Practical Method for Determining All the Minimum Solutions of Fuzzy Matrix Equation and Transitive Closure of Fuzzy Relation

In this paper,the new theory frame and practical methhod for determining all the minimum solutions of Fuzzy matrix equation and transitive closure of Fuzzy relation is described,and it has been carried out on the miero-computer quickly and accurately.

Minimum Cycle of Row Vector of a Generalized Circulant Fuzzy Matrix

In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some properties of the idempotent elements of the semigroup of generalized circulant Fuzzy matrixes in connection with minimum cycle of row vector.

Fuzzy Soft Expert Matrix Theory and Its Application in Decision-Making

A unique mathematical strategy for dealing with uncertainty is fuzzy soft set theory. In this paper, we propose fuzzy soft expert matrices and describe numerous varieties of fuzzy soft expert matrices, as well as specific operations. Finally, by applying these matrices to decision-making scenarios, we widen our methodology.

Fuzzy Consistent Matrix and Its Application

This paper presents a kind of fuzzy consistent matrix and introduces its application in analytic hierarchy process and adaptive fuzzy reasoning.

The construction and combined operation for fuzzy consistent matrixes

Fuzziness is one of the general characteristics of human thinking and objective things. Introducing fuzzy techniques into decision-making yields very good results. Fuzzy consistent matrix has many excellent characteristics, especially cen- ter-division transitivity conforming to the reality of the human thinking process in decision-making. This paper presents a new approach for creating fuzzy consistent matrix from mutual supplementary matrix in fuzzy decision-making. At the same time, based on the distance between individual fuzzy consistent matrix and average fuzzy consistent matrix, a kind of combined opera- tion for several fuzzy consistent matrixes is presented which reflects most opinions of experienced experts. Finally, a practical example shows its flexibility and practicability further.

Detection of Fabric Defects with Fuzzy Label Co-occurrence Matrix Set

Co-occurrence matrices have been successfully applied in texture classification and segmentation.However,they have poor computation performance in real-time application.In this paper,the efficient co-occurrence matrix solution for defect detection is focused on,and a method of Fuzzy Label Co-occurrence Matrix (FLCM) set is proposed.In this method,all gray levels are supposed to subject to some fuzzy sets called fuzzy tonal sets and three defective features are defined.Features of FLCM set with various parameters are combined for the final judgment.Unlike many methods,image acquired for learning hasn't to be entirely free of defects.It is shown that the method produces high accuracy and can be a competent candidate for plain colour fabric defect detection.

Solution and Application of the Matrix Equation Ax=b

In this paper,we first give the solution concept of the fuzzy matrix equation =. Secondly,we discuss the property of the solution and give the method of solving the fuzzy matrix equation A=. Finally,we present an application of solving fuzzy matrix equation A= to the fuzzy linear regression analysis,establish a new model of fuzzy linear regression,and introduce a new method of estimating parameters.

Fuzzy Clustering Method for Web User Based on Pages Classification

A new method for Web users fuzzy clustering based on analysis of user interest characteristic is proposed in this article. The method first defines page fuzzy categories according to the links on the index page of the site, then computes fuzzy degree of cross page through aggregating on data of Web log. After that, by using fuzzy comprehensive evaluation method, the method constructs user interest vectors according to page viewing times and frequency of hits, and derives the fuzzy similarity matrix from the interest vectors for the Web users. Finally, it gets the clustering result through the fuzzy clustering method. The experimental results show the effectiveness of the method. Key words Web log mining - fuzzy similarity matrix - fuzzy comprehensive evaluation - fuzzy clustering CLC number TP18 - TP311 - TP391 Foundation item: Supported by the Natural Science Foundation of Heilongjiang Province of China (F0304)Biography: ZHAN Li-qiang (1966-), male, Lecturer, Ph. D. research direction: the theory methods of data mining and theory of database.

A Fuzzy Logic-Based Method for Risk Assessment of Bridges during Construction

There are many potential sources of risks which may cause bridge failures and result in numerous economic and human losses during the construction of bridges. Therefore,risk assessment for bridges during construction should be taken rigorously to avert bridge failures and casualties. This article presents a fuzzy logic-based method which integrates the fuzzy analytical hierarchy process( FAHP) method based on a 3-point scale,fuzzy logic,and fuzzy set theory into a single synthetic method. In this method,the FAHP method based on a 3-point scale was used to identify and rank diverse risk factors,and fuzzy logic and fuzzy set theory were used to process inaccurate datasets including non-statistical information. After the concept and procedure of the FAHP method based on a 3-point scale were demonstrated,the proposed fuzzy logic-based method was used to perform risk assessment on the Aizhai Suspension Bridge with a main span length of1 176 m in China. The results show that the proposed method can more effectively carry out risk assessment of bridges during construction.

Fuzzy Methodology for Taxonomy and Knowledge Base Design

This paper summarizes the research results dealing with washer and nut taxonomy and knowledge base design, making the use of fuzzy methodology. In particular, the theory of fuzzy membership functions, similarity matrices, and the operation of fuzzy inference play important roles.A realistic set of 25 washers and nuts are employed to conduct extensive experiments and simulations.The investigation includes a complete demonstration of engineering design. The results obtained from this feasibility study are very encouraging indeed because they represent the lower bound with respect to performance, namely correctrecognition rate, of what fuzzy methodology can do. This lower bound shows high recognition rate even with noisy input patterns, robustness in terms of noise tolerance, and simplicity in hardware implementation. Possible future works are suggested in the conclusion.

