Fuzzy Matrix Research Articles

Teaching practice of environmental art design specialty based on fuzzy algorithm

This paper first introduces the relevant content of fuzzy theory system and expounds the relevant knowledge of fuzzy comprehensive evaluation in fuzzy theory. In this paper, an evaluation system for the teaching of environmental art design specialty based on the integration of production, teaching and research is established to provide scientific basis for the exploration and control of the teaching mode, and a fuzzy comprehensive evaluation model is established on the basis of the index system. Through the methods of literature retrieval, real data analysis and expert interview, 14 factors influencing the level of classroom teaching were collected, and questionnaires were distributed to teachers to collect the factor weight data, and these data were sorted out and calculated to obtain the weight indicators at all levels. Through the collection of online teaching evaluation data, the fuzzy evaluation matrix of each level index is calculated, and the matrix is combined with the corresponding weight vector to establish the fuzzy comprehensive evaluation model. Finally, the teaching evaluation results of the integrated mode of production, teaching and research are as follows: 74.8% are excellent, 12.6% are good, 7.1% are medium, and only 5.5% are poor. Through the above results, it can be concluded that the teaching effect of the integration mode of production, teaching and research is excellent.

Multiple criteria based decision making using modified VIKOR - fuzzy integration approach

Recent year development in each field and area progresses rapidly. For one particular product or service, people have multiple alternative. However, to choose best alternative is most difficult task that most of person facing. VIKOR method is most used approach for choosing best alternative based on different criteria but legging in precision. In this paper, we propose modifier VIKOR with Fuzzy logic integration approach that deal with multiple criteria while making decision as well as integratestriangular fuzzy numbers (TFN) for computing criteria values and weight importance in the processing selecting best alternative. Firstly, positive best points and negative best points were demarcated in a triangular fuzzy number evaluation matrix. Secondly, we analyze the requirements and properties of the VIKOR-based triangular fuzzy number operation rule. Thirdly, an extension of VIKOR method was proposed for comprehensive evaluation of schemes to reduce the information loss arising from defuzzification of triangular fuzzy numbers; Finally, an example demonstrate the efficiency and viability of the method. In conclusion, the proposed method solves the difficulties that subtractive computation between two triple numbers violate the arithmetic regulation, and propose a reasonable procedure according to decision making problems with triple numbers.

Energy Efficiency Assessment of Heat Insulation Building Products: Fuzzy-Probabilistic Approach

Abstract The expediency of using heat-insulating construction products from a straw at the erecting of energy-efficient envelope constructions is considered in the paper. The hierarchical model in the form of an inference tree of the factors influencing the target function – reliability of energy efficiency of heat-insulating building products made of straw has resulted. A fuzzy matrix of knowledge is proposed which reflects the influence of thermophysical, physic-mechanical and durability parameters on the target function. The hierarchical connections between classified factors proceeded by apparatus of fuzzy logic and linguistic variables. A system of fuzzy logical equations which describes linguistic expressions of input variables according to the corresponding terms is proposed. In the research the expressions which describe the objective function – reliability of energy efficiency of heat-insulating construction products made of straw were obtained. It was made with the of membership functions following linguistic variables, by taking into account both qualitative as well as quantitative factors of influence. Represented in the paper model can be used as the design and engineering tool for the prediction of thermal performance of any multilayered wall assembly at the design stage of the project to assess complex energy efficiency parameters, which could be applied in practice during the decision-making process.

An application of circulant fuzzy matrices for finding the disease in animals

An application of circulant fuzzy matrices for finding the disease in animals

A note on det-norm of circulant fuzzy matrices

A note on det-norm of circulant fuzzy matrices

A game theoretic approach to solve multiple group decision making problems with interval-valued intuitionistic fuzzy decision matrices

ABSTRACT The objective of this paper is to develop a two person zero-sum game theoretic solution approach for multiple attribute group decision making (MAGDM) problems under interval-valued intuitionistic fuzzy environment. In this way, a new order function is introduced to defuzzify the interval-valued intuitionistic fuzzy numbers (IVIFNs) and discuss its properties. In complicated and uncertain group decision-making problems, decision makers face a problem for assessing the group weights for alternatives and attributes. In this paper, the weights of present MAGDM problem with interval-valued intuitionistic fuzzy decision matrices (matrices in which entries are represented by IVIFNs) are calculated by converting it into a traditional two person zero-sum game problem. Then, the expected score for each alternative is calculated using the optimal solution of this game problem. On the basis of the calculated expected score values, the prespecified alternatives are ranked in order to find the best alternative. The validity and applicability of the developed approach are given by a numerical example.

