Ildar Z. Batyrshin

Fuzzy modeling based on generalized conjunction operations

An approach to fuzzy modeling based on the tuning of parametric conjunction operations is proposed. First, some methods for the construction of parametric generalized conjunction operations simpler than the known parametric classes of conjunctions are considered and discussed. Second, several examples of function approximation by fuzzy models, based on the tuning of the parameters of the new conjunction operations, are given and their approximation performances are compared with the approaches based on a tuning of membership functions and other approaches proposed in the literature. It is seen that the tuning of the conjunction operations can be used for obtaining fuzzy models with a sufficiently good performance when the tuning of membership functions is not possible or not desirable.

Parametric classes of generalized conjunction and disjunction operations for fuzzy modeling

It is argued that inference procedures of fuzzy models do not always require commutativity and associativity of the operations used. This raises the possibility of considering nonassociative and noncommutative conjunction and disjunction operations. Such operations are investigated in this paper and different methods for their generation are proposed. A number of new types of conjunction operations that are simpler than the known parametric classes of T-norms are given and, as an application example, the approximation of a function by a fuzzy inference system is considered.

Perception-Based Functions in Qualitative Forecasting

Summary. Perception-based function (PBF) is a fuzzy function obtained as a result of reconstruction of human judgments given by a sequence of rules Rk: If T is Tk then S is Sk, where Tk are perception-based intervals defined on the domain of independent variable T, and Sk are perception-based shape patterns of variable S on interval Tk. Intervals Tk can be expressed by words like Between N and M, Approximately M, Middle of the Day, End of the Week, etc. Shape patterns Sk can be expressed linguistically, e.g., as follows: Very Large, Increasing, Quickly Decreasing and Slightly Concave, etc. PBF differs from the Mamdani fuzzy model which defines a crisp function usually obtained as a result of tuning of function parameters in the presence of training crisp data. PBF is used for reconstruction of human judgments when testing data are absent or scarce. Such reconstruction is based mainly on scaling and granulation of human knowledge. PBF can be used in Computing with Words and Perceptions for qualitative evaluation of relations between variables. In this chapter we discuss application of PBF to qualitative forecasting of a new product life cycle. We consider new parametric patterns used for modeling convex–concave shapes of PBF and propose a method of reconstruction of PBF with these shape patterns. These patterns can be used also for time series segmentation in perception-based time series data mining.

Fuzzy expert system for solving lost circulation problem

Lost circulation is the most common problem encountered when drilling. This paper describes a distributed hybrid intelligent system, called SmartDrill, using fuzzy logic, expert system framework and Web services for helping petroleum engineers to diagnose and solve lost circulation problems. The fuzzy algebra of strict monotonic operations is used as an underlying model for expert system development. Its realization in inference procedures of expert systems is simpler than for expert systems based on lexicographic operations. Overall, the system architecture is discussed and implementation details are provided. The system is aimed to help in making decisions at the operational level and is at field testing phase in PEMEX, Mexican Oil Company.

Moving Approximation Transform and Local Trend Associations inTime Series Data Bases

Summary. The properties of moving approximation (MAP) transform and its application to time series data mining are discussed. MAP transform replaces time series values by slope values of lines approximating time series data in sliding window. A simple method of MAP transform calculation for time series with fixed time step is proposed. Based on MAP the measures of local trend associations and local trend distances are introduced. These measures are invariant under independent linear transformations and normalizations of time series values. Measure of local trend associations defines association function and measure of association between time series. The methods of application of association measure to construction of association network of time series and clustering are proposed and illustrated by examples of economic, financial, and synthetic time series.

Association networks in time series data mining

We discuss a new method of time series data mining using moving approximation (MAP) transform and association measures based on MAP. MAP transform replaces time series values by slope values of lines approximating time series data in sliding window. An effective method of MAP transform calculation for time series with fixed time step is proposed. Based on MAP, a measure of local trend associations between time series is introduced. This measure is invariant under independent linear transformations of time series. Measure of local trend associations defines association function depending on the size of sliding window for each pare of considered time series. Based on association function, different association measures may be considered to measure local trend associations or global trend associations between time series. The methods of application of association measure to construction of association network of time series are discussed and illustrated on examples of synthetic and financial time series databases. Association networks give information about relationships between time dynamics of elements of systems given by time series databases.

Generators of Fuzzy Operations for Hardware Implementation of Fuzzy Systems

The problem of effective hardware implementation of parametric operations of fuzzy systems is studied in this paper. The methods of generation of parametric classes of fuzzy conjunctions and disjunctions by means of introduced generators and basic operations are considered. Several types of generators of parametric fuzzy operations simple for hardware implementation are proposed. Examples of hardware implementation of proposed parametric operations are presented.

Towards Perception Based Time Series Data Mining

Human decision making procedures in problems related with analysis of time series data bases (TSDB) often use perceptions like “several days”, “high price”, “quickly increasing” etc. Computing with Words and Perceptions can be used to formalize perception based expert knowledge and inference mechanisms defined on numerical domains of TSDB. For extraction from TSDB perception based information relevant to decision making problems it is necessary to develop methods of perception based time series data mining (PTSDM). The paper considers different approaches used in analysis of time series databases for description of perception based patterns and discusses some methods of PTSDM.

VLSI implementation of a module for realization of basic t-norms on fuzzy hardware

Fuzzy theory applications have been explored and analyzed on fields as pattern recognition, control, data classification, signal processing, expert systems, among others. To accomplish this, more complex calculations and faster processing speed are required, turning fuzzy hardware implementation to be the perfect choice. Fuzzy operations as t-norms and t-conorms are used in fuzzy systems as conjunction and disjunction operations respectively. Commonly used t-norms for hardware implementation are minimum and algebraic product, first one is cheaper to implement; second consumes more resources. On this work FPGA technology is used to implement basic fuzzy t-norms as minimum, Lukasiewicz and drastic product into an 8 bit single circuit that allows operation selection. Timing, resources and comparative results are presented.

Perception based time series data mining with MAP transform

Import of intelligent features to time series analysis including the possibility of operating with linguistic information, reasoning and replying on intelligent queries is the prospective direction of development of such systems. The paper proposes novel methods of perception based time series data mining using perceptual patterns, fuzzy rules and linguistic descriptions. The methods of perception based forecasting using perceptual trends and moving approximation (MAP) transform are discussed. The first method uses perception based function for modeling qualitative forecasting given by expert judgments. The second method uses MAP transform and measure of local trend associations for description of perceptual pattern corresponding to the region of forecasting. Finally, the method of generation of association rules for multivariate time series based on MAP and fuzzy trends is discussed. Multivariate time series are considered as description of system dynamics. In this case association rules can be considered as relationships between system elements additional to spatial, causal etc. relations existing in the system. The proposed methods are illustrated on examples of artificial and real time series.