scholarly journals Energy and Entropy Measures of Fuzzy Relations for Data Analysis

2018 ◽  
Author(s):  
Ferdinando Di Martino ◽  
Salvatore Sessa
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Rule ◽  
Threshold Value ◽  
Fuzzy Relation ◽  
Fuzzy Rules ◽  
Fuzzy Relations ◽  
Input Output ◽  
Input And Output ◽  
Entropy Measures ◽  
The Relationship

We present a new method for assessing the strength of fuzzy rules with respect to a dataset, based on the measures of the greatest energy and smallest entropy of a fuzzy relation. Considering a fuzzy automaton (relation) in which A is the input fuzzy set and B the output fuzzy set, the fuzzy relation R1 with greatest energy provides information about the greatest strength of the input-output and the fuzzy relation R2 with the smallest entropy provides information about uncertainty of the relationship input-output. We consider a new index of the fuzziness of the input-output based over R1 and R2. In our method this index is calculated for each pair of input and output fuzzy sets in a fuzzy rule. A threshold value is set for choosing the most relevant fuzzy rules with respect to the data.

Generating Fuzzy Sets and Fuzzy Relations Based on Information

2021 ◽  
Vol 20 ◽  
pp. 178-185
Author(s):  
Radwan Abu- Gdairi ◽  
Ibrahim Noaman
Keyword(s):  
Fuzzy Sets ◽  
Knowledge Discovery ◽  
Set Theory ◽  
Membership Function ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Relation ◽  
Knowledge Discovery In Databases ◽  
Fuzzy Relations

Fuzzy set theory and fuzzy relation are important techniques in knowledge discovery in databases. In this work, we presented fuzzy sets and fuzzy relations according to some giving Information by using rough membership function as a new way to get fuzzy set and fuzzy relation to help the decision in any topic . Some properties have been studied. And application of my life on the fuzzy set was introduced

Structure Organization of Hierarchical Fuzzy Model Using Genetic Algorithm

1995 ◽  
Vol 7 (1) ◽  
pp. 29-35
Author(s):  
Toshio Fukuda ◽  
◽  
Yasuhisa Hasegawa ◽  
Koji Shimojima
Keyword(s):  
Genetic Algorithm ◽  
Hierarchical Structure ◽  
Back Propagation ◽  
Fuzzy Model ◽  
Numerical Data ◽  
Fuzzy Rules ◽  
Input And Output ◽  
The Hierarchical Structure ◽  
Input Variables ◽  
The Relationship

This paper proposes a method to organize the hierarchical structure of fuzzy model using the Genetic Algorithm and back-propagation method. The number of fuzzy rules increases exponentially with the number of input variables. Thus, a fuzzy system with many input variables has an extremely large number of fuzzy rules. Hierarchical structure of fuzzy reasoning is one of the methods to reduce the number of fuzzy rules and membership functions. However, it is very difficult to organize the hierarchical structure because the hierarchical structure cannot be constructed without considering the relationship among input and output variables. The proposed method can organize the suitable hierarchical structure for the relationship among input and output variables in teaching numerical data. It is based on the Genetic Algorithm with an evaluation function as a strategy that adopts a system with fewer fuzzy rules and more accurate outputs. The proposed method is applied to the approximation problems of multi-dimensional nonlinear functions in order to demonstrate its effectiveness.

scholarly journals Eigen Fuzzy Sets and their Application to Evaluate the Effectiveness of Actions in Decision Problems

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1999
Author(s):  
Ferdinando Di Martino ◽  
Salvatore Sessa
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Fuzzy Relation ◽  
New Method ◽  
Decision Problems ◽  
Fuzzy Relations ◽  
Italian City ◽  
Historical Center

We propose a new method based on the greatest (resp., smallest) eigen fuzzy set (GEFS, resp., SEFS) of a fuzzy relation R with respect to the max–min (resp., min–max) composition in order to implement the actions of a decisor. Using information derived from judgments of the evaluators on how much a characteristic is improved with respect to others, we construct the fuzzy relations, RMAX (resp., RMIN), where any entry RMAXijj (resp., RMINij) expresses how much the efficacy produced on the ith characteristic is equal to or greater (resp., lesser) than that one produced by the jth characteristic. The GEFS of RMAX (resp., SEFS of RMIN) are calculated in order to improve the performances of each characteristic. In the wake of previous applications based on GEFS and SEFS, we propose a method to evaluate the tourism enhancement policies in the historical center of an important Italian city. This method is new and different from those known in the literature so far. It is applied to evaluate benefits brought about by locals in order to enhance tourism in a historical center Comparison tests show that the results obtained are consistent with those expressed by the tourists interviewed

