Strong P-Lacunary statistical convergence of fuzzy function mapping sequences

This thesis consists of four chapters. We mention a short history of fuzzy numbers and some examples from daily life to understand the concept of fuzzy numbers better in the first chapter. In the second chapter, we give the definitions and properties of natural density, statistical convergence, Lacunary sequences and lacunary statistical convergence. At the same time, we present some basic definitions and theorems on Lacunary statistical convergence sequences to be used in the following chapters. In the third chapter, we give the definitions and properties of fuzzy sets, fuzzy numbers, fuzzy number sequences and convergence, statistical convergence of fuzzy transformation sequences. Later, after determining the μ order lacunary statistical convergence, definitions of the fuzzy number sequence and the μ order strong lacunary p-statistical convergence of the fuzzy number sequence, we give the relationships between them. In the fourth chapter, which is the original part of the thesis, we present (𝑓𝑡) valued function sequence f fuzzy valued function, μ degree lacunary point statistical convergence, μ strong p-lacunary statistical convergence and spaces of fuzzy mappings sequences. We obtain some scope relations between these 𝑆𝜙𝜇(𝑓),𝑁𝜙𝜇(f) and 𝑁𝜙,𝑝𝜇(f) spaces.