Bipolar Fuzzy Sets Based on Algebraic Structure
Maha Abdullah Alghamdi · 2017
The subject of this dissertation depends on the study of the properties of bipolar fuzzy sets based on BCK-modules. BCK-algebras, ideals of BCK-algebras, fuzzy sets and bipolar fuzzy sets based on BCK-algebras and ideals of BCK-algebras are basic concepts included in the first chapter of the dissertation. In Chapter two, the notion of bipolar fuzzy BCK-submodules is introduced, and some characterizations of bipolar fuzzy BCK-submodule are given. The concept of homomorphic images and preimages of bipolar fuzzy BCK-submodules are investigated. Normality and completely normality of bipolar fuzzy BCK-submodules are discussed. In Chapter three, translations and multiplications of bipolar fuzzy BCK-submodules are discussed, extensions of bipolar fuzzy BCK-submodules are introduced and relations between translations and multiplications of bipolar fuzzy BCK-submodules are presented. In Chapter four, we develop bipolar fuzzy TOPSIS method and bipolar fuzzy ELECTRE I method for solving MCDM problems that are equipped with bipolar-valued fuzzy information. Moreover, we apply a numerical example for both methods. The outcomes of this dissertation are the following papers: 1- Maha Alghamdi, Najat Muthana and Noura Alshehri, Novel concepts of bipolar fuzzy BCK-submodules, Discrete Dynamics in Nature and Society, 2017, 7 pages. 2- Maha Alghamdi, Noura Alshehri and Najat Muthana, Bipolar fuzzy sets of BCK-modules, accepted for publication in Journal of Computational Analysis and application. 3- Maha Alghamdi and Noura Alshehri, Some multi-criteria decision making methods based on bipolar-valued fuzzy sets, submitted.