Fuzzy Relational Systems

Intuitionistic fuzzy sets form an extension of fuzzy sets: while fuzzy sets give a degree to which an element belongs to a set, intuitionistic fuzzy sets give both a membership degree and a nonmembership degree. The only constraint on those two degrees is that their sum must be smaller than or equal to 1. In fuzzy set theory, an important class of triangular norms and conorms is the class of continuous Archimedean nilpotent triangular norms and conorms. It has been shown that for such t-norms T there exists a permutation /spl phi/ of [0,1] such that T is the /spl phi/-transform of the Lukasiewicz t-norm. In this paper we introduce the notion of intuitionistic fuzzy t-norm and t-conorm, and investigate under which conditions a similar representation theorem can be obtained.

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On the representation of intuitionistic fuzzy t-norms and t-conorms

Fuzzy relational equations are without doubt the most important inverse problems arising from fuzzy set theory, and in particular from fuzzy relational calculus. Indeed, the calculus of fuzzy relations is a powerful one, with applications in fuzzy control and fuzzy systems modelling in general, approximate reasoning, relational databases, clustering, etc. In this chapter, fuzzy relational equations are approached from an order-theoretical point of view. It is shown how all inverse problems can be reduced to systems of polynomial lattice equations. The exposition is limited to the description of exact solutions, and analytical ways are presented for obtaining the complete solution set when working in a broad and interesting class of distributive lattices. Ample literature pointers to approximate solution methods and application areas are provided.

Analytical solution methods for fuzzy relational equations.

This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh’s works have cristalized and popularized a concern that has appeared in the first half of the century, mainly in philosophical circles. Another purpose of the paper is to scan the basic definitions in the field, that are required for a proper reading of the rest of the volume, as well as the other volumes of the Handbooks of Fuzzy Sets Series. This Chapter also contains a discussion on operational semantics of the generally too abstract notion of membership function. Lastly, a survey of variants of fuzzy sets and related matters is provided.

Fuzzy Sets: History and Basic Notions

On the composition of intuitionistic fuzzy relations

Increasingly complex interaction between man and nature, increasingly complex interaction between man and man-made artificial systems, make it increasingly difficult to comprehend the consequences of changes in all these systems, to analyze them, to understand their dynamics, to influence their behaviour.

Fuzzy Relational Products as a Tool for Analysis and Synthesis of the Behaviour of Complex Natural and Artificial Systems

Relational-product architectures for information processing

This paper demonstrates how fuzzy relational information retrieval techniques are utilised in the context of clinical decision making by means of knowledge-based system Our example of practical application outlines the use of the methods for retrieval of patterns describing dexterity assessment of neurological patients through handwriting A partial view of the architecture of DEXTERON KBS unit is presented and the role of fuzzy information retrieval techniques in its design is outlined

The use of fuzzy information retrieval in knowledge-based management of patients' clinical profiles

Human action, the goal-directed interaction of the person with the environment, has long been a problem area for psychologists seeking to model human behaviour and for philosophers seeking to understand the interaction of body and mind. Nowadays it is a major problem area in studies of "artificial intelligence" where one seeks to mimic human action. Perhaps the major area of application of studies of human action, however, is in clinical medicine where the pathology of action in geriatric cases, or where brain injury leads to similar malfunction, is of increasing importance. However, none of these fields yet offers any overall solution to the problem of understanding, modelling, synthesizing and correcting action. There are deep problems in the philosophical foundations, the psychological studies, the artificial intelligence simulation and the clinical treatment of action in all its varied forms. Our main argument is that the problem of understanding action is a tractable but extremely complex one, and involving many closely interacting levels of discourse. The main objective of our current work is to provide a clear, methodological framework for the study of action (Gaines & Kohout, 1976). In our opinion lack of a well-defined methodological framework for analysis of action and its pathology has been a major impediment to both experimental and theoretical studies in neuroand behavioural sciences. The human, even in apparently simple actions, brings into play a complex hierarchical system. The action of a muscle can be understood only in the context of the overall tonus, the preceeding and succeeding behaviour, the intent for the overall movement, and so on. No combination of psychological and physiological observation is currently adequate to monitor all relevant detail. One has doubts that this may ever be so. We certainly need far more structural contexts in which to work than those provided by naieve experimental empiricism or behaviourism. It is also reasonable to doubt the possibily of having anything rather than ad hoc, piecemeal models of the many interacting components of the overall hierarchical system. There is a profound question as to what extent we can comprehend or model such complexity. However, I shall aim to show that this is a similar question that was faced by, for example, a chemist in coming to comprehend the structure of a natural material. Even though inhomogenous and complex, with local peculiarities, it is potentially understandable in terms of regular and simple phenomena in complex inter-relationships. The key formal structure or rather "theoretical" framework for analysis of action (Kohout & Gaines, 1976) is closely related to a generalization of a model of dynamic protection in multi-access computer systems (Kohout & Gaines, 1975). The important 397

Ladislav J. Kohout

Papers

Fuzzy Relational Products as a Tool for Analysis and Synthesis of the Behaviour of Complex Natural and Artificial Systems

Relational-product architectures for information processing

The use of fuzzy information retrieval in knowledge-based management of patients' clinical profiles

The use of fuzzy information retrieval in knowledge-based management of patients' clinical profiles

Control of movement and protection structures