Multi-Attribute Decision Making Based on Probabilistic Neutrosophic Hesitant Fuzzy Choquet Aggregation Operators

Shao, Songtao; Zhang, Xiao­hong; Zhao, Qian

doi:10.3390/sym11050623

Cited by 20 publications

(17 citation statements)

References 47 publications

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“…Hence, Equations (25), (31), and (35) are used in comparison to determine their relationship with α j of Equation (26). By the same observation, it is found that Equations (27), (32), and (36) are related to β j of Equation (28).…”

Section: Further Discussion For Aggregation Operatorsmentioning

confidence: 84%

“…In Equations (25) and (27), the most natural approach f ðxÞ = x is applied by us. Meanwhile, in Equations (31) and (32), Ye and Fu [7] used f ðxÞ = tan ðπx/4Þ, and in Equations (35) and (36) For a similarity measure, say Sim, Simð0Þ = 1, and Simð1Þ = 0 are ideal, such as in Equations (25), (27), (31), and (32) and then abstractly expressed in Equations (33) and (34), researchers use 1 − ∑ m j=1 w j f ðα j Þ or 1 − ∑ m j=1 w j f ðβ j Þ.…”

Section: Further Discussion For Aggregation Operatorsmentioning

confidence: 99%

“…Ninety-three papers have cited Ye [6] in their references. We list them in the following: Peng and Dai [8], Ye [9], Biswas et al [10], Broumi et al [11], Chatterjee et al [12,13], Cui and Ye [14], Fan [15], Fan et al [16], Fu et al [17], Gou and Wang [18], Jha et al [19,20], Li et al [21][22][23], Liu and Luo [24], Luo et al [25], Nancy and Garg [26], Nguyen et al [27], Peng [28], Peng and Dai [29], Rajangam and Annamalai [30], Şahin [31], Shao et al [32], Shi and Yuan [33], Tian et al [34], Wang et al [35], Wei and Zhang [36], Xie et al [37], Ye [38], Zhai et al [39], Zhang et al [40], Zhao et al [41], Akram et al [42], Ali et al [43], Cai and Yang [44], Fan et al [45], Garg and Nancy [46], Guan et al [47], Karaaslan and Hayat [48], Khanet al [49], Küçük and Şahin [50], Liu [51], Liu et al…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Further Study on Multiperiod Health Diagnostics Methodology under a Single-Valued Neutrosophic Set

Chou

Lin

2020

Computational and Mathematical Methods in Medicine

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Employing the concept and function of tangency with similarity measures and counterpart distances for reliable medical consultations has been extensively studied in the past decades and results in lots of isomorphic measures for application. We compared the majority of such isomorphic measures proposed by various researchers and classified them into (a) maximum norm and (b) one-norm categories. Moreover, we found that previous researchers used monotonic functions to transform an identity function and resulted in complicated expressions. In this study, we provide a theoretical foundation to explain the isomorphic nature of a newer measure proposed by the following research paper against its studied existing one in deriving the same pattern recognition results. Specifically, this study initially proposes two similarity measures using maximum norm, arithmetic mean, and aggregation operators and followed by a detailed discussion on their mathematical characteristics. Subsequently, a simplified version of such measures is presented for easy application. This study completely covers two previous methods to point out that the complex approaches used were unnecessary. The findings will help physicians, patients, and their family members to obtain a proper medical diagnosis during multiple examinations.

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Section: Further Discussion For Aggregation Operatorsmentioning

confidence: 84%

Section: Further Discussion For Aggregation Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Further Study on Multiperiod Health Diagnostics Methodology under a Single-Valued Neutrosophic Set

Chou

Lin

2020

Computational and Mathematical Methods in Medicine

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“…In the future, we will extend probabilistic to other fuzzy sets. For instance, dual hesitant sets [39], linguistic dual hesitant fuzzy sets [40], Neutrosophic Hesitant Fuzzy sets [41], Mixed-discrete Z-numbers [42], Pythagorean fuzzy Hamacher Prioritized operators [43], dual hesitant Pythagorean fuzzy sets [44], generalized Dice similarity measures of PFS [45], Pythagorean Fuzzy Hamacher Power Aggregation Operators [46], etc.…”

Section: Discussionmentioning

confidence: 99%

The Probabilistic Interval-Valued Hesitant Pythagorean Fuzzy Set and Its Application in Selecting Processes of Project Private Partner

