An advanced quality function deployment model using fuzzy analytic network process

Quality function deployment (QFD) is a customer-oriented design tool used to ensure that the voice of customers is employed throughout the product planning and design stages. QFD uses the house of quality (HOQ), which is a matrix that provides a conceptual map for inter-functional planning and communication. In this paper, an advanced QFD model, based on fuzzy analytic network process (ANP) approach, is proposed to systematically take into account the interrelationship between and within the QFD components. The proposed method is aimed at expanding the current research scope from the product planning phase to the part deployment phase to provide product developers with more valuable information (ex. the importance and bottleneck level of part characteristics). Both customer requirements and the company’s production demands will be used as the inputs for the QFD process to enhance the completeness and accuracy of the QFD analysis results. A case study is presented to illustrate the application of the proposed method.     

An exploratory framework for handling the complexity of mathematical problem posing in small groups

The paper introduces an exploratory framework for handling the complexity of students’ mathematical problem posing in small groups. The framework integrates four facets known from past research: task organization, students’ knowledge base, problem-posing heuristics and schemes, and group dynamics and interactions. In addition, it contains a new facet, individual considerations of aptness, which accounts for the posers’ comprehensions of implicit requirements of a problem-posing task and reflects their assumptions about the relative importance of these requirements. The framework is first argued theoretically. The framework at work is illustrated by its application to a situation, in which two groups of high-school students with similar background were given the same problem-posing task, but acted very differently. The novelty and usefulness of the framework is attributed to its three main features: it supports fine-grained analysis of directly observed problem-posing processes, it has a confluence nature, it attempts to account for hidden mechanisms involved in students’ decision making while posing problems.     

Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning

The purpose of this paper is to further the notion of defining as a mathematical activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate geometry course. The framework integrates the instructional design theory of Realistic Mathematics Education (RME) and distinctions between concept image and concept definition and offers other researchers and instructional designers a structured way to analyze or plan for the role of defining in students’ mathematical progress.     

Fuzzy linear programming models for NPD using a four-phase QFD activity process based on the means-end chain concept

Quality function deployment (QFD) is a customer-driven approach in processing new product development (NPD) to maximize customer satisfaction. Determining the fulfillment levels of the “hows”, including design requirements (DRs), part characteristics (PCs), process parameters (PPs) and production requirements (PRs), is an important decision problem during the four-phase QFD activity process for new product development. Unlike previous studies, which have only focused on determining DRs, this paper considers the close link between the four phases using the means-end chain (MEC) concept to build up a set of fuzzy linear programming models to determine the contribution levels of each “how” for customer satisfaction. In addition, to tackle the risk problem in NPD processes, this paper incorporates risk analysis, which is treated as the constraint in the models, into the QFD process. To deal with the vague nature of product development processes, fuzzy approaches are used for both QFD and risk analysis. A numerical example is used to demonstrate the applicability of the proposed model.     

Fuzzy linear programming models for new product design using QFD with FMEA

Quality function deployment (QFD) is a customer-driven approach in processing new product developments in order to maximize customer satisfaction. Determining the fulfillment levels of design requirements (DRs) and parts characteristics (PCs) is an important decision problem during QFD activity processes for new product development. Unlike the existing literature, which mainly focuses on the determination of DRs, this paper proposes fuzzy linear programming models to determine the fulfillment levels of PCs under the requirement to achieve the determined contribution levels of DRs for customer satisfaction. In addition, considering the design risk, this paper incorporates failure modes and effect analysis (FMEA) into QFD processes, which is treated as the constraint in the models. To cope with the vague nature of product development processes, fuzzy approaches are used for both FMEA and QFD. The illustration of the proposed models is performed with a numerical example to demonstrate the applicability in practice.     

