Linguistic Grades Research Articles

Assessing the Effectiveness of the APOS/ACE Method for Teaching Mathematics to Engineering Students

The present work focuses on a classroom application for evaluating the effectiveness of the APOS/ACE instructional treatment for teaching mathematics to engineering students. Using linguistic (qualitative) grades, the assessment of the mean student performance is realized with the help of grey numbers and the assessment of their quality performance by calculating the Grade Point Average (GPA) index. A neutrosophic assessment method is also applied for evaluating the overall student performance, because the instructor had doubts about the accuracy of the qualitative grades assigned to some students.

A Hybrid Method for Assessment with Linguistic Grades

Assessment is an important component of all human and machine activities, because it helps to determine possible mistakes and to improve performance with respect to the corresponding activity. A hybrid method is developed in this paper for assessment with linguistic grades, which uses closed real intervals and soft sets as tools. Soft sets, introduced by Molodstov in 1999, are used for a qualitative assessment in a parametic manner and the closed real intervals enable us to quantify the qualitative assessment achieved with the help of soft sets. Two examples for chess players’ and machines’ performance assessment are also presented illustrating our results.

Suppliers selection based on intuitionistic fuzzy dimensional analysis

Supplier selection is a crucial activity in the supply chain management, and fundamentally it is a multi-criteria decision-making problem. However, the interaction of the criteria, the uncertain regarding to subjectivity and the imprecise information generally present in the provider selection process is still an open issue. The main purpose of this paper is to arise a new method to support the provider selection process. In this sense, this paper introduces the intuitionistic fuzzy version of dimensional analysis under a group decision making and multi-criteria environment applied to suppliers selection. Likewise, a set of decision makers reveal their preferences about the criteria and options in evaluation by mean of a linguistic grade that are mapped via intuitionistic numbers. Consequently, the importance of each decision maker and criteria is considered in the method. Hence, the methodology assumes that exist a choice better than the rest which is called ideal alternative. Each choice in evaluation, is compared with that ideal to induce an index of similarity. Additionally, the alternative with highest index of similarity is proposed as solution to the supplier selection problem. The method offer a systematic mode to deal with the interrelationship between the criteria attached into the decision making sphere. Finally, a numerical example is addressed to supplier selection to facilitate the understanding of the proposed method.

Supporting risk management decision making by converting linguistic graded qualitative risk matrices through interval type-2 fuzzy sets

Risk matrices are widely used to present results of qualitative and semi-quantitative risk assessment for risk management decision making. There are different types of risk matrix category definitions according to the function and risk acceptance criteria. This paper reviews some general weaknesses of current risk matrices and proposes a method to improve the reading ambiguity of linguistically graded qualitative risk matrices. Main topic of this paper is the type of risk matrix that grades event consequence and frequency categories in linguistic terms. Because different people understand the meaning of these terms differently, the aim is to convert subjective quantified term inputs produced by a number of experts independently as much as possible to objective values creating at the same time a clearer and more discriminative result. In other words, the method involves asking various expert users independently to estimate numerical intervals of linguistic grades of event consequence and frequency on a continuous scale while maintaining risk acceptance levels. It is applying a second-generation fuzzy logic technique to express linguistic terms in numbers, called computing with words. This interval type-2 fuzzy system has evolved lately as a decision-making support tool and appears to be well suited to handle uncertainty intrinsic to qualitative linguistic grades, fusing different individual expert estimates in an objective way and to facilitate the reading resolution by introducing gliding numerical scales instead of discrete categories. Examples are given to illustrate the method as well as the use of the technique to aggregate a number of different qualitative risk matrix types into one unified risk matrix. The latter is useful in case a corporate-wide risk matrix exists to standardize risk management across the company, but older versions may still be around which should be fused with the newer ones.

