51
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Cosine similarity measures of bipolar neutrosophic set for diagnosis of bipolar disorder diseases. Artif Intell Med 2019; 101:101735. [PMID: 31813487 DOI: 10.1016/j.artmed.2019.101735] [Citation(s) in RCA: 67] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2019] [Revised: 09/25/2019] [Accepted: 09/26/2019] [Indexed: 11/23/2022]
Abstract
Similarity plays a significant implicit or explicit role in various fields. In some real applications in decision making, similarity may bring counterintuitive outcomes from the decision maker's standpoint. Therefore, in this research, we propose some novel similarity measures for bipolar and interval-valued bipolar neutrosophic set such as the cosine similarity measures and weighted cosine similarity measures. The propositions of these similarity measures are examined, and two multi-attribute decision making techniques are presented based on proposed measures. For verifying the feasibility of proposed measures, two numerical examples are presented in comparison with the related methods for demonstrating the practicality of the proposed method. Finally, we applied the proposed measures of similarity for diagnosing bipolar disorder diseases.
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52
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Cui WH, Ye J. Logarithmic similarity measure of dynamic neutrosophic cubic sets and its application in medical diagnosis. COMPUT IND 2019. [DOI: 10.1016/j.compind.2019.06.008] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
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53
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Luo M, Wu L, Zhou K, Zhang H. Multi-criteria decision making method based on the single valued neutrosophic sets1. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019. [DOI: 10.3233/jifs-182723] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Minxia Luo
- Department of Information and Computing Science, China Jiliang University, Hangzhou, P.R. China
| | - Lixian Wu
- Department of Information and Computing Science, China Jiliang University, Hangzhou, P.R. China
| | - Kaiyan Zhou
- Department of Information and Computing Science, China Jiliang University, Hangzhou, P.R. China
| | - Huarong Zhang
- Department of Applied Mathematics, China Jiliang University, Hangzhou, P.R. China
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54
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New multiparametric similarity measure for neutrosophic set with big data industry evaluation. Artif Intell Rev 2019. [DOI: 10.1007/s10462-019-09756-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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55
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56
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Fan C. Correlation Coefficients of Refined-Single Valued Neutrosophic Sets and Their Applications in Multiple Attribute Decision-Making. JOURNAL OF ADVANCED COMPUTATIONAL INTELLIGENCE AND INTELLIGENT INFORMATICS 2019. [DOI: 10.20965/jaciii.2019.p0421] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
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.
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57
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Multi-Attribute Decision Making Based on Probabilistic Neutrosophic Hesitant Fuzzy Choquet Aggregation Operators. Symmetry (Basel) 2019. [DOI: 10.3390/sym11050623] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Take the third-party logistics providers (3PLs) as an example, according to the characteristics of correlation between attributes in multi-attribute decision-making, two Choquet aggregation operators adoping probabilistic neutrosophic hesitation fuzzy elements (PNHFEs) are proposed to cope with the situations of correlation among criterions. This measure not only provides support for the correlation phenomenon between internal attributes, but also fully concerns the incidental uncertainty of the external space. Our goal is to make it easier for decision makers to cope with this uncertainty, thus we establish the notion of probabilistic neutrosophic hesitant fuzzy Choquet averaging (geometric) (PNHFCOA, PNHFCOG) operator. Based on this foundation, a method for aggregating decision makers’ information is proposed, and then the optimal decision scheme is obtained. Finally, an example of selecting optimal 3PL is given to demonstrate the objectivity of the above-mentioned standpoint.
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58
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Linguistic Neutrosophic Numbers Einstein Operator and Its Application in Decision Making. MATHEMATICS 2019. [DOI: 10.3390/math7050389] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Linguistic neutrosophic numbers (LNNs) include single-value neutrosophic numbers and linguistic variable numbers, which have been proposed by Fang and Ye. In this paper, we define the linguistic neutrosophic number Einstein sum, linguistic neutrosophic number Einstein product, and linguistic neutrosophic number Einstein exponentiation operations based on the Einstein operation. Then, we analyze some of the relationships between these operations. For LNN aggregation problems, we put forward two kinds of LNN aggregation operators, one is the LNN Einstein weighted average operator and the other is the LNN Einstein geometry (LNNEWG) operator. Then we present a method for solving decision-making problems based on LNNEWA and LNNEWG operators in the linguistic neutrosophic environment. Finally, we apply an example to verify the feasibility of these two methods.
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59
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Hybrid Weighted Arithmetic and Geometric Aggregation Operator of Neutrosophic Cubic Sets for MADM. Symmetry (Basel) 2019. [DOI: 10.3390/sym11020278] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
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.
