Fundamentals of Set Theory

Set theory is the branch of mathematical logic that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definition of nearly all mathematical objects. The text introduces some basic concepts in set theory, describing sets, elements, Venn diagrams and the union and intersection of sets. The book "Fundamentals of Set Theory" contains nine chapters. An innovative approach for attribute reduction in rough set theory has been inroduced in first chapter analyzes students' misconception based on rough set theory and combined with interpretive structural model (ISM) to compare students' degree of two classes. We introduce the concept of fuzzy soft expert set which is more effective and useful and study some of its properties in third chapter. The objective of fourth chapter is to formulate for the first time a fractal, multiple valued modal logic of Kabbalah and to use it as a framework for a postmodern fuzzy set and fuzzy logic theory. We present a new law which is based on the well-known duality property for the set identities in fifth chapter. The purpose of sixth chapter is to present the use of fuzzy logic to improve the calculation of weighted average cost of capital (WACC). A category approach to relation preserving functions in rough set theory has been presented in seventh chapter. In eight chapter we study uninorms more deeply and we investigate the structure of uninorms. The aim of last chapter is to propose a new way to evaluate the main emergy flows entering a system using set theory, which is a general scheme applicable to every system.