Correlated aggregation operators for simplified neutrosophic set and their application in multi-attribute group decision making

The simplified neutrosophic set (SNS) is a useful generalization of the fuzzy set that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function.

<p>Neutrosophic set (NS) is a generalization of fuzzy set (FS) that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function. In this paper, we study the multi-attribute group decision making (MAGDM) problems under neutrosophic environment with the incompletely known or completely unknown attribute weight. </p>

Extension of safety and critical effect analysis to neutrosophic sets for the evaluation of occupational risks

Neutrosophic triplet structure yields a symmetric property of truth membership on the left, indeterminacy membership in the centre and false membership on the right, as do points of object, centre and image of reflection. As an extension of a neutrosophic set, the Q-neutrosophic set was introduced to handle two-dimensional uncertain and inconsistent situations. We extend the soft expert set to generalized Q-neutrosophic soft expert set by incorporating the idea of soft expert set to the concept of Q-neutrosophic set and attaching the parameter of fuzzy set while defining a Q-neutrosophic soft expert set. This pattern carries the benefits of Q-neutrosophic sets and soft sets, enabling decision makers to recognize the views of specialists with no requirement for extra lumbering tasks, thus making it exceedingly reasonable for use in decision-making issues that include imprecise, indeterminate and inconsistent two-dimensional data. Some essential operations namely subset, equal, complement, union, intersection, AND and OR operations and additionally several properties relating to the notion of generalized Q-neutrosophic soft expert set are characterized. Finally, an algorithm on generalized Q-neutrosophic soft expert set is proposed and applied to a real-life example to show the efficiency of this notion in handling such problems.

In this paper, a new compromise algorithm for multi-objective transportation problem (MO-TP) is developed, which is inspired by Zimmermann's fuzzy programming and the neutrosophic set terminology. The proposed NCPA is characterized by assigning three membership functions for each objective namely, truth membership, indeterminacy membership and falsity membership. With the membership functions for all objectives, a neutrosophic compromise programming model is constructed with the aim to find best compromise solution (BCS). This model can cover a wide spectrum of BCSs by controlling the membership functions interactively. The performance of the NCPA is validated by measuring the ranking degree using TOPSIS approach. Illustrative examples are reported and compared with exists models in the literature. Based on the provided comparisons, NCPA is superior to fuzzy and different approaches.

Neutrosophic numbers and matrices extend classical fuzzy set theory by incorporating three components to represent uncertainty: truth membership, indeterminacy membership, and falsity membership degrees. Real neutrosophic matrices consist of neutrosophic numbers as their entries, offering a structure to model uncertain and imprecise information across various applications. This paper investigates operations on real neutrosophic matrices, such as addition, multiplication, and scalar multiplication, and defines how these operations function within the neutrosophic framework. The paper also examines the use of LU decomposition as an efficient method for solving systems of real neutrosophic linear algebraic equations. LU decomposition is a numerical technique that breaks down a matrix into lower and upper triangular matrices, enabling the solution of linear systems through forward and backward substitution.

With Chinese economic development in a new normal state, micro and small corporations have increasingly played an important role. The credit evaluation for micro and small corporations can contribute to efficient financial decisions. Traditional methods for the corporate credit evaluation rarely consider fuzzy features of micro and small entrepreneurs. Since the credit evaluation procedure for entrepreneurs consists of some alternatives and influential indicators, it can be recognized as a multi-criteria decision-making (MCDM) problem. To better express uncertainty information, a four-branch fuzzy set (FBFS) is presented to deal with the issue, which is characterized by a truth-membership function, an unknown-membership function and a falsity-membership function. In the paper, to handle the MCDM problems under four-branch fuzzy environments, the evaluation based on distance from average solution (EDAS) method is extended and utilized. These obvious improvement places include integrating an interval weight vector, determining an average solution, transforming a decision matrix and analyzing a change trend of the coefficients. To demonstrate the applicability and rationality of the proposed method in practice, an illustrative example is implemented, concerning a credit evaluation for some micro and small entrepreneurs. Its feasibility and validity are further verified by a sensitivity analysis and a comparative analysis. The results show the FBFSs and extended EDAS method can well match the reality and appropriately handle the credit evaluation problems for micro and small entrepreneurs.

<p>In this study, we give some concepts concerning the neutrosophic sets, single valued neutrosophic sets, interval-valued neutrosophic sets, bipolar neutrosophic sets, neutrosophic hesitant fuzzy sets, inter-valued neutrosophic hesitant fuzzy sets, refined neutrosophic sets, bipolar neutrosophic refined sets, multi-valued neutrosophic sets, simplified<br>\nneutrosophic linguistic sets, neutrosophic over/off/under sets, rough neutrosophic sets, rough bipolar neutrosophic sets, rough neutrosophic hyper-complex set, and their basic operations. Then we introduce triangular neutrosophic numbers, trapezoidal neutrosophic fuzzy number and their basic operations. Also some comparative studies between the existing neutrosophic sets and neutrosophic number are provided.</p>

The paper presents two new correlation coefficients of simplified neutrosophic sets (SNSs) as the further extension of the correlation coefficient of single valued neutrosophic sets (SVNSs) and investigates their properties.