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60
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Nancy, Garg H. A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019. [DOI: 10.3233/jifs-18040] [Citation(s) in RCA: 41] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Nancy
- School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala, Punjab, India
| | - Harish Garg
- School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala, Punjab, India
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61
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Fu J, Ye J, Cui W. The Dice measure of cubic hesitant fuzzy sets and its initial evaluation method of benign prostatic hyperplasia symptoms. Sci Rep 2019; 9:60. [PMID: 30635593 PMCID: PMC6329808 DOI: 10.1038/s41598-018-37228-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2018] [Accepted: 12/04/2018] [Indexed: 02/08/2023] Open
Abstract
In order to give the initial evaluation of benign prostatic hyperplasia (BPH) symptoms regarding a patient, physician usually performs the clinical inquiry of the patient, whereas his/her responses may contain hesitant fuzzy and uncertain information. However, existing evaluation/diagnosis approaches of BPH symptoms cannot cope with the hybrid problem of both hesitant and uncertain responses of patients. Furthermore, existing evaluation approaches may lose some useful responses (e.g. hesitant fuzzy information) so as to result in the unreasonable or indeterminate evaluation/diagnosis in the evaluation process of patients. To overcome this insufficiency, this study firstly introduces the concept of a cubic hesitant fuzzy set (CHFS) based on combining uncertain/interval-valued fuzzy information with hesitant fuzzy information so as to express the hybrid fuzzy information and proposes the Dice measure between CHFSs based on the extension method of the least common multiple cardinality/number (LCMC) for the hesitant fuzzy sets in CHFS. Then, the initial evaluation approach of BPH symptoms is developed by using the Dice measure of CHFSs. Lastly, the assessment results of six BPH patients are presented as the clinical actual cases to indicate the applicability and effectiveness of the developed assessment approach in CHFS setting. The comparison with existing common evaluation methods shows that the developed evaluation/diagnosis method is superior to the existing common evaluation methods in the evaluation/diagnosis process of the clinical actual cases.
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Affiliation(s)
- Jing Fu
- Shaoxing Second Hospital, 123 Yanan Road, Shaoxing, Zhejiang, 312000, P. R. China
| | - Jun Ye
- Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing, Zhejiang, 312000, P. R. China.
| | - Wenhua Cui
- Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing, Zhejiang, 312000, P. R. China
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62
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An Extended Single-Valued Neutrosophic Projection-Based Qualitative Flexible Multi-Criteria Decision-Making Method. MATHEMATICS 2019. [DOI: 10.3390/math7010039] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
With respect to multi-criteria decision-making (MCDM) problems in which the criteria denote the form of single-valued neutrosophic sets (SVNSs), and the weight information is also fully unknown, a novel MCDM method based on qualitative flexible multiple criteria (QUALIFLEX) is developed. Firstly, the improved cosine measure of the included angle between two SVNSs is defined. Then, the improved single-valued neutrosophic projection is developed, and the corresponding improved single-valued neutrosophic bidirectional projection and single-valued neutrosophic bidirectional projection difference are investigated. Moreover, the partial ordering relation of SVNSs is developed. Secondly, an extended QUALIFLEX method based on an improved single-valued neutrosophic projection measure is proposed to handle MCDM problems in which the weights of criteria are completely unknown. Finally, an example for selection of a green supplier, as well as a performance comparison analysis, are provided to demonstrate the effectiveness of the proposed method.
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63
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Liu D, Liu G, Liu Z. Some Similarity Measures of Neutrosophic Sets Based on the Euclidean Distance and Their Application in Medical Diagnosis. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2018; 2018:7325938. [PMID: 30622626 PMCID: PMC6304201 DOI: 10.1155/2018/7325938] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 07/06/2018] [Revised: 09/25/2018] [Accepted: 10/23/2018] [Indexed: 11/18/2022]
Abstract
Similarity measure is an important tool in multiple criteria decision-making problems, which can be used to measure the difference between the alternatives. In this paper, some new similarity measures of single-valued neutrosophic sets (SVNSs) and interval-valued neutrosophic sets (IVNSs) are defined based on the Euclidean distance measure, respectively, and the proposed similarity measures satisfy the axiom of the similarity measure. Furthermore, we apply the proposed similarity measures to medical diagnosis decision problem; the numerical example is used to illustrate the feasibility and effectiveness of the proposed similarity measures of SVNSs and IVNSs, which are then compared to other existing similarity measures.