New judging model of fuzzy cluster optimal dividing based on rough sets theory

To investigate the judging problem of optimal dividing matrix among several fuzzy dividing matrices in fuzzy dividing space, correspondingly, which is determined by the various choices of cluster samples in the totality sample space, two algorithms are proposed on the basis of the data analysis method in rough sets theory： information system discrete algorithm （algorithm 1） and samples representatives judging algorithm （algorithm 2）. On the principle of the farthest distance, algorithm 1 transforms continuous data into discrete form which could be transacted by rough sets theory. Taking the approximate precision as a criterion, algorithm 2 chooses the sample space with a good representative. Hence, the clustering sample set in inducing and computing optimal dividing matrix can be achieved. Several theorems are proposed to provide strict theoretic foundations for the execution of the algorithm model. An applied example based on the new algorithm model is given, whose result verifies the feasibility of this new algorithm model.

Mixed Least Square Method for Priority of Complementary Judgement Matrix and Its Algorithm

Based on the concept of multiplicative fuzzy consistent complementary judgement matrix, the mixed least square method （MLSM） for priority of complementary judgement matrix is proposed and proved. Then, the corresponding convergent iterative algorithm is given and its convergence is proved. Finally, some main properties of the developed priority method, such as rank preservation under strong condition, etc., ate introduced. The theoretical analyses show that the MLSM can sufficiently reflect the preference information of the decision maker, and is easy to realize on a computer.

A New Definition of Intuitionistic Fuzzy Similarity Degree

As far as the problem of intuitionistic fuzzy cluster analysis is concerned, this paper proposes a new formula of similarity degree with attribute weight of each index. We conduct a fuzzy cluster analysis based on the new intuitionistic fuzzy similarity matrix, which is constructed via this new weighted similarity degree method and can be transformed into a fuzzy similarity matrix. Moreover, an example is given to demonstrate the feasibility and validity of this method.

The application of fuzzy equivalence relation based on the quotient space in cluster analysis

A fuzzy clustering analysis model based on the quotient space is proposed. Firstly, the conversion from coarse to fine granularity and the hierarchical structure are used to reduce the multidimensional samples. Secondly, the fuzzy compatibility relation matrix of the model is converted into fuzzy equivalence relation matrix. Finally, the diagram of clustering genealogy is generated according to the fuzzy equivalence relation matrix, which enables the dynamic selection of different thresholds to effectively solve the problem of cluster analysis of the samples with multi-dimensional attributes.

Method to Determine Depositional Range of Sediment Transported from Multiple Sources in Water Area

- The sediment from different sources have different content of the characteristic elements. According to the fuzzy mathematical theory, corresponding calculation and cluster analysis of each sediment sample are carried out, so the main courses of sediment transport in water area can be obtained. The characteristics of sediment from different sources are analysed. It is found that the sediment deposited of certain point in water area is due to the sources' contributions which can be calculated by the formula derived in this paper. Based on the distribution of the contribution values, the depositional range of sediment from each source can be determined. The depositional range in Huangmao Bay is determined as an example.

Applying Possibility Degree Method for Ranking Interval Numbers to Partnership Selection

A new interval number ranking approach is applied for assessment of priorities of the alternative partners, where the attribute values are given out as interval numbers while the weight of each criterion is still exact numerical value pattern. After aggregating with the weighted arithmetic averaging operator, the result is still in the form of interval number. To achieve the priorities of alternative partners we take the possibility method for ranking interval numbers into account which could derive priorities from inconsistent attribute values, thus eliminating the adjustment to the inconsistent attribute values. Moreover, this method is very simple and needs less calculation. An illustrative example is given out to demonstrate this smart method.

Improved Fuzzification Method for Multi-Objective Decision-Making and Its Application in Evaluation of Highway Planning

A new fuzzification method for multi-objective decision-making and selective sorting is proposed on the basis of the fuzzy consistent relation, and the specific algorithm is presented. The method is applied to the evaluation of highway planning of Zhanjiang city. To decrease the subjectivity in the process of decision-making, the LOWA operator is introduced, and a discussion on how to select appropriate weights involved in multi-objective sorting is made. It is concluded that it is feasible to apply the fuzzy consistent relation to multi-objective decision-making analysis, and the improved fuzzication method is workable.

THE CLASSIFICATION OF THE SURROUNDINGS OF COAL MINING ROADWAYS

This paper introduces the calculation of the deformation of the surroundings of roadways and the division of surroundings into 5 levels by means of fuzzy integral assess matrix, which serves as the scientific basis for selecting supporting pattern of roadways and determining the parameters of support.

Stable fuzzy controllers via LMI approach for non-linear systems described by type-2 T-S fuzzy model

Purpose-The purpose of this paper is to stabilize the type-2 Takagi-Sugeno(T-S)fuzzy systems with the sufficient and guaranteed stability conditions.The given conditions efficaciously handle parameter uncertainties by the upper and lower membership functions of the type-2 fuzzy sets(FSs).Design/methodology/approach-This paper reports on a relevant study of stable fuzzy controllers and type-2 T-S fuzzy systems and reported that the synthesis of controller for nonlinear systems described by the type-2 T-S fuzzy model is a key problem and it can be resolve to convex problems via linear matrix inequalities(LMIs).Findings-The multigain fuzzy controllers are established to improve the solvability of the stability conditions,and the authors design multigain fuzzy controllers which have extensive information of upper and lower membership grades.Consequently,the authors derive the traditional stability condition in terms of LMIs.One simulation examples illustrate the effectiveness and robustness of the derived stabilization conditions.Originality/value-The uncertain MIMO nonlinear system described by Type-2 Takagi-Sugeno(T-S)fuzzy model,and successively LMI approach used to determine the system stability conditions.The proposed control approach will give superior fault-tolerant control permanence under the actuator fault[partial loss of effectiveness(LOE)].Also the controller robust against the unmeasurable process disturbances.Additionally,the statistical z-test are carried out to validate the proposed control approach against the control approach proposed by Himanshukumar and Vipul(2019a).