PERTURBATION OF INTUITIONISTIC FUZZY RELATIONS

2001 ◽  
Vol 09 (01) ◽  
pp. 81-103 ◽  
Author(s):  
H. BUSTINCE ◽  
P. BURILLO
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Intuitionistic Fuzzy ◽  
Do So

In this paper we present a way of perturbing reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relations afterward obtaining the perturbation of another reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relation. To do so we study the main properties of an operator that allows us to go from an intuitionistic fuzzy set to another also intuitionistic fuzzy set, we then apply this operator to intuitionistic fuzzy relations with different properties and we study the conditions there must be for the new intuitionistic fuzzy relation to maintain the original properties.

scholarly journals Implementation of Equilibrium Optimizer Algorithm for MPPT in a wind turbine with PMSG

2021 ◽  
Vol 16 ◽  
Author(s):  
Radwan Abu- Gdairi ◽  
Ibrahim Noaman
Keyword(s):  
Wind Turbine ◽  
Fuzzy Sets ◽  
Knowledge Discovery ◽  
Set Theory ◽  
Membership Function ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Relation ◽  
Knowledge Discovery In Databases ◽  
Fuzzy Relations

Fuzzy set theory and fuzzy relation are important techniques in knowledge discovery in databases. In this work, we presented fuzzy sets and fuzzy relations according to some giving Information by using rough membership function as a new way to get fuzzy set and fuzzy relation to help the decision in any topic . Some properties have been studied. And application of my life on the fuzzy set was introduced.

Extracting fuzzy rules for modeling of complex processes using neural networks

2013 ◽  
Vol 227 (12) ◽  
pp. 2861-2869 ◽  
Author(s):  
A Jamali ◽  
SJ Motevalli ◽  
N Nariman-zadeh
Keyword(s):  
Neural Networks ◽  
Fuzzy Rule ◽  
Structure Design ◽  
Fuzzy Rules ◽  
Group Method ◽  
Rule Base ◽  
Input Output ◽  
Output Data ◽  
Complex Processes ◽  
Linguistic Rules

Modeling of complex processes often leads to complex mathematical relationships between inputs and outputs, which do not reflect the influence of the independent variables on the output parameters. In this article, an innovative technique based on neural networks is presented to extract fuzzy linguistic rules for modeling some processes using some input–output data. In this way, genetic algorithm is used both for optimal structure design of those group method of data handling-type neural networks and for subsequent optimization of sub-bounds of fuzzy singleton antecedents to further optimize the obtained fuzzy rule base. Three different input–output data tables related to some complex problems of a nonlinear mathematical system, an explosive cutting process and the probability of failure estimation of a two mass-spring system are modeled by some fuzzy rules, using the technique discussed in this article.

scholarly journals RELASI FUZZY PADA GRUP FAKTOR FUZZY

2020 ◽  
Vol 14 (1) ◽  
pp. 33
Author(s):  
Ahmad Madani ◽  
Saman Abdurrahman ◽  
Na'imah Hijriati
Keyword(s):  
Group Theory ◽  
Fuzzy Set ◽  
Fuzzy Relation ◽  
Factor Group ◽  
Fuzzy Relations ◽  
Fuzzy Group ◽  
Congruence Relations ◽  
Fuzzy Congruence ◽  
Fuzzy Subgroups ◽  
Fuzzy Subsets

Fuzzy subsets on the non-empty set is a mapping of this set to the interval . The concept of fuzzy subgroups introduced from advanced concept of fuzzy set in group theory. In concept of fuzzy set there is the concept of relations is fuzzy relations. In this study examined that fuzzy relations related to the equivalence and congruence on a fuzzy group and fuzzy factor group. The results of this study was to show that a fuzzy relation    if  and    if  is a fuzzy congruence relations on fuzzy group and a fuzzy relation  defined of is a fuzzy congruence relations on fuzzy factor group.  