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Affiliation(s)
- Donghai Liu
- Department of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China
| | - Guangyan Liu
- Department of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China
| | - Zaiming Liu
- Department of Mathematics, Central South University, Changsha, Hunan 410075, China
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64
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A neutrosophic recommender system for medical diagnosis based on algebraic neutrosophic measures. Appl Soft Comput 2018. [DOI: 10.1016/j.asoc.2017.10.012] [Citation(s) in RCA: 65] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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65
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Wei G, Wei Y. Some single-valued neutrosophic dombi prioritized weighted aggregation operators in multiple attribute decision making. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2018. [DOI: 10.3233/jifs-171741] [Citation(s) in RCA: 72] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- G. Wei
- School of Business, Sichuan Normal University, Chengdu, P.R. China
- School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, P. R. China
| | - Y. Wei
- School of Finance, Yunnan University of Finance and Economics, Kunming, China
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66
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67
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Li YY, Wang JQ, Wang TL. A Linguistic Neutrosophic Multi-criteria Group Decision-Making Approach with EDAS Method. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2018. [DOI: 10.1007/s13369-018-3487-5] [Citation(s) in RCA: 56] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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68
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69
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Karaaslan F, Hayat K. Some new operations on single-valued neutrosophic matrices and their applications in multi-criteria group decision making. APPL INTELL 2018. [DOI: 10.1007/s10489-018-1226-y] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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70
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Some Generalized Dice Measures for Double-Valued Neutrosophic Sets and Their Applications. MATHEMATICS 2018. [DOI: 10.3390/math6070121] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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71
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A Forecasting Model Based on Multi-Valued Neutrosophic Sets and Two-Factor, Third-Order Fuzzy Fluctuation Logical Relationships. Symmetry (Basel) 2018. [DOI: 10.3390/sym10070245] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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72
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Multiple Attribute Decision-Making Method Using Similarity Measures of Neutrosophic Cubic Sets. Symmetry (Basel) 2018. [DOI: 10.3390/sym10060215] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
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73
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A Novel Method for Determining the Attribute Weights in the Multiple Attribute Decision-Making with Neutrosophic Information through Maximizing the Generalized Single-Valued Neutrosophic Deviation. INFORMATION 2018. [DOI: 10.3390/info9060137] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
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74
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The Cosine Measure of Single-Valued Neutrosophic Multisets for Multiple Attribute Decision-Making. Symmetry (Basel) 2018. [DOI: 10.3390/sym10050154] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
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75
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Zhang X, Bo C, Smarandache F, Dai J. New inclusion relation of neutrosophic sets with applications and related lattice structure. INT J MACH LEARN CYB 2018. [DOI: 10.1007/s13042-018-0817-6] [Citation(s) in RCA: 62] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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76
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Operations and aggregation method of neutrosophic cubic numbers for multiple attribute decision-making. Soft comput 2018. [DOI: 10.1007/s00500-018-3194-x] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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77
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Wu H, Yuan Y, Wei L, Pei L. On entropy, similarity measure and cross-entropy of single-valued neutrosophic sets and their application in multi-attribute decision making. Soft comput 2018. [DOI: 10.1007/s00500-018-3073-5] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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78
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A similarity-based method for remaining useful life prediction based on operational reliability. APPL INTELL 2018. [DOI: 10.1007/s10489-017-1128-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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79
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Some New Biparametric Distance Measures on Single-Valued Neutrosophic Sets with Applications to Pattern Recognition and Medical Diagnosis. INFORMATION 2017. [DOI: 10.3390/info8040162] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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80
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Garg H, Nancy. Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment. APPL INTELL 2017. [DOI: 10.1007/s10489-017-1070-5] [Citation(s) in RCA: 49] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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81
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82
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83
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Fan C, Ye J. The cosine measure of refined-single valued neutrosophic sets and refined-interval neutrosophic sets for multiple attribute decision-making. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2017. [DOI: 10.3233/jifs-17270] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Affiliation(s)
- ChangXing Fan
- Department of Computer Science, Shaoxing University, Shaoxing, Zhejiang, P.R. China
| | - Jun Ye
- Department of Electrical and Information Engineering, Shaoxing University, Shaoxing, Zhejiang, P.R. China
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84
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New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making. Pattern Anal Appl 2017. [DOI: 10.1007/s10044-017-0635-6] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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85
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Simplified Neutrosophic Exponential Similarity Measures for the Initial Evaluation/Diagnosis of Benign Prostatic Hyperplasia Symptoms. Symmetry (Basel) 2017. [DOI: 10.3390/sym9080154] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
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86
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87
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Ngan RT, Ali M, Son LH. δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis. APPL INTELL 2017. [DOI: 10.1007/s10489-017-0986-0] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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88
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Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making. Symmetry (Basel) 2017. [DOI: 10.3390/sym9070121] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
The neutrosophic cubic set can contain much more information to express its interval neutrosophic numbers and single-valued neutrosophic numbers simultaneously in indeterminate environments. Hence, it is a usual tool for expressing much more information in complex decision-making problems. Unfortunately, there has been no research on similarity measures of neutrosophic cubic sets so far. Since the similarity measure is an important mathematical tool in decision-making problems, this paper proposes three cosine measures between neutrosophic cubic sets based on the included angle cosine of two vectors, distance, and cosine functions, and investigates their properties. Then, we develop a cosine measures-based multiple attribute decision-making method under a neutrosophic cubic environment in which, from the cosine measure between each alternative (each evaluated neutrosophic cubic set) and the ideal alternative (the ideal neutrosophic cubic set), the ranking order of alternatives and the best option can be obtained, corresponding to the cosine measure values in the decision-making process. Finally, an illustrative example about the selection problem of investment alternatives is provided to illustrate the application and feasibility of the developed decision-making method.
