A fuzzy regression and optimization approach for setting target levels in software quality function deployment

With the rapid development of the software industry, improving the quality of software development has gained increasing importance. Software manufacturers have recently applied quality improvement techniques to software development to respond to the needs for software quality. Software quality function deployment (SQFD), as a technique for improving the quality of the software development process to create products responsive to customer expectations, is used to maximize customer satisfaction. This paper presents a fuzzy regression and optimization approach to determine target levels in SQFD. The inherent fuzziness of relationships in SQFD modeling justifies the use of fuzzy regression. Fuzzy regression is used to identify the functional relationships between customer requirements and technical attributes, and among technical attributes. Then, a mathematical programming model is developed to determine target levels of technical attributes using the functional relationships obtained by fuzzy regression. A search engine quality improvement problem is presented to illustrate the application of the proposed approach.     

An exponential membership function for fuzzy multiple objective linear programming

The operator “min” is one of the most frequently used aggregation operators in fuzzy decision. However, this operator is the softest operator and no allowance is made for any compensation. The “product” and other operators, some of them may be compensatory, are seldom used because of the nonlinearity of the resulting problem. In this paper, an exponential, instead of linear membership function is proposed. The advantages of using exponential membership are two fold. First, the resulting problems can be transformed to linear ones when the “product” and several other nonlinear aggregate operators are used. Secondly, exponential representation is more realistic than the linear ones usually used for some practical applications.     

A goal programming approach to fuzzy linear regression with fuzzy input�Coutput data

Fuzzy linear regression is an active area of research. In the literature, fuzziness is considered in outputs and/or in inputs. This paper focuses on both fuzzy inputs and fuzzy outputs. First, some approximations for multiplication of two triangular fuzzy numbers are introduced. Then, to evaluate the fuzzy linear regression, the best approximation is selected to minimize a suitable function via goal programming. An important feature of the proposed model is that it takes into account the centers of fuzzy data as well as their spreads. Moreover, it is flexible to deal with both symmetric and non-symmetric data. Furthermore, it can handle the crisp inputs and trapezoidal fuzzy outputs easily. To show the efficiency of the proposed model, some numerical examples are solved and compared with some earlier methods.     

Fuzzy measurable house of quality and quality function deployment for fuzzy regression estimation problem

In present competitive environment, it is necessary for companies to evaluate design time and effort at the early stage of product development. However, there is somewhat lacking in systemic analytical methods for product design time (PDT). For this end, this paper explores an intelligent method to evaluate the PDT. At the early development stage, designers are short of sufficient product information and have difficulty in determining PDT by subjective evaluation. Thus, a fuzzy measurable house of quality (FM-HOQ) model is proposed to provide measurable engineering information. Quality function deployment (QFD) is combined with a mapping pattern of “function → principle → structure” to extract product characteristics from customer demands. Then, a fuzzy support vector regression machine (FSVRM) model is built to fuse data and realize the estimation of PDT, which makes use of fuzzy comprehensive evaluation to simplify structure. In a word, the whole estimation method consists of four steps: time factors identification, product characteristics extraction by QFD and function mapping pattern, FSVRM learning, and PDT estimation. Finally, to illustrate the procedure of the estimation method, the case of injection mold design is studied. The results of experiments show that the fuzzy method is feasible and effective.     

A new mixed integer linear programming model for product development using quality function deployment

Quality function deployment (QFD) is a product development process performed to maximize customer satisfaction. In the QFD, the design requirements (DRs) affecting the product performance are primarily identified, and product performance is improved to optimize customer needs (CNs). For product development, determining the fulfillment levels of design requirements (DRs) is crucial during QFD optimization. However, in real world applications, the values of DRs are often discrete instead of continuous. To the best of our knowledge, there is no mixed integer linear programming (MILP) model in which the discrete DRs values are considered. Therefore, in this paper, a new QFD optimization approach combining MILP model and Kano model is suggested to acquire the optimized solution from a limited number of alternative DRs, the values of which can be discrete. The proposed model can be used not only to optimize the product development but also in other applications of QFD such as quality management, planning, design, engineering and decision-making, on the condition that DR values are discrete. Additionally, the problem of lack of solutions in integer and linear programming in the QFD optimization is overcome. Finally, the model is illustrated through an example.     

A simplified interactive multiple objective linear programming procedure

Differences in decision making styles and decision settings have motivated the development of a variety of interactive approaches to assist decision makers (DMs) in determining preferred solutions to multiple criteria decision making problems. This paper presents a Simplified Interactive Multiple Objective Linear Programming (SIMOLP) procedure which is designed to appeal to a broad range of DMs because of its simplicity and flexibility. Specifically, at any stage in the interactive process, the procedure attempts to

1. (1) minimize the inputs required from the DMs;

2. (2) provide DMs with a representative set of decision alternatives while simultaneously limiting the number of alternatives considered; and

3. (3) allow DMs to change their minds about previously eliminated alternatives. The procedure is illustrated with both graphical and numerical examples and computational experience is discussed.