A fuzzy matrix factor recommendation method with forgetting function and user features

In recent years, a variety of recommendation algorithms have been proposed. However, there are still some issues such as cold start, sparsity and timeliness. On the basis of traditional collaborative filtering, matrix decomposition technologies can greatly reduce the computational complexity and address the issues of cold start and sparsity. Based on forgetting functions and users’ multi-attribute features, in this paper, a fuzzy matrix decomposition and trace norm minimization method is proposed. Firstly, a forgetting function is incorporated into the historical scores, which makes existing scoring information more efficient. Then the user features are applied to find trusted users, which will give some valuable suggestions and possible scores to target items. The user features are also applied to list the relationships among users. In this paper, the relations between users and items are represented by the scores between them. Secondly, both time and feature information is integrated into the proposed optimization model. Then a fuzzy matrix decomposition and trace norm minimization model is established and further solved by our proposed algorithm to give better recommendations. Moreover, the convergence of the proposed algorithm is also proved in theoretically. Finally, we investigate the empirical recoverability properties of our model and analyze its advantages over classical norm minimization models. Extensive experimental results on synthetic and real-world data sets verify the efficiency and effectiveness of our method compared with the state-of-the-art algorithms.

Study on mechanism and application of water resources system adaptability under changing environment

Abstract The water resources system is in a vulnerable situation because of the influence of climate change and the changing environment. The adaptation mechanism was discussed through the analysis of the process of passive response, adaptation and even active adjustment of water resources system under changing environment. The adaptability of the water resources system can be described as natural resilience (NR) of natural system and artificial adaptation (AA) social (artificial) system. The natural resilience indexes were identified and analyzed from the aspects of water quantity, water quality and water ecology. The artificial adaptation indexes were identified and analyzed from the aspects of resource, eco-environment, socio-economic and technical factors. On this basis, the index system was constructed in accord with process mechanism of water resources system adaptability. Besides, to address the two-dimension factors of water resources system adaptability, a method of system analysis based on connection numbers–fuzzy risk matrix was proposed based on the theory of risk matrix. The synthesis interval [Apess, Aopt] of water resources system adaptability is obtained, by defining the pessimistic criterion when two-dimension factors meet the evaluation standard at the same time, and the optimistic criterion when either of the two-dimension factors meets evaluation standard. Finally, the case study in the Huaihe River basin in China was carried out. The results show that the adaptability level of water resources system in the Huaihe River basin expressed fluctuating uprising tendency in 2006–2015. The adaptability level is the lowest [1.856, 2.625] in 2009, the highest [2.500, 3.536] in 2015.

A hierarchical fuzzy comprehensive evaluation algorithm for running states of an electromechanical system

A fuzzy hierarchical comprehensive evaluation algorithm including fuzzy matrix and comprehensive evaluation matrix calculation thought is proposed to accurately evaluate the running state of an electromechanical system. The analytic hierarchy process is included in the algorithm, which calculates the state of each subsystem from top to bottom and the states are used as the evaluation factor of the upper system. The idea of degradation degrees is introduced to standardize the indicators. The paper carried out the simulation experiment for the electromechanical system with a model number of JKMD-4 × 4(Z). The experimental results show that the established state evaluation model can accurately judge the operation state of the system with not too much data.

Some Operations Over Interval-Valued Fuzzy Matrices

The objective of this paper is to apply the concept of fuzzy matrices to interval-valued fuzzy matrices. In this paper, we introduce the Hamacher operations of interval-valued fuzzy matrices and prove some desirable properties of these operations, such as commutativity, idempotency and monotonicity. Further, we prove De Morgan's laws over complement for these operations . Then we constructe the scalar multiplication (n._h A) and exponentiation (A^(∧_h n)) operations of interval-valued fuzzy matrices and investigates the algebraic properties.