As a generalization of complex fuzzy set (CFS), complex hesitation fuzzy set (CHFS) is a powerful tool to express two-dimensional fuzzy information, but it ignores the randomness that exists widely in real life. Considering the randomness and ambiguity often simultaneously occur in real-world problems, we come up with an innovative fuzzy set called complex probabilistic hesitant fuzzy set (CPHFS) in this article, which is a joint extension of CFS and probabilistic hesitant fuzzy set (PHFS). Moreover, we establish four basic operations for complex probabilistic hesitant fuzzy element(CPHFE) and a series of useful operational laws are also developed. Secondly, several aggregation operators including complex probabilistic hesitant fuzzy weighted averaging operator(CPHFWA), complex probabilistic hesitant fuzzy weighted geometric operator(CPHFWG), complex probabilistic hesitant fuzzy Heronian Mean operator(CPHFHM) and complex probabilistic hesitant fuzzy Geometric Heronian Mean operator(CPHFGHM) as well as their weighted forms that can reflect the interrelationship among all decision attributes are proposed, which is of great use in multi-attribute decision making(MADM) or in multi-attribute group decision making(MAGDM) issues when we want to synthesize multiple evaluation values into one. Besides, we also present a number of valuable properties of these provided aggregation operators. Thirdly, a MADM process is built in the CPHF environment step by step based on the aggregation operators we have just established. Furthermore, we provide an example about purchasing a most suitable car to demonstrate the effectiveness and practicability of the proposed decision process. Finally, we point out the superiorities of MADM in working under the CPHF environment through comparing it with the existing method and also offer some possible prospects for further research. The method displayed in this work can effectively solve the MADM problems where the decision-making information is described by CPHFEs and the attributes are interactive.

A multi-distance interval-valued neutrosophic approach for social failure detection in sustainable municipal waste management

The rare earth industry is a crucial strategic industry that is related to the national economy and national security. In the context of economic globalization, international competition is becoming increasingly fierce, and the rare earth industry is facing a more severe survival and development environment than ever before. Although China is the greatest world’s rare earth country in rare earth reserves, production, consumption and export volume, it is not a rare earth power. The rare earth industry has no right to speak in the international market. The comparative advantage is weakening and the security of rare earth industry appears. Therefore, studying the rare earth industry security has important theoretical and practical significance. When measuring the China’s rare earth industry security, the primary problem involves tremendous uncertainty. Neutrosophic soft set (NSS), depicted by the parameterized form of truth membership, falsity membership and indeterminacy membership, is a more serviceable pattern for capturing uncertainty. In this paper, five dimensions of rare earth industry security are identified and then prioritized against twelve different criteria relevant to structure, organization, layout, policy and ecological aspects of industry security. Then, the objective weight is computed by CRITIC (Criteria Importance Through Inter-criteria Correlation) method while the integrated weight is determined by concurrently revealing subjective weight and objective weight. Later, neutrosophic soft decision making method based CoCoSo (Combined Compromise Solution) is explored for settling the issue of low discrimination. Lastly, the feasibility and validity of the developed algorithm is verified by the issue of China’s rare earth industry security evaluation.

This paper proposes a new method to deal with the multi-attribute group decision making (MAGDM) problem. Firstly, a new distance measure between two linguistic terms is defined, then a new linguistic information aggregation operator based on the distance measure is proposed and their properties are studied. Secondly, in order to deal with multi-attribute group decision making problem under linguistic environment, a similarity measure between two linguistic preference matrices is proposed. The aggregation operator and the similarity measure are applied to a MAGDM problem. Finally, a numerical example is proposed to prove that the new operator is effective in the MAGDM problems. This method avoid the case that a numerical value times a linguistic information and the results of evaluation are still belongs to the original linguistic term set no matter how to calculate. By using the supporting of the order, the linguistic information can not be lose in the aggregation process. Keywords-Distance measure; linguistic information; aggregation operator; similarity measure; MAGDM

Interval-valued neutrosophic hesitant fuzzy set (INHFS) is a generalization of the fuzzy set (FS) that is designed for some practical situations in which each element has different truth membership hesitant function, indeterminacy membership hesitant function and falsity membership hesitant function, and permits the membership degrees to have a set of possible interval values. In this paper, we develop the correlation coefficient and the weighted correlation coefficient for INHFSs and study their properties. Then, an approach to multi- attribute decision making (MADM) within the framework of INHFS is developed by the weighted correlation coefficient. Finally, a practical application of the developed approach to the problem of investment is given, and the result shows that our approach is reasonable and effective in dealing with decision making (DM) problems.

PurposeThe purpose of this paper is to develop an agility evaluation approach to determine the most suitable agile system for implementing mass customization (MC) strategies. Evaluating the alternatives and comparing across them, the best practices of the efficient organization can be identified and transferred to different organizations.Design/methodology/approachGrey relation approach is a simple mathematical technique useful in situations where the information is not known precisely. Grey relation approach has been applied to measure the agility of various organizations based on agile entities and accordingly the organizations are ranked. The ranking so obtained is compared with the ranking obtained by a popular multi‐attribute decision making (MADM) process known as Fuzzy TOPSIS (technique for order preference by similarity to ideal solution) to test the robustness of the proposed method. It is to be noted that grey theory considers the condition of the fuzziness and can deal flexibly with the fuzziness situation.FindingsIt is demonstrated that the grey approach is an appropriate method for solving MADM problems in an uncertain situation with less computational efforts. The alternatives can easily be benchmarked and the best agile system can be selected. As the ranking obtained through grey relation approach closely agree with the ranking found from Fuzzy TOPSIS method, the robustness of the proposed approach is validated. Both the methods lead to choosing a suitable agile system related to mass customization.Research limitations/implicationsIn this paper, the proposed approach has been compared with Fuzzy TOPSIS method to test the robustness of the method. Other MADM approaches may be used for comparison purpose to gain insight into the methodology of the proposed approach.Originality/valueAn alternative approach for MADM is proposed to obtain good decisions in an uncertain environment and used for agility evaluation in selected organizations. As agile manufacturing is relatively a new concept, certain and complete information on systems are not available. In such situations, the proposed method can deal with the issue conveniently and results in workable solutions.