Matrix, Fuzzy Relation and Fuzzy Matrix

FUZZY RELATION CALCULUS IN THE COMPRESSION AND DECOMPRESSION OF FUZZY RELATIONS

International Journal of Image and Graphics ◽

10.1142/s0219467802000871 ◽

2002 ◽

Vol 02 (04) ◽

pp. 617-631 ◽

Cited By ~ 10

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.

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Traces of Fuzzy Relations Under Dual Operations

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2005.p0563 ◽

2005 ◽

Vol 9 (5) ◽

pp. 563-569 ◽

Cited By ~ 1

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.

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Fuzzy matrix games via a fuzzy relation approach

Fuzzy Optimization and Decision Making ◽

10.1007/s10700-007-9015-9 ◽

2007 ◽

Vol 6 (4) ◽

pp. 299-314 ◽

Cited By ~ 23

Author(s):

V. Vijay ◽

A. Mehra ◽

S. Chandra ◽

C. R. Bector

Keyword(s):

Fuzzy Relation ◽

Matrix Games ◽

Fuzzy Matrix ◽

Relation Approach

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A Study of Fuzzy Relation and Its Application in Medical Diagnosis

Asian Research Journal of Mathematics ◽

10.9734/arjom/2021/v17i430289 ◽

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.

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Comprehensive evaluation of kraft pulp properties from fast-growing woods

TAPPI Journal ◽

10.32964/tj9.6.34 ◽

2010 ◽

Vol 9 (6) ◽

pp. 34-39

Author(s):

AIYU QU ◽

YANHUI AO ◽

JUN YAN ◽

GUIGAN FANG

Keyword(s):

Kraft Pulp ◽

Comprehensive Evaluation ◽

Evaluation Model ◽

Evaluation Index System ◽

Evaluation Index ◽

Wood Cellulose ◽

Fuzzy Matrix ◽

Fast Growing ◽

Pulp Properties ◽

Evaluation Index Systems

To develop new wood cellulose resources and fast-growing pulpwood plantation fiber sources, it is very important to evaluate their pulping properties. A comprehensive multi-index pulping-suitability evaluation model is investigated in this paper by considering four fast-growing wood species. First, a new evaluation-index system for kraft pulp was developed based on traditional evaluation-index systems. Then, the membership degree of every index was analyzed to obtain a fuzzy matrix. The proportional contribution of each parameter to the main pulping properties could then be determined. Finally, a comprehensive evaluation model of kraft pulp properties was developed. The model is reliable compared with traditional assessment methods. The results confirmed the feasibility and rationality of developing new wood cellulose resources and fast-growing pulpwood plantations using fuzzy comprehensive evaluations.

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Objective Evaluation of Drivability in Passenger Cars with Dual-Clutch Transmission: A Case Study of Static Gearshift Condition

Mathematical Problems in Engineering ◽

10.1155/2020/2061083 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Wei Zhou ◽

Xuexun Guo ◽

Xiaofei Pei ◽

Chengcai Zhang ◽

Jun Yan ◽

...

Keyword(s):

Fuzzy Ahp ◽

Subjective Evaluation ◽

Objective Evaluation ◽

Dual Clutch Transmission ◽

Evaluation Tool ◽

Passenger Cars ◽

Denoising Method ◽

Fuzzy Matrix ◽

Predictability Score

This paper is aimed at the problem that the subjective drivability evaluation by experienced test drivers is limited in time efficiency and is of high cost and poor repeatability. In this article, an intelligent drivability objective evaluation tool (I-DOET) for passenger cars with dual-clutch transmission (DCT) is developed and verified by real vehicle testing. First, the signal denoising method and its key parameters, which are suitable for drivability evaluation, are selected based on analytic hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS). Besides, combined with the uncertainty characteristics of subjective judgment, a mathematical model of the objective drivability evaluation FARODE (fuzzy AHP-RS based on objective drivability evaluation) is proposed by using the fuzzy comprehensive assessment (FCA) method. The AHP and rough set (RS) method are used to calculate the subjective and objective weights of the drivability evaluation, respectively, and the proportion of subjective and objective weights is determined by the principle of minimum relative information entropy. The fuzzy matrix is built by membership function of the evaluation indexes. Finally, the static gearshift condition focused on by the subjective evaluation experts is taken as a case study. The predictability score is obtained by combining the drivability quantization lever vector, comprehensive weight, and fuzzy matrix. The experimental results indicate that the proposed method is applicable for objective drivability evaluation in passenger cars with DCT.

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