Advanced results in fuzzy sets and application in advanced materials

Abstract

Abstract In this paper, some results are stablished related to fuzzy sets these results are useful for mechanical and material research. Some common fixed-point theorems for R-weakly commuting mapping in soft fuzzy metric spaces are establish. Also, for this purpose expression are taken in rational form for contraction mapping. Here we define mapping by using some proved results and obtain results on the inequality of fixed points. To find the aim basic concepts of fixed-point theory are used. The Obtained results are generalized form of the well-known results of fixed-point theory. The results can be generalized in specified spaces as soft Banach space, soft metric space for rational contraction, soft s metric space, soft b metric space, soft cone space, random soft Banch spaces. All the modification can be obtained by the basic theory of soft sets and fuzzy sets. Obtained Results can be used for material research such as in phase transition study, digital electronics and image processing.