Traces of Fuzzy Relations Under Dual Operations

2005 ◽  
Vol 9 (5) ◽  
pp. 563-569 ◽  
Author(s):  
Hiroshi Hashimoto ◽  
Keyword(s):  
Fuzzy Relation ◽  
Equivalent Transformation ◽  
Matrix Inequality ◽  
Fuzzy Relations ◽  
Matrix Inequalities ◽  
Fuzzy Matrix ◽  
Dual Operations ◽  
The Given ◽  
Standard Operations

We examined dual properties of traces of a fuzzy relation using fuzzy matrices. Traces of a fuzzy relation are reflexive and transitive fuzzy relations obtained from the given fuzzy relation. Under standard operations on fuzzy matrices, fuzzy matrix inequalities and equalities are deduced by applying the well-known equivalent transformation of a fuzzy matrix inequality. We present, in particular, propositions on the construction of transitive fuzzy relations.

FUZZY RELATION CALCULUS IN THE COMPRESSION AND DECOMPRESSION OF FUZZY RELATIONS

2002 ◽  
Vol 02 (04) ◽  
pp. 617-631 ◽  
Author(s):  
VINCENZO LOIA ◽  
WITOLD PEDRYCZ ◽  
SALVATORE SESSA
Keyword(s):  
Lossy Compression ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Triangular Norm ◽  
Fuzzy Matrix ◽  
Fuzzy Relation Equations

We firstly review some fundamentals of fuzzy relation calculus and, by recalling some known results, we improve the mathematical contents of our previous papers by using the properties of a triangular norm over [0,1]. We make wide use of the theory of fuzzy relation equations for getting lossy compression and decompression of images interpreted as two-argument fuzzy matrices.The same scope is achieved by decomposing a fuzzy matrix using the concept of Schein rank. We illustrate two algorithms with a few examples.

DECOMPOSITION OF MULTIUNIVERSE FUZZY TRUTH FUNCTIONS

2001 ◽  
Vol 09 (05) ◽  
pp. 623-643
Author(s):  
DERYA ALTUNAY ◽  
TURHAN ÇİFTÇİBAŞI
Keyword(s):  
Propositional Logic ◽  
Sufficient Conditions ◽  
Fuzzy Relation ◽  
Necessary And Sufficient Conditions ◽  
Fuzzy Relations ◽  
Decomposition Problem ◽  
The Common ◽  
Necessary And Sufficient ◽  
The Given

This paper focuses on the decomposition problem of fuzzy relations using the concepts of multiuniverse fuzzy propositional logic. Given two fuzzy propositions in different universes, it is always possible to construct a fuzzy relation in the common universe through a prescribed combination. However, the converse is not so obvious, if possible at all. In other words, given a fuzzy relation, how would we know if it really represents a certain relationship between some fuzzy propositions? It is important to recognize whether the given fuzzy relation is a meaningful representation of information according to certain criteria applicable to some fuzzy propositions that constitute the fuzzy relation itself. Two basic structures of decomposition are investigated. Necessary and sufficient conditions for decomposition of multiuniverse fuzzy truth functions in terms of one-universe truth functions are presented. An algorithm for decomposition is proposed.

scholarly journals A Study of Fuzzy Relation and Its Application in Medical Diagnosis

2021 ◽  
pp. 6-11
Author(s):  
Shishir Kumar ◽  
Chhaya Gangwal
Keyword(s):  
Medical Diagnosis ◽  
Research Work ◽  
Fuzzy Relation ◽  
Final Decision ◽  
Fuzzy Relations ◽  
Fuzzy Matrix ◽  
Maximum Value ◽  
Patient Symptom ◽  
Stomach Pain ◽  
Membership Value

Objective: Medical diagnosis process extends within the degree to which they plan to affect different complicating aspects of diagnosis. In this research work, the concept of fuzzy relation with medical diagnosis is studied and the application of fuzzy relations to such problems by extending the Sanchez’s approach is introduced. Method: An application of fuzzy relation with Sanchez's approach for medical diagnosis is presented. Based on the composition of the fuzzy relations, an algorithm for medical diagnosis as follows- first input the number of objects and attributes to obtain patient symptom matrix, symptom-disease matrix and the composition of fuzzy relations to get the patient-diagnosis matrix. Then find the maximum value to evaluate which patient is suffering from what disease. Result: Using the algorithm for medical diagnosis, the disease for which the membership value is maximum gives the final decision. If almost equal values for different diagnosis in composition are obtained, the case for which non-membership is minimum and hesitation is least is considered. The output matched well with the doctor’s diagnosis. Conclusion: In the process of medical diagnosis, state of patient are given by the patient through linguistic terminology like as temperature, cough, stomach pain etc., consideration of fuzzy sets as grades for association instead of membership grades in [0,1] is more advantageous to model the state of the patient. Similarly fuzzy relation has been introduced representing the association between symptoms and diseases. Sanchez’s approach has been extended for medical diagnosis in this reference. The approach used to form fuzzy matrix showing the association of symptoms and diseases is based on the sanchez’s approach.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