Application of triangular fuzzy numbers to analogical reasoning

In this work a combination is applied of triangular fuzzy numbers (TFNs) and of the centre of gravity (COG) defuzzification technique as means for assessing student skills in solving mathematical problems by analogy. A classroom experiment is also presented performed with students of the Graduate Technological Educational Institute (T. E. I.) of Western Greece, which illustrates our results in practice. In order to check the validity of the fuzzy assessment method, its outcomes in this experiment are compared to the corresponding outcomes of two traditional assessment methods of the bi-valued logic, the calculation of the mean value of student scores and the grade point average (GPA) index. The usefulness of the fuzzy approach becomes evident when linguistic grades only and not numerical scores are used for student assessment.

Event Pattern Analysis and Prediction at Sentence Level using Neuro-Fuzzy Model for Crime Event Detection

Classifying the sentences that describe Events is an important task for many applications. In this paper, Event patterns are identified and extracted at sentence level using term features. The terms that trigger Events along with the sentences are extracted from web documents. The sentence structures are analyzed using POS tags. A hierarchal sentence classification model is proposed by considering specific term features of the sentence and the rules are derived. The rules fail to define a clear boundary between the patterns and create ambiguity and impreciseness. To overcome this, suitable fuzzy rules are derived which gives importance to all term features of the sentence. The fuzzy rules are constructed with more variables and generate sixteen patterns. Artificial Neuro-Fuzzy Inference System (ANFIS) model is proposed for training and classifying the sentence patterns for capturing the knowledge present in sentences. The obtained patterns are assigned linguistic grades based on previous classification knowledge. These grades represent the type and quality of information in the patterns. The membership function is used to evaluate the fuzzy rules. The patterns share the membership values between [0---1] which determines the weights for each pattern. Later, higher weighted patterns are considered to build Event Corpus, which helps in retrieving useful and interested information of Event Instances. The performance of the proposed approach classification is evaluated for `Crime' Event by crawling documents from WWW and also evaluated for benchmark dataset for `Die' Event. It is found that the performance of the proposed approach is encouraging when compared with recently proposed similar approaches.

Modified Hybridized Multi-agent Oriented Approach to Analyze Work-stress Data Providing Feedback in Real Time

This paper presents a hybridized multi-agent oriented approach to develop a model capable of classifying and linguistically grading the level of work-stress. The scope of this research is to implement the model to solve a psychological problem relating to work-stress. The model uses a neural network capability as agent to classify the work-related stress data. The fuzzy logic component then transforms the crisp output from the neural network into linguistic grade. The main idea of integrating neural network and fuzzy logic techniques was to neutralize each other's weaknesses and generate a superior hybrid solution. The work-stress data was analyzed using the model and feedback provided to the users about their stress levels in real time. The result demonstrated that using this technique, the work-stress data was classified efficiently and the measured stress level was successfully described in linguistic term (Human readable). This achievement provides the user with an automated mechanism that can render a first step towards identification, prevention and making perceptible changes to the working environment. The Intelligent Multi-Agent Decision Analyser (IMADA) uses a hybridized technique that provided better solution in terms of applicability, portability and efficiency in this particular psychological domain.

Hybrid grey multiple attribute decision‐making method with partial weight information

Purpose – The purpose of this paper is to attempt to propose a method based on evidential reasoning for hybrid grey attribute decision‐making problems where the attribute weights are partially known, in which the attribute values are interval grey numbers and linguistic grades.Design/methodology/approach – The method is that the decision‐maker gives whitenization of each interval grey number based on their preference and belief structure of the form of qualitative attribute values, whitenization of quantitative attributes can be equivalently expressed in the form of belief structure with the principle of utility value equivalence, and then the grade belief structure decision matrix can be determined. By using the analytical evidential reasoning algorithm, belief degrees of each alternative belonging to each linguistic grade are obtained. Two pairs of nonlinear optimization models which are solved by genetic algorithms (GA) are constructed to compute the maximum and the minimum expected utilities of each a...

