Chordal distance and non-Archimedean chordal distance between Atanassov’s intuitionistic fuzzy set

Han, Jing; Yang, Zhanpeng; Sun, Xian; Xu, Guangluan

doi:10.3233/jifs-17724

Cited by 5 publications

(7 citation statements)

References 7 publications

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“…(Norm) [ 41 ] For any non-empty set , a norm is defined as a mapping , such that it satisfies the conditions mentioned below, iff , for any ; , for ; , for , which is popularly known as the triangle inequality. …”

Section: Methods and Basic Preliminariesmentioning

confidence: 99%

“…(Distance or metric) [ 41 ] By distance or metric, we mean a mapping ‘ ’ on a set , such that, , and which satisfies the conditions, for ; if and only if ; ; , for . …”

Section: Methods and Basic Preliminariesmentioning

confidence: 99%

“…(non-Archimedean norm) [ 41 ] As per the definition of a norm already discussed, when we replace the third condition of triangular inequality by the condition, , for (known as the ultrametric inequality), what we obtain is called a non-Archimedean norm.…”

Section: Methods and Basic Preliminariesmentioning

confidence: 99%

“…(non-Archimedean valuation) [ 41 ] For a function or mapping to be termed as a non-Archimedean valuation, we must have such that the following properties hold, iff , for ; , for ; , for ; such that . (Non-triviality condition) …”

Section: Methods and Basic Preliminariesmentioning

confidence: 99%

“…(non-Archimedean chordal distance) [ 41 ] The non-Archimedean chordal distance denoted by ‘ ’ and defined as a mapping such that, for (non-empty set) and , we have. where denotes a non-Archimedean valuation or an absolute value function.…”

Section: Methods and Basic Preliminariesmentioning

confidence: 99%

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Nonlinear distance measures under the framework of Pythagorean fuzzy sets with applications in problems of pattern recognition, medical diagnosis, and COVID-19 medicine selection

Dutta

Borah

Gohain

et al. 2023

Beni-Suef Univ J Basic Appl Sci

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Background The concept of Pythagorean fuzzy sets (PFSs) is an utmost valuable mathematical framework, which handles the ambiguity generally arising in decision-making problems. Three parameters, namely membership degree, non-membership degree, and indeterminate (hesitancy) degree, characterize a PFS, where the sum of the square of each of the parameters equals one. PFSs have the unique ability to handle indeterminate or inconsistent information at ease, and which demonstrates its wider scope of applicability over intuitionistic fuzzy sets. Results In the present article, we opt to define two nonlinear distances, namely generalized chordal distance and non-Archimedean chordal distance for PFSs. Most of the established measures possess linearity, and we cannot incorporate them to approximate the nonlinear nature of information as it might lead to counter-intuitive results. Moreover, the concept of non-Archimedean normed space theory plays a significant role in numerous research domains. The proficiency of our proposed measures to overcome the impediments of the existing measures is demonstrated utilizing twelve different sets of fuzzy numbers, supported by a diligent comparative analysis. Numerical examples of pattern recognition and medical diagnosis have been considered where we depict the validity and applicability of our newly constructed distances. In addition, we also demonstrate a problem of suitable medicine selection for COVID-19 so that the transmission rate of the prevailing viral pandemic could be minimized and more lives could be saved. Conclusions Although the issues concerning the COVID-19 pandemic are very much challenging, yet it is the current need of the hour to save the human race. Furthermore, the justifiable structure of our proposed distances and also their feasible nature suggest that their applications are not only limited to some specific research domains, but decision-makers from other spheres as well shall hugely benefit from them and possibly come up with some further extensions of the ideas.

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Section: Methods and Basic Preliminariesmentioning

confidence: 99%

“…(Distance or metric) [ 41 ] By distance or metric, we mean a mapping ‘ ’ on a set , such that, , and which satisfies the conditions, for ; if and only if ; ; , for . …”

Section: Methods and Basic Preliminariesmentioning

confidence: 99%

Section: Methods and Basic Preliminariesmentioning

confidence: 99%

Section: Methods and Basic Preliminariesmentioning

confidence: 99%

Section: Methods and Basic Preliminariesmentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear distance measures under the framework of Pythagorean fuzzy sets with applications in problems of pattern recognition, medical diagnosis, and COVID-19 medicine selection

Dutta

Borah

Gohain

et al. 2023

Beni-Suef Univ J Basic Appl Sci

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An integrated generalized chordal picture fuzzy distance measure with its application to evaluate teaching quality

Wang,

Cao,

Shen

2024

Preprint

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Deepening the integration of industry and education (IIE) in classroom teaching has important strategic significance for the connotative development of higher education. The classroom teaching quality assessment is an important route to improve the level of the IIE and then promote the quality of talent training. Considering that picture fuzzy sets (PFSs) is much more efficient in comparison with fuzzy sets at handling the uncertainty in decision-making problems, this paper firstly applies PFSs to depict the indeterminacy and inaccuracy information in teaching quality assessment (TQA) process. To begin with, the related definitions of PFSs are all profiled successively. Then, we attempt to propose an integrated assessment method with the combined compromise solution (CoCoSo) and Taxonomy method (TM) to handle the TQA problem with PFSs. In this approach, we define a new cumulative method based on TM to aggregate individual opinion into group opinion. We also develop a weighting strategy based on the CRiteria Importance Through Intercriteria Correlation approach (CRITIC) to evaluate the significance of experts with PFSs. For this, we define a novel generalized chordal picture fuzzy (PF) distance measure that considers the marginal impacts of degree of refusal membership, which has a strong capacity of differentiation. Then, we evaluate its superiority and stability through some experiment comparisons. Again, a final ranking method is presented with the CoCoSo approach and the Stepwise Weight Assessment Ratio Analysis (SWARA) method. Furthermore, we apply a case study of the TQA to demonstrate the implementation of the newly proposed PF-CRITIC-SWARA-TM -CoCoSo method. The results obtained from the sensitivity analysis validate that the option “Dr. Tang” consistently achieves the highest rank and is independent of variations of balancing factor and weight information of experts and criteria. Finally, a comparison is implemented to confirm the robustness and reliability of the suggested integrated framework.

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Lorentzian knowledge measures for atanassov’s intuitionistic fuzzy sets

Qi¹,

Yang

Ren

et al. 2019

IFS

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Chordal distance and non-Archimedean chordal distance between Atanassov’s intuitionistic fuzzy set

Cited by 5 publications

References 7 publications

Nonlinear distance measures under the framework of Pythagorean fuzzy sets with applications in problems of pattern recognition, medical diagnosis, and COVID-19 medicine selection

Nonlinear distance measures under the framework of Pythagorean fuzzy sets with applications in problems of pattern recognition, medical diagnosis, and COVID-19 medicine selection

An integrated generalized chordal picture fuzzy distance measure with its application to evaluate teaching quality

Lorentzian knowledge measures for atanassov’s intuitionistic fuzzy sets

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