Inconsistent LR Fuzzy Matrix Equation

In this paper, the inconsistent LR fuzzy matrix equation A X ˜ = B ˜ is proposed and discussed. Firstly, the LR fuzzy matrix equation is transformed into two crisp matrix equations in which one determines the mean value and the other determines the left and right extends of fuzzy approximate solution. Secondly, the approximate solution of the LR fuzzy matrix equation is obtained by solving two crisp matrix equations according to the generalized inverse of crisp matrix theory. Then, sufficient conditions for the existence of strong LR fuzzy approximate solution are given. Finally, some numerical examples are given to illustrate our proposed method.

Analysing the Interrelationship among Supply Chain Knowledge Flow Barriers: A DEISMI Approach

Organisations are being aware that it is essential to utilise knowledge to maintain a position in the competitive market. Many significant factors create hindrances to knowledge flow in the supply chain. These factors are known as Supply Chain Knowledge Flow Barriers (SCKFBs). Therefore, most organisations wish to understand how different SCKFBs affect supply chain progress. This research aims to suggest a hybrid three-stage framework of Fuzzy Delphi (FD)–Interpretive Structural Modelling (ISM)–Fuzzy Matrice d’Impacts Croisés Multiplication Appliquée á un Classement (FMICMAC) methodology, combine abbreviated as the fuzzy DEISMI for investigating SCKFBs. This research identifies 26 SCKFBs through literature search and opinion from the experts. FD is used to finalise 15 significant barriers to knowledge flow in the supply chain. Further, ISM methodology helps to develop contextual relationships and a hierarchical model between these significant barriers. The evolved hierarchical model presents interrelationships and interdependencies among the identified SCKFBs. The FMICMAC is applied to identify the driving power and dependence power among SCKFBs. This study shows SCKFBs who have high value of driving power and low value of dependence power have strategic importance in supply chain development. These barriers are at the base of the hierarchical model, and policymakers should give significant consideration towards these SCKFBs.

SYSTEMATIC METHOD FOR MONITORING AND EARLY-WARNING OF GARDEN HERITAGE ONTOLOGY USED IN THE SUZHOU CLASSICAL GARDEN HERITAGE

Taking garden heritage ontologies as the object, this paper explores monitoring and early-warning methods of heritage based on fuzzy cluster analysis. A monitoring and early-warning system for garden heritage ontologies is designed and consists of monitoring indexes, a monitoring program, monitoring data collection, application of an early-warning grading evaluation model and conclusion of early-warning grading. Taking the Suzhou classical garden heritage as an example, it can be concluded that the systematic method can integrate various qualitative and quantitative index values and collectively reflect the overall state of garden heritage ontologies as well as match a heritage monitoring ontology with an early warning grade by calculating the data similarity matrix, membership matrix, fuzzy similarity matrix, fuzzy equivalent matrix and cut matrix. Five kinds of heritage ontologies with a total of twenty-seven heritage monitoring indicators are applied in the model and then be matched with MATLAB software to obtain accurate early-warning results. When types of heritage ontology need to be expanded, the heritage is further refined, or the heritage is more comprehensive, this method is applicable.

On Optimal and Asymptotic Properties of a Fuzzy L2 Estimator

A fuzzy least squares estimator in the multiple with fuzzy-input–fuzzy-output linear regression model is considered. The paper provides a formula for the L2 estimator of the fuzzy regression model. This paper proposes several operations for fuzzy numbers and fuzzy matrices with fuzzy components and discussed some algebraic properties that are needed to use for proving theorems. Using the proposed operations, the formula for the variance, provided and this paper, proves that the estimators have several important optimal properties and asymptotic properties: they are Best Linear Unbiased Estimator (BLUE), asymptotic normality and strong consistency. The confidence regions of the coefficient parameters and the asymptotic relative efficiency (ARE) are also discussed. In addition, several examples are provided including a Monte Carlo simulation study showing the validity of the proposed theorems.

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

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.

Orderings on Generalized Regular Interval Valued Fuzzy Matrices

In this paper, a special type of ordering for k - regular Interval Valued Fuzzy Matrix (IVFM) is introduced as a generalization of the minus partial ordering for regular fuzzy matrices. A set of equivalent conditions for a pair of k – regular IVFM to be under this ordering are obtained. We exhibit that this ordering is preserved under similarity relation.