Crew rostering with multiple goals: An empirical study

An empirical crew rostering problem drawn from the customer service section of a department store in southern Taiwan is addressed in this paper. The service section established relevant service facilities and functions to provide services for customers as well as distinguished guests and visitors. The crew rostering task is concerned with assigning multi-functional workers to different types of job and scheduling working shifts for each worker within a given time horizon, where the available and demand workforce vary from one shift to another. The current crew rostering method is a seniority orientation method. In developing the roster under current method, lines of job are generated and then bids are taken in order of decreasing seniority. The most senior worker has the widest range of job lines from which to select so as to best satisfy his/her preference. Successive crew members bid for the remaining lines of job. The current method has some drawbacks. To overcome the drawbacks, this paper develops a problem-specific approach with three stages to deal with the crew rostering problem, making it more equitable and personalized for workers by considering the management goals concerning worker–job suitability, worker–worker compatibility and worker–shift fondness. Due to the vagueness of job characteristics and the personal attributes, fuzzy method is used to improve the evaluation results of suitability, compatibility and fondness. The utility similarities of fuzzy assessments with the linguistic grade of very good are used to measure the fitness grade for the management goals. A linear goal programming model is proposed to fulfill the “efficient assignment/match from the right” policy. The proposed approach ensures the right workers are assigned to the right jobs, the right workers are placed together in a job and the pleasing working shifts are given to the workers. An illustrative application demonstrates the implementation of the proposed approach.

Taguchi optimization for tool wear using fuzzy deduction

In this paper, four parameters (cutting depth, feed rate, speed, tool nose runoff) with three levels (low, medium, high) are considered to optimize the tool wear for CNC (computer numerical control) finish turning based on L 9(34) orthogonal array. Additionally, twenty- seven fuzzy control rules using trapezoid membership function with respective to seventeen linguistic grades for tool wear are constructed. Considering thirty input and eighty output intervals, the defuzzification using center of gravity is moreover completed. Through the Taguchi experiment, the optimum fuzzy deduction parameters can then be received. The confirmation experiment for optimum deduction parameters is furthermore performed on an ECOCA-3807 CNC lathe. It is shown that the tool wear ratio from the fuzzy deduction optimization parameters is significantly advanced comparing to that from the benchmark. This paper not only proposes a parametric deduction optimization scheme using orthogonal array, but also contributes the satisfactory fuzzy approach to the tool wear for CNC turning with profound insight.

Fuzzy Parametric Deduction for Material Removal Rate Optimization

Problem statement: A general optimization scheme without equipment operations for CNC (computer numerical control) finish turning is deemed to be necessarily developed. Approach: In this study, four parameters (cutting depth, feed rate, speed, tool nose runoff) with three levels (low, medium, high) were considered to optimize the Material Removal Rate (MRR) based on L9(34) orthogonal array. Twenty-seven fuzzy control rules using trapezoid membership function with respective to seventeen linguistic grades for material removal rate were additionally constructed. Considering thirty input and eighty output intervals, the defuzzification using center of gravity was moreover completed. Through the Taguchi experiment, the optimum fuzzy deduction parameters could then be received. Results: The confirmation experiment for optimum deduction parameters was furthermore computed within the parameter ranges on an ECOCA-3807 CNC lathe. It is shown that the material removal rate from the fuzzy deduction optimization parameters was significantly advanced comparing to that from the benchmark. Conclusions: This study not only proposed a parametric deduction optimization scheme using orthogonal array, but also contributed the satisfactory fuzzy approach to the material removal rates for CNC turning with profound insight.

FUZZY TAGUCHI DEDUCTION OPTIMIZATION ON MULTI-ATTRIBUTE CNC TURNING

In this paper, four parameters with three levels are considered to optimize the multi-attribute finish CNC (computer numerical control) turning based on L9(34) orthogonal array. Additionally, nine fuzzy control rules with respective to five linguistic grades for each attribute are constructed. The TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) is moreover utilized to integrate and evaluate the multiple machining attributes for Taguchi experiment to receive the optimum general deduction parameters. It is shown that the attributes from the fuzzy Taguchi deduction optimization parameters are all significantly advanced comparing to those from benchmark.

