scholarly journals The Uncertainty Measure of Hierarchical Quotient Space Structure

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Qinghua Zhang ◽  
Guoyin Wang
Keyword(s):  
Membership Function ◽  
Information Entropy ◽  
Quotient Space ◽  
Space Structure ◽  
Space Structures ◽  
Fast Method ◽  
Fuzzy Concept ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
The Membership Function

In the application of fuzzy reasoning, researchers usually choose the membership function optionally in some degree. Even though the membership functions may be different for the same concept, they can generally get the same (or approximate) results. The robustness of the membership function optionally chosen has brought many researchers' attention. At present, many researchers pay attention to the structural interpretation (definition) of a fuzzy concept, and find that a hierarchical quotient space structure may be a better tool than a fuzzy set for characterizing the essential of fuzzy concept in some degree. In this paper, first the uncertainty of a hierarchical quotient space structure is defined, the information entropy sequence of a hierarchical quotient space structure is proposed, the concept of isomorphism between two hierarchical quotient space structures is defined, and the sufficient condition of isomorphism between two hierarchical quotient space structures is discovered and proved also. Then, the relationships among information entropy sequence, hierarchical quotient space structure, fuzzy equivalence relation, and fuzzy similarity relation are analyzed. Finally, a fast method for constructing a hierarchical quotient space structure is presented.

scholarly journals USING SIMILARITY DEGREES TO IMPROVE FUZZY MINING ASSOCIATION RULE BASED MODEL FOR ANALYZING IT ENTREPRENEURIAL TENDENCY

2019 ◽  
Vol 20 (2) ◽  
pp. 78-89
Author(s):  
Endang Supriyati ◽  
Mohammad Iqbal ◽  
Tutik Khotimah
Keyword(s):  
Membership Function ◽  
Association Rule ◽  
Phase 1 ◽  
Rule Model ◽  
Fuzzy Similarity ◽  
Transaction Database ◽  
Fuzzy Association Rule ◽  
Mining Association Rule ◽  
The Membership Function

Higher education has great potential in producing new startups in the IT (Information Technology) field. Many choices influence students to become IT- entrepreneurs. Association Rule can be used to obtain a model by analysing data so that it can be used to make a rule to the IT entrepreneurship-student model, but the association algorithm has disadvantages in handling large datasets. We propose reducing candidate itemsets using degrees of fuzzy similarity. The membership function in fuzzy sets can be used to measure the quality of rules obtained. The purpose of this study is to improve the algorithm by evaluating the similarity of candidate itemsets to get a good quality rule. This research method has 2 phases, namely (1) calculating the membership function with similarity itemset and (2) applying fuzzy mining association rule. Phase 1 has several steps, including: preparation of a transaction database, the taxonomy process, and identification of similar itemset. Phase 2 has several steps as well. The first is defining membership functions, and the last is a fuzzy mining fuzzy association rule. In this study, a questionnaire was distributed to 1225 students who were members of the IT entrepreneurship program. The results of this study were reduced into 823 itemsets and produced an IT entrepreneurship rule model. ABSTRAK: Pendidikan tinggi mempunyai potensi besar dalam menghasilkan permulaan baru dalam bidang IT. Banyak pilihan mempengaruhi pelajar bagi menjadi usahawan-IT. Kaedah Bersekutu boleh digunakan bagi mendapatkan model dengan menganalisa data supaya ianya dapat digunakan menjadi model kepada pelajar keusahawanan-IT, namun algoritma bersekutu mempunyai kelemahan dalam mengendalikan dataset yang besar. Kami mencadangkan pengurangan bilangan set item menggunakan tahapan persamaan kabur. Fungsi ahli dalam set kabur dapat digunakan bagi mengukur kualiti aturan yang diperoleh. Tujuan kajian ini adalah bagi meningkatkan algoritma dengan menilai persamaan set item calon bagi mendapatkan aturan kualiti yang baik. Kaedah penyelidikan ini mempunyai 2 peringkat, iaitu (1) mengira fungsi ahli dengan set item persamaan dan (2) menerapkan aturan perlombongan bersekutu kabur. Peringkat 1 mempunyai beberapa langkah, iaitu: urus niaga pangkalan data, proses taksonomi, identifikasi set item yang sama. Tahap 2 mempunyai beberapa langkah, iaitu: menentukan fungsi keahlian, dan akhirnya, aturan perlombongan bersekutu. Dalam kajian ini, soal selidik telah diedarkan kepada 1225 pelajar yang menjadi ahli program keusahawanan IT. Dapatan kajian menunjukkan pengurangan nombor dataset kepada 823 set item dan menghasilkan model aturan teknologi keusahawanan IT.

