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The monograph contains the most important elements of the Zermelo-Fraenkel axiomatic set theory with the axiom of choice: axiomatics, definitions of basic concepts, theories of binary relations, partial ordering, equivalence, functions, ordinal numbers and cardinal numbers.It was created on the basis of lectures conducted over many years by the author for philosophy students at the University of Łódź. Therefore, it does not require a thorough mathematical background; it is enough to have some logical "skills" in theorem proving, or, indeed, a knowledge of such logical constants as Boolean functions and quantifiers. It can be used not only by mathematicians and mathematics students, but also by humanists wishing to consolidate their knowledge of sets, often used in various formalization procedures. The more so because some topics have a philosophical character, including discussions about the axiom of regularity and the concept of founding a set, equivalence relation, ordinal number or axiom of choice.

Axiomatic set theory.

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This book focuses on the issues of decision-making with several numerical criteria. It introduces an original general approach to solving multicriteria problems given quantitative information about the preference relation of a decision-maker. It considers the problems with crisp as well as fuzzy preference relations, accepting the four axioms of “reasonable choice”. Further, it defines the notion of an information quantum about the preference relation of a decision-maker and studies the reduction of the Pareto set using a finite collection of information quanta, demonstrating that the original approach yields a good approximation for the set of nondominated alternatives in a multicriteria problem. Lastly, it analyzes a possible combination of the axiomatic approach with other well-known methods. Intended for a wide range of professionals involved in solving multicriteria problems, including researchers, design engineers, product engineers, developers and analysts, the book is also a valuable resource for undergraduate and postgraduate students of mathematics, economics, and engineering.

Engineering. --- Artificial intelligence. --- Computational intelligence. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Construction --- Industrial arts --- Technology --- Axiomatic set theory. --- Quantum computing. --- Multiple criteria decision making. --- Artificial Intelligence. --- Decision making with multiple objectives --- MCDM (Decision making) --- Multiattribute decisions --- Multicriteria decision analysis --- Multicriteria decision making --- Multicriteria decision making analysis --- Multiobjective decision making --- Multiple objective decision making --- Decision making --- Computation, Quantum --- Computing, Quantum --- Information processing, Quantum --- Quantum computation --- Quantum information processing --- Axioms --- Logic, Symbolic and mathematical --- Set theory