Parametric Deduction Optimization for Surface Roughness

Problem statement: Surface roughness is a major consideration in modern Computer Numerical Control (CNC) turning industry. Most existing optimization researches for CNC finish turning were either accomplished within certain manufacturing circumstances, or achieved through numerous equipment operations. Therefore, a general deduction optimization scheme is deemed to be necessary for the industry. Approach: In this study, four parameters (cutting depth, feed rate, speed, tool nose runoff) with three levels (low, medium, high) were considered to optimize the surface roughness for Computer Numerical Control (CNC) finish turning. Additionally, twenty-seven fuzzy control rules using trapezoid membership function with respective to seventeen linguistic grades for the surface roughness were constructed. Considering thirty input and eighty output intervals, the defuzzification using center of gravity was moreover completed. Through the Taguchi experiment, the optimum general deduction parameters can then be received. Results: The confirmation experiment for optimum deduction parameters was furthermore performed on an ECOCA-3807 CNC lathe. It was shown that the surface roughness from the fuzzy deduction optimization parameters are significantly advanced comparing to those from benchmark. Conclusion: This study not only proposed a parametric deduction optimization scheme using orthogonal array, but also contributed the satisfactory fuzzy approach to the surface roughness for CNC turning with profound insight.

Fuzzy Deduction Material Removal Rate Optimization for Computer Numerical Control Turning

Problem statement: Material Removal Rate (MRR) is often a major consideration in the modern Computer Numerical Control (CNC) turning industry. Most existing optimization researches for CNC finish turning were either accomplished within certain manufacturing circumstances, or achieved through numerous equipment operations. Therefore, a general deduction optimization scheme is deemed to be necessary proposed for the industry. Approach: In this study, four parameters (cutting depth, feed rate, speed, tool nose runoff) with three levels (low, medium, high) were considered to optimize the MRR in finish turning based on L9(34) orthogonal array. Additionally, nine fuzzy control rules using triangle membership function with respective to five linguistic grades for the MRR is constructed. Considering four input and twenty output intervals, the defuzzification using center of gravity was thus completed for the Taguchi experiment. Therefore, the optimum general deduction parameters can then be received. Results: The confirmation experiment for optimum general deduction parameters was furthermore performed on an ECOCA-3807 CNC lathe. It was shown that the material removal rates from the fuzzy Taguchi deduction optimization parameters are all significantly advanced comparing to those from the benchmark. Conclusion: This study not only proposed a general deduction optimization scheme using orthogonal array, but also contributed the satisfactory fuzzy linguistic approach for the MRR in CNC turning with profound insight.

Fuzzy Linguistic Optimization on Surface Roughness for CNC Turning

Surface roughness is often considered the main purpose in contemporary computer numerical controlled (CNC) machining industry. Most existing optimization researches for CNC finish turning were either accomplished within certain manufacturing circumstances or achieved through numerous equipment operations. Therefore, a general deduction optimization scheme is deemed to be necessary for the industry. In this paper, the cutting depth, feed rate, speed, and tool nose runoff with low, medium, and high level are considered to optimize the surface roughness for finish turning based onL9(34)orthogonal array. Additionally, nine fuzzy control rules using triangle membership function with respective to five linguistic grades for surface roughness are constructed. Considering four input and twenty output intervals, the defuzzification using center of gravity is then completed. Thus, the optimum general fuzzy linguistic parameters can then be received. The confirmation experiment result showed that the surface roughness from the fuzzy linguistic optimization parameters is significantly advanced compared to that from the benchmark. This paper certainly proposes a general optimization scheme using orthogonal array fuzzy linguistic approach to the surface roughness for CNC turning with profound insight.

