The cosine similarity measures of spherical fuzzy sets and their applications in decision making

Rafiq, Muhammad; Ashraf, Shahzaib; Abdullah, Saleem; Mahmood, Tahir; Muhammad, Shakoor

doi:10.3233/jifs-181922

Cited by 109 publications

(84 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, which is different from the results of the method proposed here, both in overall ranking and in best choice. Furthermore, from the Spearman's rank-correlation test, it can be inferred that the rankings produced by the methods in [32,36] are similar to that produced by the proposed method, and the ranking using methods [37,45] are uncorrelated with the ranking based on the proposed method.…”

Section: Ranking Resultsmentioning

confidence: 99%

“…The proposed method (P1) 5 4 2 1 6 3 The method using Archimedean operator by [32] (P2) 5 4 3 1 6 2 The method using logarithmic operation by [36] (P3) 5 3 2 1 6 4 The method using cosine similarity measures by [37] (P4) 3 2 4 1 5 6 The method using induced generalized aggregation operator by [45] Specifically, the method based on Archimedean operators proposed by Ashraf et al [23] is applied in this numerical example. The result of an alternative ranking is…”

Section: Ranking Resultsmentioning

confidence: 99%

“…The ranking results based on the method by Rafiq et al [37] is A 4 > A 2 > A 1 > A 3 > A 5 > A 6 . These results show that the best choice is consistent with the method proposed here, but not the overall ranking.…”

Section: Ranking Resultsmentioning

confidence: 99%

“…One of the causes is the expression of evaluation information. The methods developed by [32,36,37] can only describe the subjective evaluation information given by decision makers (SpFN); they neglect the objective information of the target criterion (NFN). In contrast, the proposed method, which combines SpFN and NFN, can depict both the subjective and the objective evaluation information.…”

Section: Ranking Resultsmentioning

confidence: 99%

“…The Spearman's rank-correlations test results are shown in Table 6. According to Table 6, we can see the similarities and differences between the methods by [32,36,37,45], and our method.…”

Section: Comparative Analysismentioning

confidence: 99%

See 4 more Smart Citations

Decision Support Algorithm for Selecting an Antivirus Mask over COVID-19 Pandemic under Spherical Normal Fuzzy Environment

Yang

Garg

et al. 2020

IJERPH

View full text Add to dashboard Cite

With the rapid outbreak of COVID-19, most people are facing antivirus mask shortages. Therefore, it is necessary to reasonably select antivirus masks and optimize the use of them for everyone. However, the uncertainty of the effects of COVID-19 and limits of human cognition add to the difficulty for decision makers to perfectly realize the purpose. To maximize the utility of the antivirus mask, we proposed a decision support algorithm based on the novel concept of the spherical normal fuzzy (SpNoF) set. In it, firstly, we analyzed the new score and accuracy function, improved operational rules, and their properties. Then, in line with these operations, we developed the SpNoF Bonferroni mean operator and the weighted Bonferroni mean operator, some properties of which are also examined. Furthermore, we established a multi-criteria decision-making method, based on the proposed operators, with SpNoF information. Finally, a numerical example on antivirus mask selection over the COVID-19 pandemic was given to verify the practicability of the proposed method, which the sensitive and comparative analysis was based on and was conducted to demonstrate the availability and superiority of our method. Admittedly, with this terrible virus, everyone is eager to get the best mask, but different groups of people should have dissimilar specific needs. Especially under the situation of COVID-19 spreading and a mask shortage, it is everyone's basic duty and obligation to resist COVID-19 without excessive protection. Therefore, for different groups of people, the rational choice and utilization of masks has pivotal practical significance. Obviously, the best masks do not mean the most expensive ones. For most people, it is not necessary to use masks with the same standard as those used by front-line medical staff. The suitability of an antivirus mask is not only related to the protective effect of the mask itself, but also to the tightness (the leakage rate) of the combination of the mask and the human face. In addition, under the severe epidemic situation and the lack of antivirus masks, the choice of masks is also relevant to factors such as reusability and quality of raw materials. Therefore, for the vast majority of people, under the severe epidemic situation, it is essential to consider multiple factors when choosing a mask to optimize the allocation of medical resources. However, people's limited knowledge and the uncertainty of the COVID-19 expansion increases the difficulty and complexity for decision-making about selecting a reasonable antivirus mask. To cope with this challenge, this paper proposed a multi-criteria decision-making (MCDM) method for selecting an antivirus mask under spherical normal fuzzy using the Bonferroni Mean operator.The study yields a number of contributions as follows:(1) A novel concept of the Spherical normal fuzzy (SpNoFS) set is defined, between which the new score, the accuracy function, and some improved operational rules are established. (2) Some new information aggregation operators based on ...

