit. All articles will be reviewed in detail. Criteria on which they will be judged include their clarity of presentation, relevance, and likely audience, and, of course, their correctness and scientific merit. As to the mathematical level, the articles in this issue are a good guide: in each case the author has striven to explain complicated topics in simple-well, tutorial-terms. There should be no (or very little) novel material: the home for archival science is the Transactions Magazine, and submissions that need to be properly peer reviewed would be rerouted there. Likewise, articles that are interesting and descriptive, but lack significant tutorial content, ought more properly be submitted to the Systems Magazine.

What is a tutorial

Fuzzy best-worst method is proposed to solve the issues under fuzzy environment.A consistency ratio for fuzzy best-worst method is proposed for verification.The results indicate the fuzzy best-worst method outperforms best-worst method.The fuzzy best-worst method has a higher comparison consistency. Considering the vagueness frequently representing in decision data due to the lack of complete information and the ambiguity arising from the qualitative judgment of decision-makers, the crisp values of criteria may be inadequate to model the real-life multi-criteria decision-making (MCDM) issues. In this paper, the latest MCDM method, namely best-worst method (BWM) was extended to the fuzzy environment. The reference comparisons for the best criterion and for the worst criterion were described by linguistic terms of decision-makers, which can be expressed in triangular fuzzy numbers. Then, the graded mean integration representation (GMIR) method was employed to calculate the weights of criteria and alternatives with respect to different criteria under fuzzy environment. According to the concept of BWM, the nonlinearly constrained optimization problem was built for determining the fuzzy weights of criteria and alternatives with respect to different criteria. The fuzzy ranking scores of alternatives can be derived from the fuzzy weights of alternatives with respect to different criteria multiplied by fuzzy weights of the corresponding criteria, and then the crisp ranking score of alternatives can be calculated by employing GMIR method for optimal alternative selection. Meanwhile, the consistency ratio was proposed for fuzzy BWM to check the reliability of fuzzy preference comparisons. Three case studies were performed to illustrate the effectiveness and feasibility of the proposed fuzzy BWM. The results indicate the proposed fuzzy BWM can not only obtain reasonable preference ranking for alternatives but also has higher comparison consistency than the BWM.

Fuzzy best-worst multi-criteria decision-making method and its applications

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.

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A Historical Account of Types of Fuzzy Sets and Their Relationships

Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems

In this paper, we investigate the multiple attribute decision making problems with picture fuzzy information. Then, we utilize arithmetic and geometric operations to develop some picture fuzzy aggregation operators: picture fuzzy weighted average (PFWA) operator, picture fuzzy weighted geometric (PFWG) operator, picture fuzzy ordered weighted average (PFOWA) operator, picture fuzzy ordered weighted geometric (PFOWG) operator, picture fuzzy hybrid average (PFHA) operator and picture fuzzy hybrid geometric (PFHG) operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the picture fuzzy multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Picture fuzzy aggregation operators and their application to multiple attribute decision making

As a variation of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete and inconsistent information that exists in the real world. Simplified neutrosophic sets SNSs have been proposed for the main purpose of addressing issues with a set of specific numbers. However, there are certain problems regarding the existing operations of SNSs, as well as their aggregation operators and the comparison methods. Therefore, this paper defines the novel operations of simplified neutrosophic numbers SNNs and develops a comparison method based on the related research of intuitionistic fuzzy numbers. On the basis of these operations and the comparison method, some SNN aggregation operators are proposed. Additionally, an approach for multi-criteria group decision-making MCGDM problems is explored by applying these aggregation operators. Finally, an example to illustrate the applicability of the proposed method is provided and a comparison with some other methods is made.

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Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems

In recent years, hesitant fuzzy sets (HFSs) and neutrosophic sets (NSs) have become a subject of great interest for researchers and have been widely applied to multi-criteria group decision-making (MCGDM) problems. In this paper, multi-valued neutrosophic sets (MVNSs) are introduced, which allow the truth-membership, indeterminacy- membership and falsity-membership degree have a set of crisp values between zero and one, respectively. Then the operations of multi-valued neutrosophic numbers (MVNNs) based on Einstein operations are defined, and a comparison method for MVNNs is developed depending on the related research of HFSs and Atanassov's intuitionistic fuzzy sets (IFSs). Furthermore, the multi-valued neutrosophic power weighted average (MVNPWA) operator and the multi-valued neutrosophic power weighted geometric (MVNPWG) operator are proposed and the desirable properties of two operators are also discussed. Finally, an approach for solving MCGDM problems is explored by applying the power aggreg...

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Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

For many companies, green product development has become a key strategic consideration due to regulatory requirements and market trends. In this paper, the life cycle assessment technique is used to develop an innovative multi-criteria group decision-making approach that incorporates power aggregation operators and a TOPSIS-based QUALIFLEX method in order to solve green product design selection problems using neutrosophic linguistic information. Differences in semantics as well as the risk preferences of decision-makers are considered in the proposed method. The practicality and effectiveness of the proposed approach are then demonstrated through an illustrative example, in which the proposed method is used to select the optimum green product design, followed by sensitivity and comparative analyses.

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Jing Wang

Papers

Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems

Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems

Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

Simplified Neutrosophic Linguistic Multi-criteria Group Decision-Making Approach to Green Product Development

An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets