Fuzzy Grade Research Articles

Characteristics of fuzzy synthetic decision methods for measuring student achievement

Traditional method of student achievement evaluation only use arithmetic mean and convert them to rankings, but this does not provide further explanatory information to proceed with more reasonable evaluations, decisions, and interpretations for the learning achievements of students, and provide a fair and appropriate consideration of the evaluation results. Therefore, this study attempts to introduce four types of fuzzy synthetic decision methods in actual scores for evaluating and ranking student’s academic achievement. Using the synthetic decision method of fuzzy theory, the four types of composite operations are used in conjunction with the membership function, and finally fuzzy means are used to express the diverse evaluation results of students. This study uses junior high school first year students in central Taiwan as research subjects, selecting the actual mid-term exam results of the gifted class and general class as research data. The fuzzy synthetic decision method is applied through four types of composite operations, proposing a ranking system that is more diverse and precise than the traditional average method. Finally, this study proposes the characteristics of the four types of fuzzy composite operations, considering the most suitable composite operations for classes with different characteristics. Results of this study can be used as a reference for educators in the field and future researchers. The contribution of this study is to provide the fuzzy grade calculation methods that are suited to students with different characteristics, in order to achieve diverse and precise ranking evaluations.

About the fuzzy grade of the direct product of two hypergroupoids

The aim of this paper is the study of the sequence of join spacesand fuzzy subsets associated with a hypergroupoid. In thispaper we give some properties of the membership function$widetildemu_{otimes}$ corresponding to the direct pro-duct oftwo hypergroupoids and we determine the fuzzy grade of thehypergroupoid $langle Htimes H, otimesrangle$ in a particularcase.

Research on Fault Recognition for Centrifugal Compressor Based on Fuzzy Gray Relational Grade

In practical centrifugal compressor fault diagnosis, it is very difficult to improve the fault recognition rate, especially when the sample sizes are small. To solve this problem, a new fault recognition method based on fuzzy gray relational grade was proposed. Firstly, according to fuzzy set theory, the fuzzy relation coefficient (FRC), fuzzy relation degree (FRD) and fuzzy relative weights (FRW) of all fault features were calculated. Secondly, the gray system theory was used to obtain the gray relational coefficients (GRC). Thirdly, by combining FRW and GRC, two fuzzy gray relation grades (FGRG) were presented, which is the Hamming distance-based fuzzy gray relation grade (HD-FGRG) and the Euclidean distance-based fuzzy gray relation grade (ED-FGRG), respectively. Finally, the fault recognition results were obtained by using the max membership degree principle. The centrifugal compressor fault diagnosis results show that the ED-FGRG method is more effective and accurate than traditional gray relational analysis (T-GRA) method, the weighted gray relational analysis (W-GRA) method, and the entropy weight-based gray relational analysis (EW-GRA) method and the HD-FGRG method.

Fuzzy Grading for Content Management in E-Learning Systems

The authors are motivated by the concept of refinement in elearning systems so as to provide more support for the e-learners. A technique has been proposed for providing a customized knowledge in the form of graphics, text, analogy etc by grading mechanism using fuzzy techniques through which the knowledge level of user or learner can be determined and enhanced. It is impossible to satisfy every learner with a single example, so there arises the need of a system which would take feedback from the learner and dynamically customize the learning materials as per the understanding level of the end-user or learner. The content Management Tool (CMT) of the proposed framework of Expert E- Tutoring system plays a vital role for extracting the required contents from content repository by making use of fuzzy techniques. The proposed framework may also keep track of users’ learning capability based on fuzzy grading on a given topic, which helps to refine the e-learning content appropriately for the use of a learner .

Atanassov’s intuitionistic fuzzy grade of hypergroups

This paper deals with connections between hypergroupoids and Atanassov’s intuitionistic fuzzy sets. First a sequence of join spaces is associated with a hypergroupoid H; the length of the sequence is called Atanassov’s intuitionistic fuzzy grade of H. Second, a theorem about the existence of a hypergroup with Atanassov’s intuitionistic fuzzy grade equal to n is proved. Furthermore, some properties of the complete hypergroups in connection with this argument are presented and discussed.