scholarly journals Robust Gaussian Noise Detection and Removal in Color Images using Modified Fuzzy Set Filter

2020 ◽  
Vol 30 (1) ◽  
pp. 240-257
Author(s):  
Akula Suneetha ◽  
E. Srinivasa Reddy
Keyword(s):  
Image Quality ◽  
Mean Square Error ◽  
Fuzzy Set ◽  
Digital Image ◽  
Gaussian Noise ◽  
Digital Images ◽  
Structural Similarity ◽  
Fuzzy Rules ◽  
Mean Square ◽  
Image Edges

Abstract In the data collection phase, the digital images are captured using sensors that often contaminated by noise (undesired random signal). In digital image processing task, enhancing the image quality and reducing the noise is a central process. Image denoising effectively preserves the image edges to a higher extend in the flat regions. Several adaptive filters (median filter, Gaussian filter, fuzzy filter, etc.) have been utilized to improve the smoothness of digital image, but these filters failed to preserve the image edges while removing noise. In this paper, a modified fuzzy set filter has been proposed to eliminate noise for restoring the digital image. Usually in fuzzy set filter, sixteen fuzzy rules are generated to find the noisy pixels in the digital image. In modified fuzzy set filter, a set of twenty-four fuzzy rules are generated with additional four pixel locations for determining the noisy pixels in the digital image. The additional eight fuzzy rules ease the process of finding the image pixels,whether it required averaging or not. In this scenario, the input digital images were collected from the underwater photography fish dataset. The efficiency of the modified fuzzy set filter was evaluated by varying degrees of Gaussian noise (0.01, 0.03, and 0.1 levels of Gaussian noise). For performance evaluation, Structural Similarity (SSIM), Mean Structural Similarity (MSSIM), Mean Square Error (MSE), Normalized Mean Square Error (NMSE), Universal Image Quality Index (UIQI), Peak Signal to Noise Ratio (PSNR), and Visual Information Fidelity (VIF) were used. The experimental results showed that the modified fuzzy set filter improved PSNR value up to 2-3 dB, MSSIM up to 0.12-0.03, and NMSE value up to 0.38-0.1 compared to the traditional filtering techniques.

scholarly journals Aggregation of Indistinguishability Fuzzy Relations Revisited

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1441
Author(s):  
Juan-De-Dios González-Hedström ◽  
Juan-José Miñana ◽  
Oscar Valero
Keyword(s):  
Equivalence Relation ◽  
Fuzzy Relations ◽  
Measure Of Similarity ◽  
Dual Notion ◽  
The Relationship

Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot.

scholarly journals Recessive Transition Mechanism of Arable Land Use Based on the Perspective of Coupling Coordination of Input–Output: A Case Study of 31 Provinces in China

Land ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 41
Author(s):  
Yi Lou ◽  
Guanyi Yin ◽  
Yue Xin ◽  
Shuai Xie ◽  
Guanghao Li ◽  
...  
Keyword(s):  
Land Use ◽  
Evaluation Model ◽  
Arable Land ◽  
Temporal Trends ◽  
Mainland China ◽  
Input Output ◽  
Transition Mechanism ◽  
Input And Output ◽  
Spatio Temporal ◽  
Arable Land Use

In the rapid process of urbanization in China, arable land resources are faced with dual challenges in terms of quantity and quality. Starting with the change in the coupling coordination relationship between the input and output on arable land, this study applies an evaluation model of the degree of coupling coordination between the input and output (D_CCIO) on arable land and deeply analyzes the recessive transition mechanism and internal differences in arable land use modes in 31 provinces on mainland China. The results show that the total amount and the amount per unit area of the input and output on arable land in China have presented different spatio-temporal trends, along with the mismatched movement of the spatial barycenter. Although the D_CCIO on arable land increases slowly as a whole, 31 provinces show different recessive transition mechanisms of arable land use, which is hidden in the internal changes in the input–output structure. The results of this study highlight the different recessive transition patterns of arable land use in different provinces of China, which points to the outlook for higher technical input, optimized planting structure, and the coordination of human-land relationships.

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