In this manuscript, spherical fuzzy set (SFS) and T-spherical fuzzy set (TSFS) are discussed, which are two generalizations of fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PFS) and picture fuzzy set (PFS). As TSFS is more capable of processing and expressing unknown information in unknown environment, it is widely used in various areas. However, how to accurately measure the distance between TSFSs is still an unsolved problem. This manuscript discusses some limitations of the existing divergence measures and the problems that the existing divergence measures cannot be applied to the information provided in the TSFSs environment by some numerical examples. Therefore, a new divergence measure under TSFSs structure is proposed by utilizing the advantages of Jensen-Shannon divergence, which is called TSFSJS distance. This TSFSJS distance not only satisfies the distance measurement axiom, but also can better distinguish the difference between TSFSs than other distance measures. More importantly, this TSFSJS distance can avoid counter-intuitive results through the argument of some numerical results in the paper. The proposed approach can deal with more types of uncertain information as demonstrated by establishing a comparative study. INDEX TERMST-spherical fuzzy set (TSFS), divergence measures, Jensen-Shannon divergence, pattern recognition.

In this manuscript, nine similarity measures of T-spherical fuzzy set (TSFS) considering the membership degree, the hesitancy degree, the non-membership degree and the refusal degree are developed according to the cosine function. Besides, the generalizations of existing similarity measures are the similarity measures of TSFS proposed in this paper, which indicates the breadth and novelty of the proposed similarity measures. More importantly, the nine similarity measures of TSFSs are applied to pattern recognition. Then, we make a comparative study, that is, we apply the nine similarity measures of TSFSs developed in this manuscript to picture fuzzy environment, and the results obtained are consistent with the previous results. This application make the problem of building material recognition better solved in the real world. Finally, two numerical examples show the validity of the proposed similarity measure between TSFSs.

An investigation is performed into the optical, electrical, and microstructural properties of Ti-Ga–doped ZnO films deposited on polyimide (PI) flexible substrates and then annealed at temperatures of 300 °C, 400 °C, and 450 °C, respectively. The X-ray diffraction (XRD) analysis results show that all of the films have a strong (002) Ga doped ZnO (GZO) preferential orientation. As the annealing temperature is increased to 400 °C, the optical transmittance increases and the electrical resistivity decreases. However, as the temperature is further increased to 450 °C, the transmittance reduces and the resistivity increases due to a carbonization of the PI substrate. Finally, the crystallinity of the ZnO film improves with an increasing annealing temperature only up to 400 °C and is accompanied by a smaller crystallite size and a lower surface roughness.

No abstract

No abstract