USING MULTIPLE CORRESPONDENCE ANALYSIS WITH MEMBERSHIP VALUES WHEN THE SYSTEM STUDY YIELDS MISCELLANEOUS DATASETS

This article explains the main role that space windowing plays in preliminary knowledge extraction from multifactor and multivariate databases coming from complex system empirical studies. The explanation is based on the general case of a database with a hyperparallelepipedic structure in which the directions correspond to the factors and where the measurement variables may be quantitative or qualitative, temporal or nontemporal, and objective or subjective. First, the data in each cell of the hyperparallelepiped is transformed into membership values that can be averaged over factors, such as time or individual. Then, several graphic techniques can be exploited to investigate membership values. This article mainly focuses on the use of multiple correspondence analysis (MCA). A didactic example with several factors and several kinds of variables—nontemporal vs. temporal where each one may be either quantitative or qualitative—is used to illustrate the widespread use of the pair “space windowing/MCA.” The discussion presents the advantages and disadvantages of using space windowing to perform a preliminary analysis of a multifactor multivariate system study.     

ON STOCHASTIC CONVERGENCE THEOREMS FOR THE FUZZY C-MEANS CLUSTERING PROCEDURE∗

The fuzzy c-means clustering algorithm has been well studied for equal weight distributions on a finite set. Suppose that this situation is generalized to an arbitrary probability distribution on a finite dimensional Euclidean space, assuming that the second moment of the distribution is finite. Now choose ever larger finite random samples from this distribution and compute the standard optimal membership functions for a fuzzy partition into c clusters. Then the convergence of the cluster center points is established in the Hausdorff sense with probability one, provided that there is a unique optimal center point set. These optimal center points are the fixed point of a simple operator, and there is a corresponding iterative algorithm that generalizes the usual procedure.     

The selection of technology forecasting method using a multi-criteria interval-valued intuitionistic fuzzy group decision making approach

Technological forecasting is a tool for organizations to develop their technology strategies. The quality of forecasting is extremely important for the accuracy of the results and in turn company future. Therefore a proper selection methodology of forecasting technique that considers the characteristics of technology and resources needed such as cost, time is essential. On the other hand, although many forecasting techniques are available, there is a high uncertainty in choosing the most appropriate technique among a set of available techniques. In this paper interval valued intuitionistic fuzzy technique for order preference by similarity to ideal solution (TOPSIS) method is proposed for the solution of technological forecasting technique selection problem. The proposed method includes seven selection criteria and twelve forecasting technique alternatives. The methodology is applied for 3D TV technology. The results revealed that Fisher Pry method is found as the most appropriate method for forecasting since it has the highest closeness coefficient.     

Theory of Fuzzy Generalized Morphisms and Relational Inequalities

We present here the theory of generalized morphisms and fuzzy relational inequalities and discuss some of these applications. Results presented in this paper extend the work of Bandler and Kohout (1986) ["On the general theory of relational morphisms", International Journal of General Systems, 13, pp. 47-66] published in this journal previously, to relational systems based on residuated t-norm fuzzy logics.     

QUO VADIS FUZZY SYSTEMS: A CRITICAL EVALUATION OF RECENT METHODOLOGICAL TRENDS

The paper critically examines some foundational aspects of Fuzzy Sets and Systems. The systemic character of Zadeh's approach is stressed, as is the neccessity of understanding the interplay of holism and atomism for the proper evaluation of the formalized epistemology of fuzzy sets. This link between holism and atomism is provided by the systemic epistemology of T. G. Masaryk, adumbrated in Sec. 2. The linguistic theories of the Prague School, which are based on the epistemology utilizing the notions purpose, function, communication, meaning, normative structure etc. are also discussed, and their relevance to the methodology of Fuzzy Sets and Systems is stressed. Section 5 is devoted to formal analysis of possibilistic constructions and structures. It is demonstrated that the so called “Theory of possibility” is just one special instance of the general possibilistic construction.

The paper of Zelený, appearing elsewhere in this issue, is critically evaluated, as is the Graham-Johnstone controversy. The latter contained heated discussions about pros and cons of research concerning fuzzy sets. The phenomenon of the epistemological and methodological split within the field of fuzzy systems (which I refer to as “The schism of the third decade”) is observed and its causes briefly analyzed.     

CONCEPTS OF FUZZY INFORMATION MEASURES ON CONTINUOUS DOMAINS

Measures of information based on fuzzy sets (possibility distributions) had been defined only for finite domains of discourse. This paper presents a method of defining such information functions on a continuous universe of discourse—a domain which is a measurable space of measure 1. The method is based on the concept of “rearangement” of a function, used in lieu of sorting discrete possibility values. For technical reasons, it is preferred to express information value as information distance to the most “uninformed” (constant possibility 1) distribution. The final form of the information for possibility distribution f is

The paper then discusses related information distances and approximations using discrete information functions.     

FUZZY LOGICAL OPERATORS ON FINITE CHAINS

Abstract

The extension of classical binary logical operators to multi-valued operators is a very interesting topic, both from a theoretical and a practical point of view. In this paper we pay special attention to fuzzy implication operators on the unit interval and on finite chains. We discuss some properties and define several special classes, in particular the class of Lukasiewicz-like implicators. On the unit interval we prove a nice characterization for this class, while we have to replace the continuity condition on [0,1] by a smoothness condition on finite chains to obtain a similar characterization. In contrast to implicators on [0,1], there is no direct way to construct implicators on a finite chain. Therefore, we discuss several algorithms that generate different types of implicators. In this way we also obtain the number of implicators on a finite chain, which gives us an idea of the restrictivity of the involved properties.     

On the selection of variables for qualitative modelling of dynamical systems

Behavioural modelling of physical systems from observations of their input/output behaviour is an important task in engineering. Such models are needed for fault monitoring as well as intelligent control of these systems. The paper addresses one subtask of behavioural modelling, namely the selection of input variables to be used in predicting the behaviour of an output variable. A technique that is well suited for qualitative behavioural modelling and simulation of physical systems is Fuzzy Inductive Reasoning (FIR), a methodology based on General System Theory. Yet, the FIR modelling methodology is of exponential computational complexity, and therefore, it may be useful to consider other approaches as booster techniques for FIR. Different variable selection algorithms: the method of the unreconstructed variance for the best reconstruction, methods based on regression coefficients (OLS, PCR and PLS) and other methods as Multiple Correlation Coefficients (MCC), Principal Components Analysis (PCA) and Cluster analysis are discussed and compared to each other for use in predicting the behaviour of a steam generator. The different variable selection algorithms previously named are then used as booster techniques for FIR. Some of the used linear techniques have been found to be non-effective in the task of selecting variables in order to compute a posterior FIR model. Methods based on clustering seem particularly well suited for pre-selecting subsets of variables to be used in a FIR modelling and simulation effort.     

Fuzzy and simulation-based techniques for industrial safety and risk assessment

This paper characterizes the development of a hybrid computer-based tool supporting design for safety practices in industrial plant component specification and layout definition. The tool combines simulation and fuzzy logic techniques for the systematic risk assessment of specified design and layout configurations for plants dealing with hazardous materials. In the hybrid system architecture, the simulation module provides the historical experience for a priori hazard identification and ranking, accounting for the domino effects of possible accidental occurrences, while the fuzzy module provides the correlation matrices for concurrent hazard evaluation and overall risk assessment. In particular, the fuzzy module enables the quantitative assessment and comparison among alternative design solutions providing design guidelines, which can be further tested and verified through simulation.