Liu

2019

IEEE Access

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The expression of fuzzy information under multi-attribute decision making (MADM) is constantly expanded by scholars to solve the problem of uncertain decision making in various application fields. Such as select project private partners, which is difficult to make an appropriate select in a complex and changeable environments. Although the aggregation operator under interval-valued hesitant Pythagorean fuzzy environment is an effective method to solve uncertain decision-making problems, there are still some drawbacks in aggregating operators that do not consider the information loss. In this paper, we develop Hamacher operations and Choquet integral-based method to solve select project private partner problem under probabilistic interval-valued hesitant Pythagorean fuzzy information, which could express decisionmakers' preference information more flexibly and consider the significance and the correlations among the elements. Firstly, we define the probabilistic interval-valued hesitant Pythagorean fuzzy set (PIVHPFS) as an extended mathematical expression of fuzzy sets (FS). Afterward, the Hamacher algorithm concepts are given under the PIVHPFS environment. Besides, we utilize Hamacher operations and Choquet interval-based method to develop the probabilistic interval-valued hesitant Pythagorean fuzzy Hamacher Choquet integral geometric (PIVHPFHCIG) operator. At the same time, some definitions and theorems based on PIVHPFH-CIG operator are proposed. After that, we utilize the PIVHPFHCIG operator to develop an approach to solve the MADM problems under the PIVHPFS situation. The new method is feasible to overcome the drawback of information loss, and it is more reasonable for obtaining a better decision result. Finally, the introduction of the best project private partner selecting problem proves the effectiveness and feasibility of PIVHPFS, and the comparison between PIVHPFS and other similar techniques decision methods are also provided. INDEX TERMS Multi-attribute decision making (MADM), probabilistic interval-valued hesitant pythagorean fuzzy Hamacher Choquet integral geometric (PIVHPFHCIG) operator, Hamacher algorithm, Choquet integral-based.

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“…Regarding the studies in the area of neutrosophic theory, it can be underline the fact that the neutrosophic theory and its derivates has been extensively applied in the last two decades various economic and social fields such as-decision making [2][3][4][5][6][7][8][9][10][11][12][13], supply chain management [14], best product selection [15], management [16] forecasting [17], sentiment analysis [18,19] and so forth.…”

Section: Literature Reviewmentioning

confidence: 99%

Neutrosophic Portfolios of Financial Assets. Minimizing the Risk of Neutrosophic Portfolios

2019

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This paper studies the problem of neutrosophic portfolios of financial assets as part of the modern portfolio theory. Neutrosophic portfolios comprise those categories of portfolios made up of financial assets for which the neutrosophic return, risk and covariance can be determined and which provide concomitant information regarding the probability of achieving the neutrosophic return, both at each financial asset and portfolio level and also information on the probability of manifestation of the neutrosophic risk. Neutrosophic portfolios are characterized by two fundamental performance indicators, namely: the neutrosophic portfolio return and the neutrosophic portfolio risk. Neutrosophic portfolio return is dependent on the weight of the financial assets in the total value of the portfolio but also on the specific neutrosophic return of each financial asset category that enters into the portfolio structure. The neutrosophic portfolio risk is dependent on the weight of the financial assets that enter the portfolio structure but also on the individual risk of each financial asset. Within this scientific paper was studied the minimum neutrosophic risk at the portfolio level, respectively, to establish what should be the weight that the financial assets must hold in the total value of the portfolio so that the risk is minimum. These financial assets weights, after calculations, were found to be dependent on the individual risk of each financial asset but also on the covariance between two financial assets that enter into the portfolio structure. The problem of the minimum risk that characterizes the neutrosophic portfolios is of interest for the financial market investors. Thus, the neutrosophic portfolios provide complete information about the probabilities of achieving the neutrosophic portfolio return but also of risk manifestation probability. In this context, the innovative character of the paper is determined by the use of the neutrosophic triangular fuzzy numbers and by the specific concepts of financial assets, in order to substantiating the decisions on the financial markets.

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Multi-Attribute Decision Making Based on Probabilistic Neutrosophic Hesitant Fuzzy Choquet Aggregation Operators

Cited by 20 publications

References 47 publications

A Further Study on Multiperiod Health Diagnostics Methodology under a Single-Valued Neutrosophic Set

A Further Study on Multiperiod Health Diagnostics Methodology under a Single-Valued Neutrosophic Set

The Probabilistic Interval-Valued Hesitant Pythagorean Fuzzy Set and Its Application in Selecting Processes of Project Private Partner

Neutrosophic Portfolios of Financial Assets. Minimizing the Risk of Neutrosophic Portfolios

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