Objective Evaluation of Textile Fabric Appearance. Part 2: SET Opti-grade Tester, Grading Algorithms, and Testing

This is the second paper in a series devoted to the problem of textile fabric quality evaluation. The statistical evidence, basic principles of objective evaluation, and different approaches for the grading procedure are described in Part 1. The second part of the paper contains implementation of the results for all types of test methods and testing results for the SET Opti-Grade device that were elaborated on the basis of this research. High level correspondence between the expert and the SET machine grades has shown the effectiveness of the conception that is based on an analysis of the fabric profile and probability neural networks for hologram/picture, pills, and fuzzy grading. Furthermore, it has shown that the threshold approach has good results for hairiness and snagging grading.

A fuzzy neural network with fuzzy impact grades

Fuzzy rule derivation is often difficult and time-consuming, and requires expert knowledge. This creates a common bottleneck in fuzzy system design. In order to solve this problem, many fuzzy systems that automatically generate fuzzy rules from numerical data have been proposed. In this paper, we propose a fuzzy neural network based on mutual subsethood (MSBFNN) and its fuzzy rule identification algorithms. In our approach, fuzzy rules are described by different fuzzy sets. For each fuzzy set representing a fuzzy rule, the universe of discourse is defined as the summation of weighted membership grades of input linguistic terms that associate with the given fuzzy rule. In this manner, MSBFNN fully considers the contribution of input variables to the joint firing strength of fuzzy rules. Afterwards, the proposed fuzzy neural network quantifies the impacts of fuzzy rules on the consequent parts by fuzzy connections based on mutual subsethood. Furthermore, to enhance the knowledge representation and interpretation of the rules, a linear transformation from consequent parts to output is incorporated into MSBFNN so that higher accuracy can be achieved. In the parameter identification phase, the backpropagation algorithm is employed, and proper linear transformation is also determined dynamically. To demonstrate the capability of the MSBFNN, simulations in different areas including classification, regression and time series prediction are conducted. The proposed MSBFNN shows encouraging performance when benchmarked against other models.

Evaluating students’ answerscripts based on interval-valued fuzzy grade sheets

In this paper, we propose two new methods for evaluating students’ answerscripts based on interval-valued fuzzy grade sheets. The marks awarded to the answers in the students’ answerscripts are represented by interval-valued fuzzy sets. Each element in the universe of discourse belonging to an interval-valued fuzzy set is represented by an interval between zero and one. The degree of similarity between an interval-valued fuzzy mark and a standard interval-valued fuzzy set is calculated by a similarity function. An index of optimism λ determined by the evaluator is used to indicate the degree of optimism of the evaluator, where λ∈[0,1]. The experimental results show that the proposed methods are more stable than Biswas’s method for students’ answerscripts evaluation. They can evaluate students’ answerscripts in a more flexible and more intelligent manner.

On the fuzzy grade of hypergroups

In some previous papers, the second author studied the possibility to associate a sequence of membership functions and of join spaces with a hypergroupoid H. Here we establish a sufficient condition in order to have two consecutive associated join spaces i H and i + 1 H non-isomorphic. We find also a property of the quotient hypergroup determined by the join space i H and the relation associated with the fuzzy set μ ˜ and finally, we determine a necessary and sufficient condition for the join space i H in order to be a reduced hypergroup.

Appraising the performance of high school teachers based on fuzzy number arithmetic operations

This paper presents a new method for appraising the performance of high school teachers based on fuzzy number arithmetic operations. It uses fuzzy numbers to represent fuzzy grades. The fuzzy weights of criteria are automatically generated from the opinions of evaluators. The simplified fuzzy number arithmetic operations are used for calculating the average of fuzzy numbers. It can appraise the performance of high school teachers in a more flexible and more intelligent manner.

NOTION OF FUZZY IC-BAGS

In the present paper, the author introduces the notion of fuzzy IC-bags and does some characterizations of them. The concepts of fuzzy base sets, base equivalent fuzzy IC-Bags, cardinally equispaced fuzzy IC-Bags, and cardinally equivalent fuzzy IC-Bags have been developed. The types of peak elements, and the concerned types of peak membership grades have been discussed. It is observed that the collection of any particular type of peak elements together with their membership grades actually form fuzzy bags. A set of operations on fuzzy IC-Bags have been defined and some propositions have been proved. We note that under the conditions of uncertainty, where the counts of objects are not fixed, then the interval counts can occur with different fuzzy membership grades for each particular object in the collection, and the framework for fuzzy IC-Bags provides us with the opportunity to justify and model the organized complexity as a part of the associated intolerance embedded in the subjective patterns.

Antenatal fetal risk assessment using a neurofuzzy technique.

This study defines an intelligent neurofuzzy system for antepartum fetal evaluation, The task is to investigate the Doppler ultrasound measurements of the umbilical artery (UA) and the cerebral artery (CA) to relate the health conditions of fetuses. We thus use the UA blood flow velocity waveforms [pulsality index, resistance index, and systolic/diastolic ratio] and the ratios of cerebral-umbilical resistance indices in terms of weeks. We then make a decision on the basis of a fuzzy-rule-based system combined with data-based learning strategies such as a radial basis function network and a multilayer perceptron for assessing the hypoxia suspicion. A fuzzy grade of membership is used for the evaluation of the seriousness of the situation of the fetus, and the diagnostic interpretations for doctors such as good, suspicious, and alarming conditions of fetus are derived.

Fuzzy set approach to the assessment of student-centered learning

Assessment of student learning is an important task in a teaching and learning process. It has a strong influence on students' approaches to learning and their outcomes. Development in tertiary education has shifted its emphasis from teacher-centered learning to student-centered learning. In a student-centered learning environment, criterion-referenced assessment techniques are often used in current education research and practice. However, it sometimes happens that the assessment criteria and their corresponding weights are solely determined by the lecturers in charge. This may reduce the interest of students' participation and lower the quality of their learning. This paper presents an integrated fuzzy set approach to assess the outcomes of student-centered learning. It uses fuzzy set principles to represent the imprecise concepts for subjective judgment and applies a fuzzy set method to determine the assessment criteria and their corresponding weights. Based on the commonly agreed assessment criteria, students' learning outcomes are evaluated on a fuzzy grade scale. The proposed fuzzy set approach incorporates students' opinions into assessment and allows them to have a better understanding on the assessment criteria. It aims at encouraging students to participate in the whole learning process and providing an open and fair environment for assessment.

Entropy-based operations on fuzzy sets

By using a fuzzy entropy approach, three sets of new generalized operators are presented. After a general discussion on fuzzy entropy, the concept of an elementary entropy function of a fuzzy set is introduced. Using this mapping, the generalized intersections and unions are defined as mappings that assign the least and the most fuzzy membership grade to each of the elements of the domain of the operators, respectively. It is shown that these operators can be constructed from the conventional min and max operations. Next, two modified sets of operations are introduced. The second part of the paper investigates the applicability of the new operators in fuzzy logic controllers. Simulations have been carried out so as to determine the effects of the operators on the performance of the fuzzy controllers. It is concluded that the first set of operators does not provide stable control, but the performance of the fuzzy controller can be improved by using the modified operations for a class of plants.

Multi‐scale classification of remotely sensed data by the maximization of fuzzy membership grades

Abstract Recent studies have shown that the optimal spatial resolution of remotely sensed data for the identification of scene elements is extremely variable depending on several factors. In particular, for the classification of each cover class using satellite sensor imagery there is generally an optimum aggregation level which is mainly related to the average size of the ground plots and to their internal homogeneity. In the present paper a methodology is presented for finding the relative optimum filtering size for the attribution of all pixels to some ground classes based on the maximization of fuzzy membership grades. Since these grades are indicative of the confidence of the pixel attribution to the classes, they can be used to select the best scale among differently filtered images. This hypothesis is investigated by means of a case study concerning a rugged, complex area in Central Italy sensed by bi‐temporal TM scenes. The results testify to the good performance of the approach which also shows p...

