Similarity Measures in Neutrosophic Sets-I

Chatterjee, Rajashi; Majumdar, Parthasarathi; Samanta, Sourav

doi:10.1007/978-3-030-00045-5_11

Cited by 5 publications

(3 citation statements)

References 26 publications

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“…such that in Equation 27, for M w 2 , f ðxÞ = x, and in Equation (32), for T w 2 , f ðxÞ = tan ðπ x/4Þ. Consequently, we can further simplify C 1 ðA, BÞ of Equation (12) and C 2 ðA, BÞ of Equation (13) proposed by Ye [6] as follows…”

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%

“…There are 49 papers that have cited Ye and Fu [7] in their references. We list them in the following: Liu et al [100], Peng and Dai [8], Awang et al [101], Chatterjee et al [12,13], Cui and Ye [14], Fu et al [17], Gou and Wang [18], Hu et al [102], Li et al [21], Long et al [103], Luo et al [25], Nancy and Garg [26], Nguyen et al [27], Rajangam and Annamalai [30], Ren et al [104], Shen et al [105], Shi and Yuan [33], Smith [106], Xie et al [37], Akram et al [107], Ali et al [43], Hu et al [108], Ji et al [109][110][111], Karaaslan [112], Karaaslan and Hayat [48], Khan et al [113], Liu [51], Mondal et al [55][56][57], Naz et al [114], Peng and Dai [115], Tu et al [65], Uluçay et al [116], Wu et al [67], Ye [70], Ashraf et al [117], Chen and Ye [73], Fu and Ye [76], Guan et al [118], Guo et al [119], Hu et ...…”

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: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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An application of hybrid weighted similarity measure of neutrosophic set in medical diagnosis

Mustapha,

Alias,

Md Yasin

et al. 2024

ITM Web Conf.

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The study introduces a hybrid weighted similarity measure (HWSM) for the analysis of symptoms and diseases in patients using a neutrosophic set (NS). NS proves valuable for modeling uncertainty by accommodating contradictory and ambiguous information. The development of a similarity measure for NS information is crucial in various applications, particularly in medical diagnostics, to quantify similarity between sets. While existing literature provides various similarity measures for NS, only a limited number incorporates hybrid techniques. This study proposes a hybrid similarity measure that combines existing measures and integrates them with an entropy weight measure. To elaborate, distance- based similarity measures for NS are initially considered. Subsequently, an entropy weight measure is employed to calculate the attributes' weight of the attributes. The work includes formulating the properties of the proposed HWSM and its practical application in medical diagnosis, focusing on assessing the possibility of medical diagnoses in a patient. The study examines five symptoms which are fever, headache, stomach pain, cough, and chest pain. The HWSM is applied to analyze these symptoms across five different diseases, resulting in consistent and reliable outcomes. This research contributes to the ongoing enhancement of diagnostic tools for medical practitioners, addressing challenges associated with uncertainty in patient information.

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Medical Diagnosis and Pattern Recognition Based on Generalized Dice Similarity Measures for Managing Intuitionistic Hesitant Fuzzy Information

Albaity

Mahmood

2022

Mathematics

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Pattern recognition is the computerized identification of shapes, designs, and reliabilities in information. It has applications in information compression, machine learning, statistical information analysis, signal processing, image analysis, information retrieval, bioinformatics, and computer graphics. Similarly, a medical diagnosis is a procedure to illustrate or identify diseases or disorders, which would account for a person’s symptoms and signs. Moreover, to illustrate the relationship between any two pieces of intuitionistic hesitant fuzzy (IHF) information, the theory of generalized dice similarity (GDS) measures played an important and valuable role in the field of genuine life dilemmas. The main influence of GDS measures is that we can easily obtain a lot of measures by using different values of parameters, which is the main part of every measure, called DGS measures. The major influence of this theory is to utilize the well-known and valuable theory of dice similarity measures (DSMs) (four different types of DSMs) under the assumption of the IHF set (IHFS), because the IHFS covers the membership grade (MG) and non-membership grade (NMG) in the form of a finite subset of [0, 1], with the rule that the sum of the supremum of the duplet is limited to [0, 1]. Furthermore, we pioneered the main theory of generalized DSMs (GDSMs) computed based on IHFS, called the IHF dice similarity measure, IHF weighted dice similarity measure, IHF GDS measure, and IHF weighted GDS measure, and computed their special cases with the help of parameters. Additionally, to evaluate the proficiency and capability of pioneered measures, we analyzed two different types of applications based on constructed measures, called medical diagnosis and pattern recognition problems, to determine the supremacy and consistency of the presented approaches. Finally, based on practical application, we enhanced the worth of the evaluated measures with the help of a comparative analysis of proposed and existing measures.

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Similarity Measures in Neutrosophic Sets-I

Cited by 5 publications

References 26 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

An application of hybrid weighted similarity measure of neutrosophic set in medical diagnosis

Medical Diagnosis and Pattern Recognition Based on Generalized Dice Similarity Measures for Managing Intuitionistic Hesitant Fuzzy Information

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