Fuzzy Relational Structure Research Articles

Two-mode weakly linear systems of fuzzy relation equations: Structures of solutions, computation methods, and applications

The problem of aggregating large fuzzy relational structures is of major importance. One of the main issues is seeking a simpler fuzzy relational structure, while keeping the structure properties of the original fuzzy relational structure as much as possible. This paper covers the mathematical foundations of the described problem, and deals with the solvability issues of two-mode weakly linear systems over complete residuated lattices. Within these systems, our objective is to identify a pair of unknown fuzzy relations that are present on both sides of the equation or inequality. We provide a characterization of the set of all pairs of fuzzy relations that are solutions to two-mode weakly linear systems to a desired degree, and develop an algorithm to compute the greatest such pair. We also present an algorithm to determine a pair that solves a two-mode weakly linear system to a given extent, such that each component is a fuzzy preorder (resp. fuzzy equivalence). Ultimately, we demonstrate the application aspects of aggregating fuzzy relational structures.

G-normal fuzzy relational models are universal approximators

Making a fuzzy relational model (FRM) g-normal by a specific configuration of the FRM and putting some constraints on both its fuzzifier and its fuzzy relational matrix, results in some favorite features at the expense of loosing some degrees of freedom. In this paper, we show that the g-normal fuzzy relational modeling structure has the universal approximation property despite all the constraints that makes the model g-normal. Indeed, we prove that any real function in Lp (including continuous functions) can be modeled by a g-normal model with any arbitrary accuracy when the universe of discourse is a compact set.

Fuzzy approximations of fuzzy relational structures

In social network analysis, relational structures play a crucial role in the processing of complex data. This paper proposes a fuzzy relational structure which consists of a non-empty universal set and a set of fuzzy relations of finite arity. In order to deduce knowledge hidden in a fuzzy relational structure we present the concept of bisimulations as indiscernibility with respect to the fuzzy relational structure. Furthermore, we give a method of computing the largest bisimulations over fuzzy relational structures and present computational examples of the method. Finally, the fuzzy rough set analysis of fuzzy relational structures is discussed.

Construction and applications of a modified Fuzzy Relational Model

A modified fuzzy relational modeling structure is presented in this paper by proposing a fuzzy relational inner composition. This leads to an integrated framework for representing multilevel fuzzy relational equations which is able to provide multi-dimensional models of complex systems very effectively. A potentially online derivative-based identification algorithm is also presented for the proposed model. The identification procedure is based on the special t-norm-based and t-conorm-based operations leading to an easy and fast implementation of the proposed algorithm. The proposed modeling structure is customized and used for two different applications. The simulation results show high modeling capability of the proposed fuzzy relational model.

Integration of OT and IRS to Explore Structure of Statistics Concepts

The purpose of this study is to integrate two methodological approaches to explore concept structures. One approach is student-problem chart (S-P chart) and ordering theory (OT) and the other is fuzzy clustering and item relational structure (IRS). S-P chart is adopted to classify all students into proper learning styles. OT is to determine hierarchies of concept structures. Fuzzy clustering is soft computation to cluster features of students and combine IRS so as to determine the precondition and ordering relationship among items. The empirical data is statistics concepts test of university students. The results show that integration of these two approaches is feasible for cognition diagnosis and would be helpful for remedial instruction. Finally, some suggestions and recommendations for future research and educational research are provided.

Fuzzy trees in decision support systems

This paper is based on the following assumption: that there exists a fuzzy tree structure and a distance between fuzzy trees which provides the basis for fuzzy decision-making. The paper provides the following: (1) a new definition of the fuzzy relational tree structure, (2) the development of a new comparative method for fuzzy trees and its experimental testing and evaluation, (3) a new descriptive method of military structures in a fuzzy tree format and the development of a fuzzy decision support system.

A framework for intelligent medical diagnosis using the theory of evidence

In designing fuzzy logic systems for fault diagnosis, problems can be encountered in the choice of symptoms to use fuzzy operators and an inability to convey the reliability of the diagnosis using just one degree of membership for the conclusion. By turning to an evidential framework, these problems can be resolved whilst still preserving a fuzzy relational model structure. The theory of evidence allows for utilisation of all available information. Relationships between sources of evidence determine appropriate combination rules. By generating belief and plausibility measures it also communicates the reliability of the diagnosis, and completeness of information. In this contribution medical diagnosis is considered using the theory of evidence, in particular the diagnosis of inadequate analgesia is considered.

Fuzzy Sets and Fuzzy Relational Structures as Chu Spaces

Chu spaces, which derive from the Chu construct of *-autonomous categories, can be used to represent most mathematical structures. Moreover, the logic of Chu spaces is linear logic. Most efforts to incorporate fuzzy set theory into the realm of linear logic are based on the assumption that fuzzy and linear negation are identical operations. We propose an incorporation based on the opposite assumption and we provide an interpretation of some linear connectives. Furthermore, we show that it is possible to represent any fuzzy relational structure as a Chu space by means of the functor G.

FUZZY SETS AND FUZZY RELATIONAL STRUCTURES AS CHU SPACES

Chu spaces, which derive from the Chu construct of *-autonomous categories, can be used to represent most mathematical structures. Moreover, the logic of Chu spaces is linear logic. Most efforts to incorporate fuzzy set theory into the realm of linear logic are based on the assumption that fuzzy and linear negation are identical operations. We propose an incorporation based on the opposite assumption and we provide an interpretation of some linear connectives. Furthermore, we show that it is possible to represent any fuzzy relational structure as a Chu space by means of the functor G.

Extraction Method of the Difference between Fuzzy Graphs

We discuss the extraction method of the structural difference between fuzzy graphs, which is useful for instructional design, sociometrie analysis and so on. The method is called FRS (Fuzzy Relational Structure) Analysis based on the fuzzy decision. As a reasonable application, we describe the educational analysis of the logical structure using the test data, which provides us with effective information to evaluate the instructional program, to design CAI (Computer Aided instruction) courseware and so on. In this paper, we present the FRS Analysis and explain its application to the instructional design.

A fuzzy representation of data for relational databases

A structure for representing inexact information in the form of a relational database is presented. The structure differs from ordinary relational databases in two important respects: Components of tuples need not be single values and a similarity relation is required for each domain set of the database. Two critical properties possessed by ordinary relational databases are proven to exist in the fuzzy relational structure. These properties are (1) no two tuples have identical interpretations, and (2) each relational operation has a unique result.