ABSTRACT
To deal with situations involving uncertainty, Fermatean fuzzy sets are more effective than Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. Applications for fuzzy similarity measures can be found in a wide range of fields, including clustering analysis, classification issues, medical diagnosis, etc. The computation of the weights of the criteria in a multi-criteria decision-making problem heavily relies on fuzzy entropy measurements. In this paper, we employ t-conorms to suggest various Fermatean fuzzy similarity measures. We have also discussed all of their interesting characteristics. Using the suggested similarity measurements, we have created some new entropy measures for Fermatean fuzzy sets. By using numerical comparison and linguistic hedging, we have established the superiority of the suggested similarity metrics and entropy measures over the existing measures in the Fermatean fuzzy environment. The usefulness of the proposed Fermatean fuzzy similarity measurements is shown by pattern analysis. Last but not least, a novel multi-attribute decision-making approach is described that tackles a significant flaw in the order preference by similarity to the ideal solution, a conventional approach to decision-making, in a Fermatean fuzzy environment.
ABSTRACT
Picture fuzzy set is an efficient tool for dealing with uncertainty and vagueness, particularly in situations that require assimilation of more dimensions of linguistic assessment such as human voting, feature selection, etc. The correlation coefficient of picture fuzzy sets is a tool to determine the association of two picture fuzzy sets. It has several applications in various disciplines like science, engineering, and management. The prominent applications include decision-making, pattern recognition, clustering analysis, medical diagnosis, etc. In this paper, we introduce a new correlation coefficient for picture fuzzy sets with the justification of its advantages. This correlation coefficient is better than the existing correlation coefficients and other such measures in the picture fuzzy theory because it considers the picture fuzzy set as a whole and also expresses the nature (positive or negative) as well as the extent of association between two PFSs. By performing some comparative analysis based on the computation of correlation degree and linguistic hedges, we establish the effectiveness of the suggested correlation measure over some available correlation measures in a picture fuzzy environment. Further, in the context of pattern recognition, we examine the performance of the proposed correlation measure over some existing picture fuzzy correlation measures. Finally, we apply the suggested picture fuzzy correlation coefficient to a decision-making problem involving the selection of an appropriate COVID-19 mask.
ABSTRACT
Fermatean fuzzy sets are more powerful than fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets in handling various problems involving uncertainty. The distance measures in the fuzzy and non-standard fuzzy frameworks have got their applicability in various areas such as pattern analysis, clustering, medical diagnosis, etc. Also, the fuzzy and non-standard fuzzy knowledge measures have played a vital role in computing the criteria weights in the multicriteria decision-making problems. As there is no study concerning the distance and knowledge measures of Fermatean fuzzy sets, so in this paper, we propose some novel distance measures for Fermatean fuzzy sets using t-conorms. We also discuss their various desirable properties. With the help of suggested distance measures, we introduce some knowledge measures for Fermatean fuzzy sets. Through numerical comparison and linguistic hedges, we establish the effectiveness of the suggested distance measures and knowledge measures, respectively, over the existing measures in the Pythagorean/Fermatean fuzzy setting. At last, we demonstrate the application of the suggested measures in pattern analyis and multicriteria decision-making.