The invention of new sequences through classifying and counting fuzzy matrices

The novelty of this paper is to construct several explicit formulas for the number of distinct fuzzy matrices of a finite order which leads us to invent new integer sequences and helps to develop fuzzy subgroups of some finite groups of matrices. In order to achieve the sequences, we analyze the behavioral study of a natural equivalence relation on the set of all fuzzy matrices of a given order. In addition, this paper derives some important relevant results by enumerating non-equivalent class of fuzzy matrices. We achieve these results by incorporating the notion of $$k$$ -level fuzzy matrices, $$\alpha$$ -cuts and chains.

Investigating additive manufacturing implementation factors using integrated ISM-MICMAC approach

PurposeThe purpose of this paper is to identify various factors influencing additive manufacturing (AM) implementation from operational performance in the Indian manufacturing sector and to establish the hierarchical relationship among them.Design/methodology/approachThe methodology includes three phases, namely, identification of factors through systematic literature review (SLR), interviews with experts to capture industry perspective of AM implementation factors and to develop the hierarchical model and classify it by deriving the interrelationship between the factors using interpretive structural modeling (ISM), followed with the fuzzy Matrice d’Impacts Croisés Multiplication Appliqués à un Classement (MICMAC) analysis.FindingsThis research has identified 14 key factors that influence the successful AM implementation in the Indian manufacturing sector. Based on the analysis, top management commitment is an essential factor with high driving power, which exaggerates other factors. Factors, namely, manufacturing flexibility, operational excellence and firm competitiveness are placed at the top level of the model, which indicates that they have less driving power and organizations need to focus on those factors after implementing the bottom-level factors.Research limitations/implicationsAdditional factors may be considered, which are important for AM implementation from different industry contexts. The variations from different industry contexts and geographical locations can foster the theoretical robustness of the model.Practical implicationsThe proposed ISM model sets the directions for business managers in planning the operational strategies for addressing AM implementation issues in the Indian manufacturing sector. Also, competitive strategies may be framed by organizations based on the driving and dependence power of AM implementation factors.Originality/valueThis paper contributes by identification of AM implementation factors based on in-depth literature review as per SLR methodology and validation of these factors from a variety of industries and developing hierarchical model by integrative ISM-MICMAC approach.

Application of deep learning and cloud data platform in college teaching quality evaluation

In this paper, the author introduces the theory of fuzzy mathematics into the evaluation of higher education. By determining the set of evaluation factors and comments, the author constructs the relevant mathematical model and processes the data, thus turning the evaluation problem into the multiplication problem of the fuzzy matrix. Deep learning is a very active branch of machine learning research in recent years. By increasing the depth and breadth of the model, i.e. increasing the number of operations from the input end to the output end and the number of channels of the model, the scale of parameters of the model is increased, so that the model has the ability to express complex functions. It is appropriate to use deep learning in teaching quality evaluation. The simulation results show that the deep learning model is very effective in dealing with data diversity and extracting complex implicit rules. It can effectively model experts’ professional knowledge and experience. Deep neural network has powerful expressive ability, and can effectively extract the deep-seated laws affecting the teaching quality. It can be used as an assistant technology for the evaluation of teaching quality in Colleges.

Solving Two Coupled Fuzzy Sylvester Matrix Equations Using Iterative Least-squares Solutions

ABSTRACT In this paper, five iterative methods for solving two coupled fuzzy Sylvester matrix equations are considered. The two coupled fuzzy Sylvester matrix equations are expressed by using the generalized inverse of the coefficient matrix, then iterative solutions are constructed by applying the hierarchical identification principle and by using the block-matrix inner product (the star product for short). A proposed modification to this algorithm to solve the first coupled fuzzy Sylvester matrix equations is suggested. This proposed modification is compared with the first algorithm where our modification exhibits fast convergence behavior. Also, we suggested two least-squares iterative algorithm by applying a hierarchical identification principle to solve the two coupled fuzzy Sylvester matrix equations. The proposed methods are illustrated by numerical examples.