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 »
We have developed original concept of fuzzy control. Our idea goes back to the roots of fuzzy control: The process is a black box; we know, how to control it but the process itself is not known to us. It may also happen that mathematical description of the process is too complicated to be solved,… Read More »
1. Introduction One of methods of data mining which are under development in our institute is mining of linguistic associations from numerical data [3],[4]. Data mining is regarded as a non-trivial process of identifying valid, novel, potentially useful, and ultimately understandable knowledge in large scale data-sets [1]. Particularly interesting are associations that reflect relationships among… Read More »
Linguistic fuzzy IF-THEN make it possible to distinguish sufficiently subtly and, at the same time, aptly, various degrees of fulfilling of the respective criteria, their various importance and, moreover, it may also overcome possible discrepancies. Degrees of importance are naturally included in the linguistic characterization and so, the usual problem of assigning weights to the… Read More »
A new methodology of forecasting time series has been proposed. It is based on combination of two soft computing techniques: fuzzy transform and perception-based logical deduction (PbLD). The technique of fuzzy transforms has been introduced in [6] and then elaborated, in [4], [5]. The second technique based on logical deductions is presented in [2], [3].… Read More »
In the practise the relation that we are going to approximate respresents an “ideal situation“, which is unreachable due to our limited expressing power (i.e. constrained vocabulary given by interpretability, incorporated vagueness, display resolution, computational precision etc.). Therefore, we admit some imprecision or an error of expressing the given situation to compensate it by readibility… Read More »