Jernej Virant

The fuzzy logic approach to the car number plate locating problem

Fuzzy logic is applied to the problem of locating the number plate in digital images of cars. The intention of the paper is to show the capability of fuzzy logic in this field. Our aim was to locate the number plate by use of intuitive rules and experience. By extending or changing the rules the system can easily be adapted to locate other patterns. The results obtained by the system are very good and reliable.

Attention to time in fuzzy logic

Abstract Todays fuzzy logic deals with fuzzification, fuzzy inference, and defuzzification problems at a fixed time point. But in binary logic, as a comparable option to fuzzy logic, we have by the side of decisions within a fixed time point still memory, time dependent switching functions, finite automata, regular expressions and so on. All these items need time as a basic variable. If we ask ourselves for such or similar items within fuzzy logic, we can rapidly conclude that we must in the first instance make basic definitions and relations for the time variable. This paper considers a time variable in the domain of fuzzy logic. We try to put up a fuzzy set as a fuzzy time variable, time dependent fuzzy rule, fuzzy time operator and similar items, which can give us a new time extension of fuzzy logic.

Fuzzy automata with fuzzy relief

This paper shows a definition of a fuzzy automaton, which has the state, input, and output sets as fuzzy sets. The state transition function is defined as moving on a fuzzy relief with fuzzy peak-states and boundaries between different membership functions. After the definition of fuzzy automaton with fuzzy relief, the paper deals with a generalization, simulation and realization of such a fuzzy automaton. The paper links the defined fuzzy automaton to an existing fuzzy JK memory cell and to well-known fuzzy automata defined on the basis of crisp sets. >

T-type fuzzy memory cells

Abstract The paper deals with design problems of trigger (T)-type fuzzy memory cell. The authors suggest six types of T cell, which can be used in temporal fuzzy logic: memory item of 1 fuzzy bit information, converter from fuzzy date to fuzzy time interval, cell of fuzzy register, item of fuzzy memory, fuzzy delay circuit and so on. Generally speaking, in addition to Hirota and Ozawas fuzzy JK flip-flop, fuzzy T memory cells, which introduce time (memory) action into fuzzy inference machines, are observed.

Fuzzy Sequential Circuits and Automata

Publisher Summary This chapter presents the theory, simulation, and practical examples of fuzzy sequential circuits and fuzzy automata. It focuses on time-dependent switching functions, which are taken as the starting point for the design of a fuzzy memory cell (as a device that can store one fuzzy bit of information), fuzzy sequential circuits, fuzzy memory, and fuzzy automata. Further, as an extension of the well-known binary cells D, T, RS, the chapter gives the definitions of the fuzzy memory cells. In the domain of the fuzzy T memory cell, guidelines are presented to move the cell-state equilibrium (critical) point out from the working range used. The chapter presents how effective these fuzzy memory cells are for Dubois–Prade temporal logic. The chapter begins to deal with composed fuzzy sequential circuits. There are simulation schemes and simulation results of fuzzy memory, shift, cyclic, and delay registers as well as serial-to-parallel and parallel-to-serial conversions. Fuzzy automata are observed from the design point of view. The chapter shows how to implement given fuzzy memory cells and sequential circuits in the structure of a fuzzy automaton and presents automata structures learning as an alternative in designing fuzzy automata. The chapter also demonstrates how a fuzzy variable can be transferred to fuzzy memory. The chapter shows the transformation of a fuzzy automaton into a list of fuzzy rules and vice versa. All simulations in this chapter flow with the MATLAB & SIMULINK environment. This environment also includes the Fuzzy Logic TOOLBOX, which is oriented toward fuzzy system design.

Notes on fuzzy cellular automata

Abstract In our paper we present some characteristics of cellular automata fuzzification. More precisely, we would like to incorporate fuzzy logic theory to cellular automata. We also present the use of such a generalized approach by applying fuzzy cellular automata in a simple application examples.

Pattern recognition with fuzzy neural network

Abstract This paper explains the character code recognition with the Boolean classifier. The binary values are used both for inputs and outputs, while the learning of the circuit with a set of patterns is done by modified algorithms used in some Boolean neural networks. The use of the fuzzy logic approach offers the possibility of creating a character recognition theory which is fault-tolerant and applicable to all sorts of typefaces and fonts. It provides several examples of patterns scanned with different resolutions and learned with a part of the same set of samples which demonstrates the quality of the fuzzy Boolea classifier.

Edge detector: towards the solid ground of an image retrieval system

Examines a simple and effective color similarity model which is the basis for the development of an edge detection function. An intuitive edge definition is provided. The proposed edge detector is used to obtain the image features describing the edges in terms of orientation, strength and defining color. The parameters that control the image analysis process can be used to manage the trade-off between the computational demand, speed and the depth of the analysis. The results obtained are proposed to act as core building blocks of a query-by-image-content system.

Calculation and Display Errors

We present fuzzy events within an infinite or finite time space T containing moments t. Moments t are not different from real numbers so from the mathematical point of view T = R. Processing of item A(t) in general can be executed within continuous or discrete time. Processing means adaptation of values of some variable at all moments, of which, in continuous space T there are infinitely many. In fuzzy logic continuous calculation cannot be applied from a practical point of view, as it would last infinitely long. Computer processing or calculation of fuzzy item A(t) has to be done in the shortest possible time. In other spheres of work the situation is probably similar, with the difference that in fuzzy logic we have to deal with discreteness directly, while in other fields of work it is skilfully incorporated in calculation procedures and is in this way implicit for the user or observer. In spite of the wish to have the shortest possible calculation times, it is important not to miss the essence of the fuzzy algorithm to which calculation refers because of approximate results. In this Chapter we are firstly going to observe low-density fuzzy inference processing and its influence on the results. Low-density fuzzy processing can reduce processing time, and thus usually lead to higher performance of the fuzzy system.

Temporality of Propositions

We may say that time is the most common and indeed the most vital variable related to human life and work. Temporality is implanted in peoples lives and work in a manner which allows their relations to all surrounding activities to be defined in micro and macro perspective. It comes then as no surprise that temporality is interwoven with our natural languages so skillfully that it seems to be a part of our subconscious processes and understood quite by itself. However, there are certain difficulties hidden here.