On Sheffer Stroke Operation
Project no. 20772 · Status: Kapanmış · 2019
Summary
This thesis essentially consists of six chapters. In the first chapter, we mentioned the traces of Sheffer stroke operation, Hilbert, nonassociative MV- and BL-algebras, their usage areas and many applications. Also, we presented information about different results of the researchers and summarized the contents of the chapters comprising the thesis. In the second chapter, necessary fundamental denitions and notions were given in order to facilitate the legibility of the thesis. In the third chapter, Sheffer stroke Hilbert algebras were defined and independency of the axiom system, ideals of filters, deductive systems, quotients, homomorphisms, fuzzy structures and cartessian products were contructed. In the fourth chapter, we determined strong Sheffer stroke nonassociative MV-algebras and proved three fundamental isomorphism theorems on these algebraic structures by means of various properties, subalgebras, filters, quotients and homomorphisms. In the fifth chapter, Sheffer stroke BL-algebras were described and their (fuzzy) filters were introduced. Then we investigated relationships between them in detail. In the last chapter, it was broadly emphasized all studies done during the thesis and the conclusions. Keywords: Sheffer stroke operation, Sheffer stroke Hilbert algebra, strong Sheffer stroke nonassociative MV-algebra, Sheffer stroke BL-algbera, (fuzzy) filter, homomorphism.