1. Introduction to the problem Classical logic is based on the lattice structure of the simplest non-degenerated lattice L = {0,1}. Fuzzy logics are based mostly on the lattice L = [0,1] equipped with some special functions and the algebraic structure of such tuples (e.g., BL-algebra, MTL-algebra, etc.) heavily influence the corresponding fuzzy logic. Deeper… Read More »
1. Introduction to the problem Mathematical fuzzy logic is a special formal theory of many-valued logic generalizing classical mathematical logic that focuses on the development of tools for modeling vagueness phenomenon. We distinguish fuzzy logic in narrow (FLn) and in broader sense (FLb). Fuzzy logic has been initiated at the end of sixties and beginning… Read More »
1. Introduction to the problem Fuzzy logic is known by many applications in various areas. A common denominator of them in most cases is the ability of FL to capture, in a certain sense, semantics of a part of natural language semantics. A crucial role is played by the, so called evaluative linguistic expressions and… Read More »
1. Introduction to the problem Fuzzy approximation is a special phenomenon which explains how complicated functions can be described by a set of fuzzy IF-THEN rules. In many cases, the way of designing the concrete set of these rules is left unexplained, or rather exhaustive technique based on neural networks or genetic algorithms is used.… Read More »
1 Introduction to the problem The global optimization problem with box constraints follows the form: minimize f(x) subject to x ε D where x is a continuous variable with the domain D from Rd, and f(x) : D→ R is a continuous function. The domain D is defined by specifying lower (aj) and upper (bj)… Read More »