Some Similarity and Distance Measures between Complex Interval-Valued q-Rung Orthopair Fuzzy Sets Based on Cosine Function and their Applications

Abstract

The purpose of this paper is to present a new method to solve the decision-making algorithm based on the cosine similarity and distance measures by utilizing the uncertain and vague information. A complex interval-valued q-rung orthopair fuzzy set (CIVQROFS) is a reliable and competent technique for handling the uncertain information with the help of the complex-valued membership grades. To address the degree of discrimination between the pairs of the sets, cosine similarity measures (CSMs) and distance measures (DMs) are an accomplished technique. Driven by these, in this manuscript, we defined some CSMs and DMs for the pairs of CIVQROFSs and investigated their several properties. Choosing that the CSMs do not justify the axiom of the similarity measure (SM), then we investigate a technique to developing other CIVQROFSs-based SMs using the explored CSMs and Euclidean DMs, and it fulfills the axiom of the SMs. In addition, we find the cosine DMs (CDMs) by considering the inter-relationship between the SM and DMs; then, we have modified the procedure for the rank of partiality by similarity to the ideal solution method for the CDMs under investigation, which can deal with the associated decision-making problems not only individually from the argument of the opinion of geometry but also the fact of the opinion of algebra. Finally, we provide a numerical example to demonstrate the practicality and effectiveness of the proposed procedure, which is also in line with existing procedures. Graphical representations of the measures developed are also used in this manuscript.

Multiple Attribute Decision-Making Method Based upon Intuitionistic Fuzzy Partitioned Dual Maclaurin Symmetric Mean Operators

“…The study is in intuitionistic fuzzy environment, spherical fuzzy sets, Pythagorean fuzzy sets and q-rung orthopair fuzzy sets are extension of IFS, and the introduced operator PDMSM can be used for spherical fuzzy sets [50,51] which introduced operations of spherical fuzzy sets and Pythagorean fuzzy sets [52] which introduced operators and q-rung orthopair fuzzy sets [53,54] which introduced a new type and ranking of q-rung orthopair fuzzy sets to solve DMPS. The established operator PDMSM can combine with TOP-SIS method [55,56] which established similarity and distance of Complex Interval-Valued q-Rung Orthopair Fuzzy Sets and consider the unknown weights of the attributes to solve DMPS. These are future works.…”

Exponential Function-Based Similarity Measures for q-Rung Linear Diophantine Fuzzy Sets and Their Application to Clustering Problem

“…Akram et al [13,14] and Liu et al [15] interested in 𝑞-rung type extensions of FSs and proposed correlational decision making frameworks under these set structures. Some authors studied the different types of the similarity measures (SMs) for the IFSs, PyFSs and 𝑞-ROFSs [16][17][18][19]. Thus, they endeavored to measure the intuitionistic fuzzy information, the Pythagorean fuzzy information and the 𝑞rung orthopair fuzzy information.…”