scholarly journals Correlation coefficients of credibility interval-valued neutrosophic sets and their group decision-making method in single- and interval-valued hybrid neutrosophic multi-valued environment

Author(s):  
Jun Ye ◽  
Shigui Du ◽  
Rui Yong

AbstractAlthough a single-valued neutrosophic multi-valued set (SVNMVS) can reasonably and perfectly express group evaluation information and make up for the flaw of multi-valued/hesitant neutrosophic sets in group decision-making problems, its information expression and group decision-making methods still lack the ability to express and process single- and interval-valued hybrid neutrosophic multi-valued information. To overcome the drawbacks, this study needs to propose single- and interval-valued hybrid neutrosophic multi-valued sets (SIVHNMVSs), correlation coefficients of consistency interval-valued neutrosophic sets (CIVNSs), and their multi-attribute group decision-making (MAGDM) method in the setting of SIVHNMVSs. First, we propose SIVHNMVSs and a transformation method for converting SIVHNMVSs into CIVNSs based on the mean and consistency degree (the complement of standard deviation) of truth, falsity and indeterminacy sequences. Then, we present two correlation coefficients between CIVNSs based on the multiplication of both the correlation coefficient of interval-valued neutrosophic sets and the correlation coefficient of neutrosophic consistency sets and two weighted correlation coefficients of CIVNSs. Next, a MAGDM method is developed based on the proposed two weighted correlation coefficients of CIVNSs for performing MAGDM problems under the environment of SIVHNMVSs. At last, a selection case of landslide treatment schemes demonstrates the application of the proposed MAGDM method under the environment of SIVHNMVSs. By comparative analysis, our new method not only overcomes the drawbacks of the existing method, but also is more extensive and more useful than the existing method when tackling MAGDM problems in the setting of SIVHNMVSs.

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jun Ye ◽  
Shigui Du ◽  
Rui Yong

The notion of multifuzzy sets (MFSs) or multi-interval-valued fuzzy sets (MIVFSs) provides a new method to represent some problems with a sequence of the different and/or same fuzzy/interval-valued fuzzy membership values of an element to the set. Then, a fuzzy cubic set (FCS) consists of a certain part (a fuzzy value) and an uncertain part (an interval-valued fuzzy value) but cannot represent hybrid information of both MFS and MIVFS. To adequately depict the opinion of several experts/decision-makers by using a union/sequence of the different and/or same fuzzy cubic values for an object assessed in group decision-making (GDM) problems, this paper proposes a multifuzzy cubic set (MFCS) notion as the conceptual extension of FCS to express the hybrid information of both MFS and MIVFS in the fuzzy setting of both uncertainty and certainty. Then, we propose three correlation coefficients of MFCSs and then introduce correlation coefficients of MFSs and MIVFSs as special cases of the three correlation coefficients of MFCSs. Further, the multicriteria GDM methods using three weighted correlation coefficients of MFCSs are developed under the environment of MFCSs, which contains the MFS and MIVFS GDM methods. Lastly, these multicriteria GDM methods are applied in an illustrative example on the selection problem of equipment suppliers; then their decision results and comparative analysis indicate that the developed GDM methods are more practicable and effective and reflect that either different correlation coefficients or different information expressions can also impact on the ranking of alternatives. Therefore, this study indicates the main contribution of the multifuzzy cubic information expression, correlation coefficients, and GDM methods in the multifuzzy setting of both uncertainty and certainty.


2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Shenqing Jiang ◽  
Wei He ◽  
Fangfang Qin ◽  
Qingqing Cheng

In this paper, we focus on new methods to deal with multiple attribute group decision-making (MAGDM) problems and a new comparison law of interval-valued dual hesitant fuzzy elements (IVDHFEs). More explicitly, the interval-valued dual hesitant fuzzy 2nd-order central polymerization degree (IVDHFCP2) function is introduced, for the case that score values of different IVDHFEs are identical. This function can further compare different IVDHFEs. Then, we develop a series of interval-valued dual hesitant fuzzy power Heronian aggregation operators, i.e., the interval-valued dual hesitant fuzzy power Heronian mean (IVDHFPHM) operator, the interval-valued dual hesitant fuzzy power geometric Heronian mean (IVDHFPGHM) operator, and their weighted forms. Some desirable properties and their special cases are discussed. These proposed operators can simultaneously reflect the interrelationship of aggregated arguments and reduce the influence of unreasonable evaluation values. Finally, two approaches for interval-valued dual hesitant fuzzy MAGDM with known or unknown weight information are presented. An illustrative example and comparative studies are given to verify the advantages of our methods. A sensitivity analysis of the decision results is analyzed with different parameters.


PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0258772
Author(s):  
Yuan Xu ◽  
Shifeng Liu ◽  
Jun Wang

Fuzzy set theory and its extended form have been widely used in multiple-attribute group decision-making (MAGDM) problems, among which the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) got a lot of attention for its ability of capturing information denoted by interval values. Based on the previous studies, to find a better solution for fusing qualitative quantization information with fuzzy numbers, we propose a novel definition of interval-valued q-rung orthopair uncertain linguistic sets (IVq-ROULSs) based on the linguistic scale functions, as well as its corresponding properties, such as operational rules and the comparison method. Furthermore, we utilize the power Muirhead mean operators to construct the information fusion method, and provide a variety of aggregation operators based on the proposed information description environment. A model framework is constructed for solving the MAGDM problem utilizing the proposed method. Finally, we illustrate the performance of the new method and investigate its advantages and superiorities through comparative analysis.