Fuzzy Grading System

The difficulties associated with translating a set of scores into letter-grades are discussed. A novel method for automating this process, the Fuzzy Grading System, is developed and compared to traditional practices. Letter-grades are recognized to be fuzzy descriptors of students' performance. Thus, operations aimed at defining letter-grade boundaries are naturally carried out in the context of fuzzy set theory and logic. The Fuzzy Grading System utilizes students' and instructor's performance measures in order to modify a set of collectively approved, a priori fuzzy grades, so as to produce a fair mark distribution. The validity of grades is increased by compensating for factors that are not directly accessible to simpler, traditional grading methods. >

Power system security assessment using pattern recognition and fuzzy estimation

A simple, fast, efficient and reliable method for power system security assessment is presented. The method is based on pattern recognition and fuzzy estimation techniques. The security status of a power system operating condition is recognized from the stored knowledge about similar operating conditions. The method is able to classify the system operating condition into secure/insecure state; and for the insecure state it provides information about pertinent contingencies which may cause insecurity. The knowledge about the system operating conditions (patterns) are stored in a structured memory by grouping similar patterns into clusters which are arranged into a hierarchical tree structure. This enables a very fast two level search for the near neighbours of the input pattern. The security status of the input pattern is determined using a fuzzy estimation technique. This not only provides a very reliable security classification, but the fuzzy grade membership also provides a quantitative ‘level of confidence’ for the security classification. Digital simulation results exhibiting the characteristics of the proposed method are presented.

Grouping trips by fuzzy similarity for scheduling of demand‐responsive transportation vehicles

A method which groups trip reservations is presented and tested for application to scheduling demand responsive transportation vehicles. The method is used for examining similarity among the individual trips and grouping them before any of the existing scheduling algorithms is applied. Trips are grouped based on the fuzzy notion of similarity. The strength of similarity is expressed by the fuzzy similarity grade. This method emulates the subjective trip grouping process which is normally performed under manual scheduling, and implements such a process under the computerized scheduling environment. The effectiveness of the method is demonstrated by comparing two schedules: one without using the grouping method and the other using the method. The latter case is shown to yield more efficient fleet utilization, less passenger disutility, and less computation time than the former. The method uses the fuzzy integral concept in developing the overall similarity by aggregating different similarity criteria. This ...

Scheduling Demand‐Responsive Transportation Vehicles using Fuzzy‐Set Theory

A scheduling algorithm for the time‐window‐based, many‐to‐many, dial‐a‐ride problem is presented. The algorithm is based on two steps: developing the initial route and inserting leftover trips. These two steps are applied to the scheduling of one vehicle at a time. The paper introduces fuzziness in the values of two basic input parameters, travel time and the desired time of vehicle stop, and applies fuzzy‐arithmetic rules and logic to develop the schedules. Since travel time is fuzzy, the possibility of inserting a stop between two existing stops is evaluated by fuzzy grade. Further, the degree that the arrival time of the vehicle satisfies the desired time of the passenger is evaluated by the intersection of two fuzzy sets: arrival time and desired time of vehicle arrival. Thus, the feasibility of inserting a stop between two existing stops is evaluated by two criteria: (1) The feasibility of stopping at the stop; and (2) user satisfaction. Threshold values that specify the minimum acceptable level of s...

A Support System for Beam Adjustment of Cyclotron Based on Fuzzy Grading Model and Texture Display

For inexperienced operators of cyclotron, an operational support system using computer systems is acquiring a greater importance as cyclotrons have recently become popular in industrial applications. In start-up operation, many components should be tuned up in order to maximize beam extraction efficiency. Experienced operators somehow manage this process through trial and error using their experience and intuition. This paper proposes the following methods:(1)Adjustment sequence is divided into six blocks. The independent adjustment operation for those blocks can make the operation simple and reduce the operators' burden.(2)A model which represents the relation between the beam distribution patterns and the experienced operators' grade is easily formulat ed by using fuzzy integral. This grading model is very useful for inexperienced operators who judge these patterns.(3)A multi-dimensional data display using polka-dot texture is proposed as an intuitive display . It is a mapping of features of the beam pattern onto properties of texture. Inexperienced operators can easily analyze the beam pattern through this texture display.