Abstract
A cubic bipolar fuzzy set (CBFS) is a robust paradigm to express bipolarity and vagueness in terms of bipolar fuzzy numbers and interval-valued bipolar fuzzy numbers. The abstraction of similarity measures (SMs) has a large number of applications in various fields. Therefore, in this study, taking the advantage of CBFSs, three cosine similarity measures for CBFSs are proposed successively by using cosine of the angle between two vectors, new distance measures, and cosine function. Some key properties of these similarity measures (SMs) are explored. Based on suggested SMs, the problem of bacteria recognition is analyzed and an important application is provided to exhibit the efficiency of proposed SMs for CBF information. Moreover, the TOPSIS approach based on cosine SMs is developed for multicriteria group decision-making (MCGDM) problems. An illustrative example about the selection of sustainable plastic recycling process is presented to discuss the efficiency of the suggested MCGDM technique.
Highlights
Fuzzy set (FS) theory [1] by using the concept of membership function (MF) is a robust approach for modeling uncertainty
An intervalvalued fuzzy set (IVFS) [2] is the generalization of FS that assigns an interval of membership grades to the elements in the universe. e idea of orthopair has been extended to the ordered pair of membership grade (MG) and nonmembership grade (NMG) in the studies of intuitionistic fuzzy sets (IFSs) [3], Pythagorean fuzzy sets (PFSs) [4, 5], and q-rung orthopair fuzzy sets (q-ROPFSs) [6]. e values of MG and NMG are the elements of [0, 1], i.e., any real number between 0 and 1
The idea of ordered triples with three components (MG, indeterminacy, and NMG) of neutrosophic set (NS) [7] and single-valued neutrosophic set (SVNS) [8] has been focused by many researchers. e concepts of spherical fuzzy sets [9,10,11] and picture fuzzy sets [12, 13] are strong models to deal with uncertain real-life problems with three components
Summary
Fuzzy set (FS) theory [1] by using the concept of membership function (MF) is a robust approach for modeling uncertainty. Hussian and Yang [29] introduced Pythagorean fuzzy Hausdorff metric-based new distance and similarity measures and TOPSIS approach for MCDM. Ey proposed a nonlinear-programming-based MCDM approach to deal with cubic intuitionistic fuzzy (CIFS) uncertain information. (2) To define cosine SMs between CBFSs based on cosine of the angle between two vectors, new distance measures, and cosine function. (4) To propose the TOPSIS approach based on cosine SMs to deal with the plastic recycling method selection problem.
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