scholarly journals Fuzzy Covering-Based Three-Way Clustering

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Dandan Yang
Keyword(s):  
Nearest Neighbor ◽  
Structural Information ◽  
Boundary Region ◽  
Global Perspective ◽  
Semantic Interpretation ◽  
Entropy Theory ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
The Universe ◽  
Better Than

This paper investigates the three-way clustering involving fuzzy covering, thresholds acquisition, and boundary region processing. First of all, a valid fuzzy covering of the universe is constructed on the basis of an appropriate fuzzy similarity relation, which helps capture the structural information and the internal connections of the dataset from the global perspective. Due to the advantages of valid fuzzy covering, we explore the valid fuzzy covering instead of the raw dataset for RFCM algorithm-based three-way clustering. Subsequently, from the perspective of semantic interpretation of balancing the uncertainty changes in fuzzy sets, a method of partition thresholds acquisition combining linear and nonlinear fuzzy entropy theory is proposed. Furthermore, boundary regions in three-way clustering correspond to the abstaining decisions and generate uncertain rules. In order to improve the classification accuracy, the k-nearest neighbor (kNN) algorithm is utilized to reduce the objects in the boundary regions. The experimental results show that the performance of the proposed three-way clustering based on fuzzy covering and kNN-FRFCM algorithm is better than the compared algorithms in most cases.

GENERALIZED FUZZY ROUGH SETS BY CONDITIONAL PROBABILITY RELATIONS

2002 ◽  
Vol 16 (07) ◽  
pp. 865-881 ◽  
Author(s):  
ROLLY INTAN ◽  
MASAO MUKAIDONO
Keyword(s):  
Conditional Probability ◽  
Rough Set ◽  
Real World ◽  
Rough Sets ◽  
Similarity Relation ◽  
Fuzzy Rough Set ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
Real World Applications ◽  
The Universe

In 1982, Pawlak proposed the concept of rough sets with a practical purpose of representing indiscernibility of elements or objects in the presence of information systems. Even if it is easy to analyze, the rough set theory built on a partition induced by equivalence relation may not provide a realistic view of relationships between elements in real-world applications. Here, coverings of, or nonequivalence relations on, the universe can be considered to represent a more realistic model instead of a partition in which a generalized model of rough sets was proposed. In this paper, first a weak fuzzy similarity relation is introduced as a more realistic relation in representing the relationship between two elements of data in real-world applications. Fuzzy conditional probability relation is considered as a concrete example of the weak fuzzy similarity relation. Coverings of the universe is provided by fuzzy conditional probability relations. Generalized concepts of rough approximations and rough membership functions are proposed and defined based on coverings of the universe. Such generalization is considered as a kind of fuzzy rough set. A more generalized fuzzy rough set approximation of a given fuzzy set is proposed and discussed as an alternative to provide interval-value fuzzy sets. Their properties are examined.

Empirical Formula Considering the Smoke Ventilation for Air Temperature in Large Space Structure under Fire

2011 ◽  
Vol 94-96 ◽  
pp. 587-593 ◽  
Author(s):  
Jin Liang ◽  
Su Duo Xue ◽  
Xiong Yan Li
Keyword(s):  
Air Temperature ◽  
Empirical Formula ◽  
Steel Structures ◽  
Space Structure ◽  
Space Structures ◽  
Large Space ◽  
Fire Temperature ◽  
Large Space Structure ◽  
Fire Smoke ◽  
Resistance Performance

Abstract.The fire smoke is one of the most important factors for the fire temperature field. Once the fire smoke has been exhausted effectively, the fire temperature will be reduced and the fire-resistance performance of steel structures may be improved as well. However, the research on the fire temperature in the space structures is almost bold, which could lead to the theoretical analysis result on fire temperature is quite different from the real condition. Accordingly, the air temperature condition on fire for large-space structures has been analyzed. Taken into account smoke ventilation, the empirical formula for air temperature in large space structure under fire has been modified.