Author(s):  
Changxing Fan ◽  

The paper presents the correlation coefficient of refined-single valued neutrosophic sets (Refined-SVNSs) based on the extension of the correlation of single valued neutrosophic sets (SVNSs), and then a decision making method is proposed by the use of the weighted correlation coefficient of Refined-SVNSs. Through the weighted correlation coefficient between the ideal alternative and each alternative, we can rank all alternatives and the best one of all alternatives can be easily identified as well. Finally, to prove this decision making method proposed in this paper is useful to deal with the actual application, we use an example to illustrate it.


2011 ◽  
Vol 3 (3) ◽  
pp. 15-41 ◽  
Author(s):  
John Robinson P. ◽  
Henry AmirtharajE. C.

This paper extends the technique for order preference by similarity to ideal solution (TOPSIS) for solving multi-attribute group decision making (MAGDM) problems under triangular intuitionistic fuzzy sets by using its correlation coefficient. In situations where the information or the data is of the form of triangular intuitionistic fuzzy numbers (TIFNs), some arithmetic aggregation operators have to be defined, namely the triangular intuitionistic fuzzy ordered weighted averaging (TIFOWA) operator and the triangular intuitionistic fuzzy hybrid aggregation (TIFHA) operator. An extended TOPSIS model is developed to solve the MAGDM problems using a new type of correlation coefficient defined for TIFNs based on the triangular intuitionistic fuzzy weighted arithmetic averaging (TIFWAA) operator and the TIFHA operator. With an illustration this proposed model of MAGDM with the correlation coefficient of TIFNs is compared with the other existing methods.


2021 ◽  
pp. 1-16
Author(s):  
Mian Yan ◽  
Jianghong Feng ◽  
Su Xiu Xu

In recent years, the problem of complex multi-attribute group decision-making (MAGDM) in uncertain environments has received increasing attention. In evaluating MAGDM problems, obtaining the objective attribute weights is very important. Considering the excellent performance of intuitive fuzzy linguistic sets in dealing with uncertain information, this paper introduces a new interval-valued intuitionistic pure linguistic entropy weight (IVIPLEW) method for determining attribute weights and evaluating MAGDM problems. The IVIPLEW method considers the cases of missing values, and uses the conventional interval-valued intuitionistic pure linguistic (IVIPL) expectations to supplement the missing values. This method of dealing with missing values not only considers the expectations of experts, but also prevents fluctuations in linguistic variables from impacting the decision results. This paper establishes an analysis framework that allows the IVIPLEW method to be applied to MAGDM problems, and presents a practical case study that illustrates the practicality and effectiveness of IVIPLEW. The results are quite satisfactory. The effectiveness of the proposed method is demonstrated through a comparison with the IVIPL information aggregation method. Furthermore, the robustness of the IVIPLEW method is verified through a sensitivity analysis. The results presented in this paper show that the IVIPLEW method is applicable to a wide range of MAGDM problems.


2014 ◽  
Vol 513-517 ◽  
pp. 721-724 ◽  
Author(s):  
Chen Guang Xu ◽  
Dong Xiao Liu ◽  
Min Li

In this paper, we First utilize the induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision makers into a collective interval-valued intuitionistic fuzzy decision matrix. Based on the basic ideal of traditional VIKOR method, we establish an optimization model to determine the weights of attributes. Then, calculation steps based on the collective interval-valued intuitionistic fuzzy decision matrix and traditional VIKOR method for solving the MAGDM problems with interval-valued intuitionistic fuzzy assessments and partially known weight information are given. Finally, a numerical example is used to illustrate the applicability of the proposed approach.


2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Rana Muhammad Zulqarnain ◽  
Xiao Long Xin ◽  
Muhammad Saqlain ◽  
Waseem Asghar Khan

The correlation coefficient between the two parameters plays a significant part in statistics. Furthermore, the exactness of the assessment of correlation depends upon information from the set of discourses. The data collected for various statistical studies are full of ambiguities. The idea of interval-valued intuitionistic fuzzy soft sets is an extension of intuitionistic fuzzy soft sets that is used to express insufficient evaluation, uncertainty, and anxiety in decision-making. Intuitionistic fuzzy soft sets consider two different types of information, such as membership degree and nonmembership degree. In this paper, the concepts and properties of the correlation coefficient and the weighted correlation coefficient of interval-valued intuitionistic fuzzy soft sets are proposed. A prioritization technique for order preference by similarity to the ideal solution based on interval-valued intuitionistic fuzzy soft sets of correlation coefficients and the weighted correlation coefficient is introduced. We also proposed interval-valued intuitionistic fuzzy soft weighted average and interval-valued intuitionistic fuzzy soft weighted geometric operators and developed decision-making techniques based on the proposed operators. By using the developed techniques, a method for solving decision-making problems is proposed. To ensure the applicability of the proposed methods, an illustrative example is given. Finally, we present a comparison of some existing methods with our proposed techniques.


2014 ◽  
Vol 513-517 ◽  
pp. 725-728 ◽  
Author(s):  
Chen Guang Xu

In this paper, we investigate the multi-attribute group decision making (MAGDM) problems in which all the information provided by the decision makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFN), and the information about attribute weights is partially known. First, we utilize the induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision makers into a collective interval-valued intuitionistic fuzzy decision matrix. Based on the basic ideal of traditional VIKOR method, we establish an optimization model to determine the weights of attributes. Then, calculation steps based on the collective interval-valued intuitionistic fuzzy decision matrix and traditional VIKOR method for solving the MAGDM problems with interval-valued intuitionistic fuzzy assessments and partially known weight information are given. Finally, a numerical example is used to illustrate the applicability of the proposed approach.


Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 441 ◽  
Author(s):  
Wuhuan Xu ◽  
Xiaopu Shang ◽  
Jun Wang ◽  
Weizi Li

This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method.


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