show abstract

Section: Ranking Resultsmentioning

confidence: 99%

Section: Ranking Resultsmentioning

confidence: 99%

Section: Ranking Resultsmentioning

confidence: 99%

Section: Ranking Resultsmentioning

confidence: 99%

“…The Spearman's rank-correlations test results are shown in Table 6. According to Table 6, we can see the similarities and differences between the methods by [32,36,37,45], and our method.…”

Section: Comparative Analysismentioning

confidence: 99%

See 3 more Smart Citations

Decision Support Algorithm for Selecting an Antivirus Mask over COVID-19 Pandemic under Spherical Normal Fuzzy Environment

Yang

Garg

et al. 2020

IJERPH

View full text Add to dashboard Cite

show abstract

Emergency decision support modeling for COVID‐19 based on spherical fuzzy information

Ashraf

Abdullah

2020

Int J Intell Syst

Self Cite

View full text Add to dashboard Cite

Significant emergency measures should be taken until an emergency event occurs. It is understood that the emergency is characterized by limited time and information, harmfulness and uncertainty, and decision‐makers are always critically bound by uncertainty and risk. This paper introduces many novel approaches to addressing the emergency situation of COVID‐19 under spherical fuzzy environment. Fundamentally, the paper includes six main sections to achieve appropriate and accurate measures to address the situation of emergency decision‐making. As the spherical fuzzy set (FS) is a generalized framework of fuzzy structure to handle more uncertainty and ambiguity in decision‐making problems (DMPs). First, we discuss basic algebraic operational laws (AOLs) under spherical FS. In addition, elaborate on the deficiency of existing AOLs and present three cases to address the validity of the proposed novel AOLs under spherical fuzzy settings. Second, we present a list of Einstein aggregation operators (AgOp) based on the Einstein norm to aggregate uncertain information in DMPs. Thirdly, we are introducing two techniques to demonstrate the unknown weight of the criteria. Fourthly, we develop extended TOPSIS and Gray relational analysis approaches based on AgOp with unknown weight information of the criteria. In fifth, we design three algorithms to address the uncertainty and ambiguity information in emergency DMPs. Finally, the numerical case study of the novel carnivorous (COVID‐19) situation is provided as an application for emergency decision‐making based on the proposed three algorithms. Results explore the effectiveness of our proposed methodologies and provide accurate emergency measures to address the global uncertainty of COVID‐19.

show abstract

Multiple attribute decision making problem using GRA method with incomplete weight information based on picture hesitant fuzzy setting

et al. 2020

View full text Add to dashboard Cite

The cosine similarity measures of spherical fuzzy sets and their applications in decision making

Cited by 109 publications

References 35 publications

Decision Support Algorithm for Selecting an Antivirus Mask over COVID-19 Pandemic under Spherical Normal Fuzzy Environment

Decision Support Algorithm for Selecting an Antivirus Mask over COVID-19 Pandemic under Spherical Normal Fuzzy Environment

Emergency decision support modeling for COVID‐19 based on spherical fuzzy information

Multiple attribute decision making problem using GRA method with incomplete weight information based on picture hesitant fuzzy setting

Contact Info

Product

Resources

About