Possibility-Based Design Optimization Method for Design Problems With Both Statistical and Fuzzy Input Data

2005 ◽  
Vol 128 (4) ◽  
pp. 928-935 ◽  
Author(s):  
Liu Du ◽  
K. K. Choi ◽  
Byeng D. Youn ◽  
David Gorsich
Keyword(s):  
Design Optimization ◽  
Optimum Design ◽  
Membership Function ◽  
Input Data ◽  
Performance Measure ◽  
Sufficient Data ◽  
Design Problems ◽  
Fuzzy Variables ◽  
Fuzzy Input ◽  
The Membership Function

The reliability based design optimization (RBDO) method is prevailing in stochastic structural design optimization by assuming the amount of input data is sufficient enough to create accurate input statistical distribution. If the sufficient input data cannot be generated due to limitations in technical and/or facility resources, the possibility-based design optimization (PBDO) method can be used to obtain reliable designs by utilizing membership functions for epistemic uncertainties. For RBDO, the performance measure approach (PMA) is well established and accepted by many investigators. It is found that the same PMA is a very much desirable approach also for the PBDO problems. In many industry design problems, we have to deal with uncertainties with sufficient data and uncertainties with insufficient data simultaneously. For these design problems, it is not desirable to use RBDO since it could lead to an unreliable optimum design. This paper proposes to use PBDO for design optimization for such problems. In order to treat uncertainties as fuzzy variables, several methods for membership function generation are proposed. As less detailed information is available for the input data, the membership function that provides more conservative optimum design should be selected. For uncertainties with sufficient data, the membership function that yields the least conservative optimum design is proposed by using the possibility-probability consistency theory and the least conservative condition. The proposed approach for design problems with mixed type input uncertainties is applied to some example problems to demonstrate feasibility of the approach. It is shown that the proposed approach provides conservative optimum design.

scholarly journals Controllable Effective Threshold Based Fusion Coverage Algorithm in Mobile Sensor Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Yong Lu ◽  
Na Sun
Keyword(s):  
Sensor Networks ◽  
Membership Function ◽  
Network Lifetime ◽  
Physical Parameters ◽  
Network Coverage ◽  
Target Node ◽  
Effective Threshold ◽  
Coverage Quality ◽  
Monitoring Area ◽  
The Membership Function

The coverage quality and network lifetime are two key parameters in the research of sensor networks. The coverage quality shows direct influences on the network lifetime. Meanwhile, it is influenced by many other factors such as physical parameters and environmental parameters. To reveal the connection between the coverage quality and the parameters of target node concerned, a fusion coverage algorithm with controllable effective threshold is proposed based on the sensing probability model. We give the model for the membership function of coverage intensity as well as the prediction model for the fusion operator. The range for the effective threshold is presented according to the membership function model. Meanwhile, the maximum of the effective coverage intensity for the target nodes within the monitoring area is derived. The derivation of the maximal fusion coverage intensity is elaborated utilizing a processing function on the distances from the target node to the ones in the sensor node set. Furthermore, we investigate different network properties within the monitoring area such as network coverage quality, the dynamic change of parameters, and the network lifetime, based on the probability theory and the geometric theory. Finally, we present numerical simulations to verify the performances of our algorithm. It is shown under different settings that, compared with the demand coverage quality, the proposed algorithm could improve the network coverage quality by 15.66% on average. The simulation experiment results show that our proposed algorithm has an average improvement by 10.12% and 13.23% in terms of the performances on network coverage quality and network lifetime, respectively. The research results are enlightening to the edge coverage and nonlinear coverage problems within the monitoring area.

scholarly journals Mathematical modeling of transformable space structure dynamics

2019 ◽  
Vol 221 ◽  
pp. 01018 ◽  
Author(s):  
Vladimir Zimin ◽  
Alexey Krylov ◽  
Sergey Churilin ◽  
Zikun Zhang
Keyword(s):  
Strain State ◽  
Element Model ◽  
Space Structure ◽  
Space Structures ◽  
Elastic Rod ◽  
Stress Strain ◽  
Large Space ◽  
Structure Dynamics ◽  
Stress Strain State ◽  
Large Space Structure

Today large space structures are in focus of attention of engineers and designers of rocket and space equipment. In ground-based experiments, it is not always possible to carry out complex tests of large space structure functionality. Therefore, the development of mathematical models describing properly the transformable structure dynamics when they opened from the densely packed transport state to the operating position in the orbit becomes very important. To determine the stress-strain state of the frame elements when it is unfolding the shape of the framework is taken at the moments when relative velocities of the adjacent sections are maximal. Supposed, that at these moments the frame elements are getting on the stops limiting their relative angular displacements, and the structure behaves as an elastic rod with specified characteristics. Numerical analysis of the stress-strain state in the framework is carried out by means of a finite element model. Therefore, the represented mathematical model can be effectively used to predict the functional suitability of such transformable space structures already on the early stages of their development.

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