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89
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Some Single-Valued Neutrosophic Dombi Weighted Aggregation Operators for Multiple Attribute Decision-Making. Symmetry (Basel) 2017. [DOI: 10.3390/sym9060082] [Citation(s) in RCA: 49] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
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90
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91
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Thanh ND, Ali M, Son LH. A Novel Clustering Algorithm in a Neutrosophic Recommender System for Medical Diagnosis. Cognit Comput 2017. [DOI: 10.1007/s12559-017-9462-8] [Citation(s) in RCA: 51] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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92
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Şahin R. Normal neutrosophic multiple attribute decision making based on generalized prioritized aggregation operators. Neural Comput Appl 2017. [DOI: 10.1007/s00521-017-2896-9] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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93
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Estimation of the joint roughness coefficient (JRC) of rock joints by vector similarity measures. BULLETIN OF ENGINEERING GEOLOGY AND THE ENVIRONMENT 2017. [DOI: 10.1007/s10064-016-0947-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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94
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Deli I, Şubaş Y. Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision making problems. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2017. [DOI: 10.3233/jifs-151677] [Citation(s) in RCA: 45] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Irfan Deli
- Muallim Rıfat Faculty of Education, Kilis 7 Aralık University, Kilis, Turkey
| | - Yusuf Şubaş
- Kilis Vocational High School, Kilis 7 Aralık University, Kilis, Turkey
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95
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Ye J. Exponential operations and aggregation operators of interval neutrosophic sets and their decision making methods. SPRINGERPLUS 2016; 5:1488. [PMID: 28018779 PMCID: PMC5147724 DOI: 10.1186/s40064-016-3143-z] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/23/2016] [Accepted: 08/24/2016] [Indexed: 02/08/2023]
Abstract
An interval neutrosophic set (INS) is a subclass of a neutrosophic set
and a generalization of an interval-valued intuitionistic fuzzy set, and then the
characteristics of INS are independently described by the interval numbers of its
truth-membership, indeterminacy-membership, and falsity-membership degrees. However,
the exponential parameters (weights) of all the existing exponential operational
laws of INSs and the corresponding exponential aggregation operators are crisp
values in interval neutrosophic decision making problems. As a supplement, this
paper firstly introduces new exponential operational laws of INSs, where the bases
are crisp values or interval numbers and the exponents are interval neutrosophic
numbers (INNs), which are basic elements in INSs. Then, we propose an interval
neutrosophic weighted exponential aggregation (INWEA) operator and a dual interval
neutrosophic weighted exponential aggregation (DINWEA) operator based on these
exponential operational laws and introduce comparative methods based on cosine
measure functions for INNs and dual INNs. Further, we develop decision-making
methods based on the INWEA and DINWEA operators. Finally, a practical example on the
selecting problem of global suppliers is provided to illustrate the applicability
and rationality of the proposed methods.
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Affiliation(s)
- Jun Ye
- Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing, 312000 Zhejiang Province People's Republic of China
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96
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Peng HG, Zhang HY, Wang JQ. Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems. Neural Comput Appl 2016. [DOI: 10.1007/s00521-016-2702-0] [Citation(s) in RCA: 74] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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97
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Multi-criteria Group Decision-Making Based on Interval Neutrosophic Uncertain Linguistic Variables and Choquet Integral. Cognit Comput 2016. [DOI: 10.1007/s12559-016-9428-2] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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98
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99
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Peng JJ, Wang JQ, Wu XH. An extension of the ELECTRE approach with multi-valued neutrosophic information. Neural Comput Appl 2016. [DOI: 10.1007/s00521-016-2411-8] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Tian ZP, Wang J, Zhang HY, Wang JQ. Multi-criteria decision-making based on generalized prioritized aggregation operators under simplified neutrosophic uncertain linguistic environment. INT J MACH LEARN CYB 2016. [DOI: 10.1007/s13042-016-0552-9] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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