Generalized dice similarity measures for complex q-Rung Orthopair fuzzy sets and its application
- PDF / 551,675 Bytes
- 20 Pages / 595.276 x 790.866 pts Page_size
- 66 Downloads / 206 Views
ORIGINAL ARTICLE
Generalized dice similarity measures for complex q-Rung Orthopair fuzzy sets and its application Harish Garg1
· Zeeshan Ali2 · Tahir Mahmood2
Received: 3 January 2020 / Accepted: 15 September 2020 © The Author(s) 2020
Abstract Complex q-rung orthopair fuzzy set (Cq-ROFS) is an extension of Complex fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, to cope with complicated and inconsistence information in the environment of fuzzy set theory with a wider domain. In Cq-ROFS, each attribute is characterized by the degree of membership and non-membership degree over the unit-disc of the complex plan. Keeping the advantages of Cq-ROFSs, in this manuscript, we present a concept of the dice similarity and generalized dice similarity measures between the pairs of the sets. The basic axioms and properties are also stated. Further, we extend the proposed measures to weighted dice similarity measures and investigated their properties. The certain properties and the special cases of the proposed work are also derived. The applicability of the proposed measures is demonstrated with some numerical examples related to medical diagnoses and pattern recognition. The superiority and advantages of the measures over the existing ones are also illustrated with certain numerical examples. Keywords Complex q-Rung Orthopair fuzzy Sets · Dice similarity Measures · Generalized dice similarity measures · Medical diagnosis
Introduction Decision making process includes the examination of a limited arrangement of options and positioning them as far as the fact that they are so trustworthy to decision-maker(s) when all the rules are thought of at the same time. In this procedure, the rating estimations of every option incorporate both exact information and specialists’ subjective data. However, generally, the information which is collected from the various data sources is limited in nature and involves high range of uncertainties. To cope with such uncertainties, a theory of fuzzy set (FS), developed by Zadeh [1] provides an important tool to deal with uncertain and unpredictable information in the environment of real life issues. In FS, each element consists of the membership function, whose range is [0,1]. Since their appearance, a lot of attentions have been made by the
B
Harish Garg [email protected]
1
School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala 147004, Punjab, India
2
Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan
researchers and applied them in the different fields such as aggregation operators [2], medical diagnosis [3] etc. The theory of FS is widely used but their scope is limited in nature due to the consideration of only membership degree. Atanassove’s-intuitionistic fuzzy set (A-IFS) [4] is a generalization of FS, which described the truth degree and the falsity degree with a condition that the sum of truth degree and falsity degree is less than or equal to one. A-IFS can help to deal with
Data Loading...