Rating technical attributes in fuzzy QFD by integrating fuzzy weighted average method and fuzzy expected value operator

Quality function deployment (QFD) is a planning and problem-solving tool that is gaining acceptance for translating customer requirements into the technical attributes of a product. Deriving the rating order of technical attributes from input variables is a crucial step in applying QFD. When the relative weights of customer requirements and the relationship measures between customer requirements and technical attributes are expressed as fuzzy numbers, calculating the importance of each technical attribute falls into the category of fuzzy weighted average, in which the derived membership function of the fuzzy importance of each technical attribute is not explicitly known. Thus, most ranking methods are not suitable under these circumstances. A method is proposed in this paper using fuzzy weighted average method in the fuzzy expected value operator in order to rank technical attributes in fuzzy QFD. An example of a flexible manufacturing system design is cited to demonstrate the application of the proposed approach.     

Compromising prioritization from pairwise comparisons considering type I and II errors

We explore an important problem in prioritizing product design alternatives, using a real-world case. Despite the importance of prioritization in the area of new product development, the development of systematic schemes has been limited and the concepts and methods developed in the decision analysis area do not seem to be used actively. Therefore, we propose a new method, referred to as the compromising prioritization technique, to prioritize the product design alternatives based on paired comparisons. It introduces type I and type II errors and compromises these two errors to arrive at a desirable order of alternatives. To accomplish this, the two indices of homogeneity and separation are developed together with a heuristic algorithm. A comparative study is also conducted to support our method for use in product development and analogous areas. We then demonstrate how to use the developed compromising prioritization technique using a case study on the asymmetric digital subscriber line (ADSL)-based high-speed internet service product.     

Quality function deployment for the good of soccer

This article presents a model for prioritizing and designing rule changes for the game of soccer in order to make it more attractive to soccer enthusiasts. The model, which is loosely based on quality function deployment (QFD), incorporates market segments, sports enthusiast interests, soccer activities, and rules of the game as rows and columns of interconnected QFD matrices. In addition, analytic hierarchy process (AHP) is used to determine the intensity of the relationship between the row and column variables of each matrix, while analytic network process (ANP) is used to determine the intensity of synergy effects among column variables. Finally, a trend extrapolation forecasting technique is used to suggest rule change specifications. The model fine-tunes and adds precision to the otherwise ad hoc process concerning the improvement of the game of soccer, and can provide insight about improvements in other professional sports.     

House of quality: A fuzzy logic-based requirements analysis

House Of Quality (HOQ) is one of the matrices of an iterative process called Quality Function Deployment (QFD). The foundation of the HOQ is the belief that products should be designed to reflect customers' desires and taste. HOQ is performed by a multidisciplinary team representing marketing, design engineering, manufacturing engineering, and any other functions considered critical by the company. In general, it provides a framework in which all participants can communicate their thoughts about a product. More specifically, HOQ is often used to identify the relationships between requirements based on different viewpoints. There are two issues in analyzing these requirements using HOQ. First, requirements are often described informally using vague terms. However, lack of formal way in interpreting the semantics of these requirements makes it difficult to determine if a realization of the system meets its customer's needs. Second, identifying relationships between requirements is often time consuming. Sometimes, it is difficult to arrive at a group consensus on a particular relationship between requirements. To address these issues, we have developed a fuzzy logic-based extension to HOQ for capturing imprecise requirements to both facilitate communication of team members and have a formal representation of requirements. Based on this representation, we developed a heuristic inference scheme to reason about the implicit relationships between requirements. We illustrate our approach using a textile mill supply business application.     

Students’ use of technological features while solving a mathematics problem

The design of technology tools has the potential to dramatically influence how students interact with tools, and these interactions, in turn, may influence students’ mathematical problem solving. To better understand these interactions, we analyzed eighth grade students’ problem solving as they used a java applet designed to specifically accompany a well-structured problem. Within a problem solving session, students’ goal-directed activity was used to achieve different types of goals: analysis, planning, implementation, assessment, verification, and organization. As we examined students’ goals, we coded instances where their use of a technology feature was supportive or not supportive in helping them meet their goal. We categorized features of this applet into four subcategories: (1) features over which a user does not have any control and remain static, (2) dynamic features that allow users to directly manipulate objects, (3) dynamic features that update to provide feedback to users during problem solving, and (4) features that activate parts of the applet. Overall, most features were found to be supportive of students’ problem solving, and patterns in the type of features used to support various problem solving goals were identified.     

An evolving framework for describing student engagement in classroom activities

Student engagement in classroom activities is usually described as a function of factors such as human needs, affect, intention, motivation, interests, identity, and others. We take a different approach and develop a framework that models classroom engagement as a function of students’ conceptual competence in the specific content (e.g., the mathematics of motion) of an activity. The framework uses a spatial metaphor—i.e., the classroom activity as a territory through which students move—as a way to both capture common engagement-related dynamics and as a communicative device. In this formulation, then, students’ engaged participation can be understood in terms of the nature of the “regions” and overall “topography” of the activity territory, and how much student movement such a territory affords. We offer the framework not in competition with other instructional design approaches, but rather as an additional tool to aid in the analysis and conduct of engaging classroom activities.     

Using interactive algebra software to support a discourse community

In this work we studied the impact of using NuCalc, an interactive computer algebra software, on the development of a discourse community in a college level mathematics class. Qualitative and quantitative data were collected over the course of 3 weeks of instruction. We examined the influence of the software on: group interactions; the mathematical investigations of learners; and the teacher’s interactions with students. Data points to four distinct ways in which the presence of NuCalc positively impacted the learning community we studied: (1) it served as a tool for extending students’ mathematical thinking, (2) it motivated students’ engagement in group discourse, (3) it became a tool for mediating discourse, (4) it became a catalyst for refining the culture of classroom, shifting the patterns of interactions between the teacher and learners.     

High school students’ understandings of geometric transformations in the context of a technological environment

This study investigated the nature of students’ understandings of geometric transformations, which included translations, reflections, rotations, and dilations, in the context of the technological tool, The Geometer’s Sketchpad. The researcher implemented a seven-week instructional unit on geometric transformations within an Honors Geometry class. Students’ conceptions of transformations as functions were analyzed using the APOS theory and were informed by an analysis of students’ interpretations and uses of representations of geometrical objects using the constructs of drawing and figure. The analysis suggests students’ understandings of key concepts including domain, variables and parameters, and relationships and properties of transformations were critical for supporting the development of deeper understandings of transformations as functions.     

Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking

Recent work by researchers has focused on synthesizing and elaborating knowledge of students’ thinking on particular concepts as core progressions called learning trajectories. Although useful at the level of curriculum development, assessment design, and the articulation of standards, evidence is only beginning to emerge to suggest how learning trajectories can be utilized in teacher education. Our paper reports on two studies investigating practicing and prospective elementary teachers’ uses of a learning trajectory to make sense of students’ thinking about a foundational idea of rational number reasoning. Findings suggest that a mathematics learning trajectory supports teachers in creating models of students’ thinking and in restructuring teachers’ own understandings of mathematics and students’ reasoning.     

Promoting productive mathematical classroom discourse with diverse students

Productive mathematical classroom discourse allows students to concentrate on sense making and reasoning; it allows teachers to reflect on students’ understanding and to stimulate mathematical thinking. The focus of the paper is to describe, through classroom vignettes of two teachers, the importance of including all students in classroom discourse and its influence on students’ mathematical thinking. Each classroom vignette illustrates one of four themes that emerged from the classroom discourse: (a) valuing students’ ideas, (b) exploring students’ answers, (c) incorporating students’ background knowledge, and (d) encouraging student-to-student communication. Recommendations for further research on classroom discourse in diverse settings are offered.     

Ways of talking and ways of positioning: Students’ beliefs in an inquiry-oriented differential equations class

As part of developmental research for an inquiry-oriented differential equations course, this study investigates the change in students’ beliefs about mathematics. The discourse analysis has identified two different types of perspective modes - i.e., discourse of the third-person perspective and discourse of the first-person perspective - in the students’ mathematical narratives, depending on their ways of positioning themselves with respect to mathematics. In the third-person perspective discourse, the students positioned themselves as passive recipients of mathematics that has been established by some external authority. In the first-person perspective discourse, the students positioned themselves as active mathematical inquirers and produced mathematics by interweaving their own mathematical ideas and experiences. Over the semester, students’ mathematical discourse changed from third-person perspective narratives to first-person perspective narratives. This change in their discourse pattern is interpreted as an indication of change in their beliefs about mathematics. Finally, this article discusses the instructional features that promote the change.     