Matrix, Fuzzy Relation and Fuzzy Matrix

2018 ◽  
pp. 41-71
Author(s):  
Hao-Ran Lin ◽  
Bing-Yuan Cao ◽  
Yun-zhang Liao
Keyword(s):  
Fuzzy Relation ◽  
Fuzzy Matrix

On the Compatibility of a Ternary Relation with a Binary Fuzzy Relation

2019 ◽  
Vol 27 (04) ◽  
pp. 595-612 ◽  
Author(s):  
Omar Barkat ◽  
Lemnaouar Zedam ◽  
Bernard De Baets
Keyword(s):  
Order Relation ◽  
Fuzzy Relation ◽  
Ternary Relation ◽  
The Given

Recently, De Baets et al. have characterized the fuzzy tolerance relations that a given strict order relation is compatible with. In general, the compatibility of a strict order relation with a binary fuzzy relation guarantees also the compatibility of its associated betweenness relation with that binary fuzzy relation. In this paper, we study the compatibility of an arbitrary ternary relation with a binary fuzzy relation. We prove that this compatibility can be expressed in terms of inclusions of the binary fuzzy relation in the traces of the given ternary relation.

scholarly journals Observer-based fault estimation for linear systems with distributed time delay

2013 ◽  
Vol 23 (2) ◽  
pp. 169-186 ◽  
Author(s):  
Anna Filasová ◽  
Daniel Gontkovič ◽  
Dušan Krokavec
Keyword(s):  
Time Delay ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Structured Matrix ◽  
Continuous Time Systems ◽  
Distributed Time Delay ◽  
And Performance ◽  
Time Systems

The paper is engaged with the framework of designing adaptive fault estimation for linear continuous-time systems with distributed time delay. The Lyapunov-Krasovskii functional principle is enforced by imposing the integral partitioning method and a new equivalent delaydependent design condition for observer-based assessment of faults are established in terms of linear matrix inequalities. Asymptotic stability conditions are derived and regarded with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. Simulation results illustrate the design approach, and demonstrates power and performance of the actuator fault assessment.

The Application of Linear Algebra Algorithm in the Production of Linear Matrix Inequalities

2012 ◽  
Vol 192 ◽  
pp. 406-411
Author(s):  
Hui Zhang
Keyword(s):  
Problem Solving ◽  
Linear Algebra ◽  
Linear Matrix Inequalities ◽  
Polynomial Matrix ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Application System ◽  
And Control ◽  
Problem Data

Discusses the theory and symbolic of the algorithm gives another potential application, but also in the system and control. For example, for the question, has made with special structure, but LMI problem data, may cause factorizations LMI more compact. One can even imagine using the algorithm around, looking for the opportunity to LMI automatic eliminate variables, so simplify problem solving, before they get a lot of influence and a potential solutions. We describe theory, the algorithm can be used to factor in the non commuting variable polynomial matrix and application system switches and control problem into a linear matrix inequality.

scholarly journals Bipolar Fuzzy Relations

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1044 ◽  
Author(s):  
Jeong-Gon Lee ◽  
Kul Hur
Keyword(s):  
Equivalence Class ◽  
Level Set ◽  
Equivalence Relation ◽  
Level Sets ◽  
Equivalence Classes ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Transitive Relation ◽  
Fuzzy Partition

We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an ( a , b ) -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their ( a , b ) -level sets.

scholarly journals On rough sets induced by fuzzy relations approach in semigroups

2018 ◽  
Vol 16 (1) ◽  
pp. 1634-1650
Author(s):  
Rukchart Prasertpong ◽  
Manoj Siripitukdet
Keyword(s):  
Prime Ideal ◽  
Rough Set ◽  
Rough Sets ◽  
Sufficient Conditions ◽  
Unit Interval ◽  
Fuzzy Relation ◽  
Prime Ideals ◽  
Fuzzy Relations ◽  
Completely Prime Ideal

AbstractIn this paper, we introduce a rough set in a universal set based on cores of successor classes with respect to level in a closed unit interval under a fuzzy relation, and some interesting properties are investigated. Based on this point, we propose a rough completely prime ideal in a semigroup structure under a compatible preorder fuzzy relation, including the rough semigroup and rough ideal. Then we provide sufficient conditions for them. Finally, the relationships between rough completely prime ideals (rough semigroups and rough ideals) and their homomorphic images are verified.

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