Effects of neutrosophic tri̇plet sets on modules in algebraic structures

This thesis is generally concerned with the neutrosophic triplet module structure formed by a neutrosophic triplet on the commutative R ring. In this thesis, it is aimed to establish a module structure on the neutrosophic triplet. Then, the definitions and theorems of neutrosophic triplet submodule, neutrosophic triplet quotient module and neutrosophic triplet module homomorphisms are given with examples. This thesis consists of six chapters. In the introductory part of the thesis, the historical development process of the neutrosophic structure theory is given. In the second part, the necessary preliminary information about the neutrosophic triplet modules has been compiled. In the third chapter, the subjects of the neutrosophic extended triplet, subgroup, coset, normal subgroup and factor group were studied. In addition to this study, the definitions of neutrosophic extended triplet image, neutrosophic extended triplet kernel and neutrosophic extended triplet inverted image are included. In the fourth chapter, the subject of neutrosophic triplet modules is examined in detail. In addition, the definitions of ascending chain condition (ACC) and descending chain condition (DCC) used in neutrosophic triplet R-module structure chain conditions are given. In the fifth chapter, an example of neutrosophic decision tree model is given by including indeterminancy into classical logic. Finally, in the sixth chapter, the results and suggestions obtained in the thesis are given. As a result of the studies, it has been observed that the neutrosophic triplet algebra structure is different from the classical algebra structure.