A combined approach for fuzzy multi-objective multiple knapsack problems for defence project selection

In this study, a model representing military requirements as scenarios and capabilities is offered. Pair-wise comparisons of scenarios are made according to occurrence probabilities by using the Analytical Hierarchy Process (AHP). The weights calculated from AHP are used as the starting weights in a Quality Function Deployment (QFD) matrix. QFD is used to transfer war fighter requirements into the benefit values of projects. Two levels of QFD matrices are used to evaluate new capability areas versus capabilities and capabilities versus projects. The benefit values of the projects are used in a multi-objective problem (multi-objective multiple knapsack problem) that considers the project benefit, implementation risks and environmental impact as multiple objectives. Implementation risk and environmental impact values are also calculated using the same combined AHP and QFD methodology. Finally, the results of the fuzzy multi-objective goal programming suggest a list of projects that offers optimal benefit when carried out within multiple budgets.     

A QFD-based fuzzy MCDM approach for supplier selection

Supplier selection is a highly important multi-criteria group decision making problem, which requires a trade-off between multiple criteria exhibiting vagueness and imprecision with the involvement of a group of experts. In this paper, a fuzzy multi-criteria group decision making approach that makes use of the quality function deployment (QFD) concept is developed for supplier selection process. The proposed methodology initially identifies the features that the purchased product should possess in order to satisfy the company’s needs, and then it seeks to establish the relevant supplier assessment criteria. Moreover, the proposed algorithm enables to consider the impacts of inner dependence among supplier assessment criteria. The upper and the lower bounds of the weights of supplier assessment criteria and ratings of suppliers are computed by using the fuzzy weighted average (FWA) method. The FWA method allows for the fusion of imprecise and subjective information expressed as linguistic variables or fuzzy numbers. The method produces less imprecise and more realistic overall desirability levels, and thus it rectifies the problem of loss of information. A fuzzy number ranking method that is based on area measurement is used to obtain the final ranking of suppliers. The computational procedure of the proposed framework is illustrated through a supplier selection problem reported in an earlier study.     

The function of graphs and gestures in algorithmatization

The purpose of this paper is to present evidence supporting the conjecture that graphs and gestures may function in different capacities depending on whether they are used to develop an algorithm or whether they extend or apply a previously developed algorithm in a new context. I illustrate these ideas using an example from undergraduate differential equations in which students move through a sequence of Realistic Mathematics Education (RME)-inspired instructional materials to create the Euler method algorithm for approximating solutions to differential equations. The function of graphs and gestures in the creation and subsequent use of the Euler method algorithm is explored. If students’ primary goal was algorithmatizing ‘from scratch’, they used imagery of graphing and gesturing as a tool for reasoning. However if students’ primary goal was to make predictions in a new context, they used their previously developed Euler algorithm to reason and used graphs and gestures to clarify their ideas.     

A practical prioritization by multi-level group decision support

Military capability is proposed to be defined according to the DYNPOT scoring method. Multiobjective resource allocation of shared resources by group decision-making can combine analytic and qualitative modeling. Recently it has been pointed out that the goal programming model is superior to other models though it remained to be answered how to take into account hierarchy of decision makers (and objectives) (Stummer and Vetschera in Cent Eur J Oper Res 11:3–260, 2003). In this article it is tried to present, that the quantitative model can be easily adapted to the qualitative STT/QFD model of objectives of top-level group of decision-makers. The subsequent phases of the qualitative and the analytic solution of a multiobjective cooperative resource allocation problem can be applied within the group decision-making framework of defence requirements capability-based planning.