Tool Wear Optimization for General CNC Turning Using Fuzzy Deduction

Tool wear is frequently considered in the modern CNC (computer numerical control) turning industry. Most existing optimization researches for CNC finish turning were either accomplished within certain manufacturing circumstances, or achieved through numerous equipment operations. Therefore, a general deduction optimization scheme proposed is deemed to be necessary for the industry. In this paper, four parameters (cutting depth, feed rate, speed, tool nose runoff) with three levels (low, medium, high) are considered to optimize the tool wear for finish turning based on orthogonal array. Additionally, nine fuzzy control rules using triangle membership function with respective to five linguistic grades for tool wear are constructed. Considering four input and twenty output intervals, the defuzzification using center of gravity is then completed and introduced as the S/N (signal-to-noise) ratio. Thus, the optimum general deduction parameters can then be received. The confirmation experiment for optimum general deduction parameters is furthermore performed on an ECOCA-3807 CNC lathe. It is shown that the tool wear ratio from the fuzzy deduction optimization parameters is significantly advanced comparing to those from benchmark. This paper not only proposes a general deduction optimization scheme using orthogonal array, but also contributes the satisfactory fuzzy linguistic approach to tool wear in CNC turning with profound insight.

Multi-criteria linguistic interval group decision-making approach *

For group decision-making problems with linguistic assessment information, a new method based on two-tuple and WC-OWA operator is proposed, in which the criteria's weights and the decision-makers' preference information might take the form of linguistic grade, or might be between two continuous linguistic grades, or might be linguistic interval, or might be default. In this method, all linguistic values are transformed into two-tuple, and an aggregative decision-making matrix is obtained by using interval operation. The group aggregative values of each criterion on alternatives are computed by using a WC-OWA operator, the aggregative values on alternatives are worked out, and transformed into two-tuple. And the rank of the alternatives is obtained by using the order property of two-tuple. An example shows the feasibility and effectiveness of the proposed method.

Type 2 Fuzzy Sets: An Appraisal of Theory and Applications

This paper provides a guide and tutorial to type 2 fuzzy sets. Type 2 fuzzy sets allow for linguistic grades of membership thus assisting in knowledge representation. They also offer improvement on inferencing with type 1 sets. The various approaches to knowledge representation and inferencing are discussed, with worked examples, and some of the applications of type 2 sets are reported.

Level of public transport service evaluation: A fuzzy set approach

AbstractThe success of any enterprise, in a market‐oriented economy, depends upon it's quality. This paper describes the results of a survey of commuters on the quality of services and their relative weights, and of the attributes that determine the service level of bus transport undertakings. The model uses the theory of fuzzy sets to process the information obtained. A composite index, called level‐of‐public transport‐service (LOPTS), is defined and used to measure the service qualities. This approach is presented with guidelines for rating the quality of services, fuzzy‐set representations of the linguistic grades, definition of LOPTS and its use in a public transport quality data base. An example is presents how the approach can be employed to analyse data bases generated from a quality survey. This approach is compared with the numerical rating approach with single number representation.

Unified Pavement Distress Index for Managing Flexible Pavements

One of the innovative approaches for maintaining and rehabilitating the nation's highways is to develop and implement some form of pavement management system (PMS). This paper documents results of a survey on PMS use in the United States. In addition, a simple method for a PMS based on priority ranking is presented. The model uses the theory of fuzzy sets to process the information obtained from a typical pavement condition survey. An index, called unified pavement distress index (UPDI), is defined and used to measure the pavement distress condition. The new approach is presented in a few key elements: guidelines for rating of six types of distresses, weights among the different types of distresses, fuzzy‐set representations of the linguistic grades and fuzzy mathematics, and the definition of UPDI and its use in a pavement data base. An example is presented to show how the new approach can be employed to analyze data bases generated from a pavement condition survey. While the proposed approach has shown its potential in the example application, more positive feedbacks from large‐scale field tests are needed to demonstrate its reliability and ease of use.