     

A linear goal programming approach to determining the relative importance weights of customer requirements in quality function deployment

Quality function deployment (QFD) is a planning tool used in new product development and quality management. It aims at achieving maximum customer satisfaction by listening to the voice of customers. To implement QFD, customer requirements (CRs) should be identified and assessed first. The current paper proposes a linear goal programming (LGP) approach to assess the relative importance weights of CRs. The LGP approach enables customers to express their preferences on the relative importance weights of CRs in their preferred or familiar formats, which may differ from one customer to another but have no need to be transformed into the same format, thus avoiding information loss or distortion. A numerical example is tested with the LGP approach to demonstrate its validity, effectiveness and potential applications in QFD practice.     

An extension of interactive method for solving multiple objective linear programming with fuzzy parameters

In this paper, we propose a method which introduce a relative distance from an ideal value as a criterion that assist the decision maker(DM)'s judgement in pair of comparisons. Further, to consider the fuzziness of each coefficients in modelling the multiple objective linear programming(MOLP) problem and the fuzziness of satisfaction toward the attainment of the goals, we introduce a fuzzy number to the coefficients and fuzzy goals, respectively.     

A multiple objective integer programming approach for planning franchise expansion

The number and configuration of franchise outlets in a market defines the distribution strategy of a franchise company. The introduction of new franchise outlets contributes to conflict between the franchisee and franchisor over the degree of market penetration. The selection of sites for new franchises is an important factor in the long-term profitability of many types of franchises. This selection process requires consideration of objectives of the franchisee and franchisor which are often conflicting in nature. This paper deals with the problem of locating new franchises in an existing franchise network using multiple objective integer programming models and methods.     

Subset selection in multiple linear regression: a new mathematical programming approach

A new mathematical programming model is proposed to address the subset selection problem in multiple linear regression where the objective is to select a minimal subset of predictor variables without sacrificing any explanatory power. A parametric solution of this model yields a number of efficient subsets. To obtain this solution, an optimal or one of two heuristic algorithms is repeatedly used. The subsets generated are compared to ones generated by several standard procedures. The results suggest that the new approach finds subsets that compare favorably against the standard procedures in terms of the generally accepted measure: adjusted R².     

An accelerated approach for solving fuzzy relation equations with a linear objective function

In literature, the optimization model with a linear objective function subject to fuzzy relation equations has been converted into a 0-1 integer programming problem by Fang and Li (1999). They proposed a jump-tracking branch-and-bound method to solve this 0-1 integer programming problem. In this paper, we propose an upper bound for the optimal objective value. Based on this upper bound and rearranging the structure of the problem, we present a backward jump-tracking branch-and-bound scheme for solving this optimization problem. A numerical example is provided to illustrate our scheme. Furthermore, testing examples show that the performance of our scheme is superior to the procedure in the paper by Fang and Li. Several testing examples show that our initial upper bound is sharp.     

A computerized quality function deployment approach for retail services

Product and service quality can only be effectively improved when the most important needs of customers are satisfied. Quality Function Deployment (QFD) is an approach used to guide R&D, manufacturing, and management toward the development of products and services that satisfy the needs of consumers. The QFD operations are performed by way of a diagram called the House of Quality (HOQ). The HOQ contains information about the customers' needs (what), mechanisms to address these needs (how), and the criterion for deciding which “what” is the most important and which “how” provides the greatest customer satisfaction. A less familiar application of QFD is for the improvement of retail services. When QFD is applied to retail services, a computerized HOQ approach becomes integral to the process for providing continuous, iterative quality improvement. The objective of this research is to develop a formal QFD methodology for the retail industry and to build a computerized retail QFD system. The system provides a HOQ architecture for specifying and analyzing the customers' needs, deriving improvement strategies, and formalizing records of progress. Furthermore, two ranking methods that apply customer satisfaction theory are used to assist managers improve retail services. This system provides an integrated workbench for building retail HOQs and designing retail service strategies.     

A criteria weighting approach by combining fuzzy quality function deployment with relative preference relation

In past, fuzzy multi-criteria decision-making (FMCDM) models desired to find an optimal alternative from numerous feasible alternatives under fuzzy environment. However, researches seldom focused on determination of criteria weights, although they were also important components for FMCDM. In fact, criteria weights can be computed through extending quality function deployment (QFD) under fuzzy environment, i.e. fuzzy quality function deployment (FQFD). By FQFD, customer demanded qualities expressing the opinions of customers and service development capabilities presenting the opinions of experts can be integrated into criteria weights for FMCDM. However, deriving criteria weights in FQFD may be complex and different to multiply two fuzzy numbers in real world. To resolve the tie, we will combine FQFD with relative preference relation on FMCDM problems. With the relative preference relation on fuzzy numbers, it is not necessary multiplying two fuzzy numbers to derive criteria weights in FQFD. Alternatively, adjusted criteria weights will substitute for original criteria weights through relative preference relation. Obviously, adjusted criteria weights are clearly determined and then utilized in FMCDM models.     

A revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals

Conventional Fuzzy regression using possibilistic concepts allows the identification of models from uncertain data sets. However, some limitations still exist. This paper deals with a revisited approach for possibilistic fuzzy regression methods. Indeed, a new modified fuzzy linear model form is introduced where the identified model output can envelop all the observed data and ensure a total inclusion property. Moreover, this model output can have any kind of spread tendency. In this framework, the identification problem is reformulated according to a new criterion that assesses the model fuzziness independently from the collected data distribution. The potential of the proposed method with regard to the conventional approach is illustrated by simulation examples.     

A weight space-based approach to fuzzy multiple-objective linear programming

In this paper, the effects of uncertainty on multiple-objective linear programming models are studied using the concepts of fuzzy set theory. The proposed interactive decision support system is based on the interactive exploration of the weight space. The comparative analysis of indifference regions on the various weight spaces (which vary according to intervals of values of the satisfaction degree of objective functions and constraints) enables to study the stability and evolution of the basis that correspond to the calculated efficient solutions with changes of some model parameters.     

Interactive computer programs for fuzzy linear programming with multiple objectives

In this article, we present interactive computer programs fof solving fuzzy linear programming problems with multiple objectives. Through the use of five types of membership functions including non-linear functions, the fuzzy of imprecise goals of the decision maker are quantified. Although the formulated problem becomes a nonlinear programming problem, it can be reduced to a set of linear inequalities if some variable is fixed. Based on this idea, we propose a new method by combined use of bisection method and linear programming method. On the basis of the proposed method, FORTRAN programs that run in conversational mode are developed to implement man-machine interactive procedures. The commands in our programs and major prompt messages are also explained. An illustrative numerical example for the interactive processes is demonstrated together with the computer outputs     

A quantitative approach for setting technical targets based on impact analysis in software quality function deployment (SQFD)

Target setting in software quality function deployment (SQFD) is very important since it is directly related to development of high quality products with high customer satisfaction. However target setting is usually done subjectively in practice, which is not scientific. Two quantitative approaches for setting target values: benchmarking and primitive linear regression have been developed and applied in the past to overcome this problem (Akao and Yoji, 1990). But these approaches cannot be used to assess the impact of unachieved targets on satisfaction of customers for customer requirements. In addition, both of them are based on linear regression and not very practical in many applications. In this paper, we present an innovative quantitative method of setting technical targets in SQFD to enable analysis of impact of unachieved target values on customer satisfaction. It is based on assessment of impact of technical attributes on satisfaction of customer requirements. In addition both linear and non linear regression techniques are utilized in our method, which certainly improves the existing quantitative methods which are based on only linear regression. Frank Liu is currently an associate professor and a director of the McDonnel Douglass Foundation software engineering laboratory in the University of Missouri-Rolla. He has been working on requirements engineering, software quality management, and knowledge based software engineering since 1992. He has published about 50 papers in peer-reviewed journals and conferences in the above areas and several other software engineering application areas. He participates in research projects with a total amount of funds of more than four millions dollars as a PI or Co-PI sponsored by the National Science Foundation, Sandia National Laboratory, U.S. Air Force, University of Missouri Research Board, and Toshiba Corporation. He has served as a program committee member for many conferences. He was a program committee vice chair for the 2000 International Conference on Software Engineering and Knowledge Engineering. Kunio Noguchi is a senior quality expert in the software engineering center in the Toshiba Corporation. He has published several papers in the area of quality management systems. Anuj Dhungana was a M.S. graduate student in the computer science department at the Texas Tech University when he performed this research. V.V.N.S.N. Srirangam A. was a M.S. graduate student in the computer science department at the Texas Tech University when he performed this research. Praveen Inuganti was a M.S. graduate student in the computer science department at the University of Missouri-Rolla when he performed this research.     

A new integrated approach for engineering characteristic prioritization in quality function deployment

As a customer-driven quality improvement tool, quality function deployment (QFD) can convert customer requirements (CRs) into appropriate engineering characteristics (ECs) in product design and development. However, the conventional QFD method has been criticized for a variety of drawbacks, which limit its efficiency and potential applications. In this study, a new QFD approach integrating picture fuzzy linguistic sets (PFLSs) and the evaluation based on distance from average solution (EDAS) method is proposed for the determination of ranking order of ECs. The PFLSs are utilized to express the judgements of experts on the relationships among CRs and ECs. Then, the EDAS method is extended under picture fuzzy linguistic environment for the prioritization of the ECs identified in QFD. Moreover, a combined weighing method based on technique for order of preference by similarity to ideal solution (TOPSIS) and maximum entropy theory is established to calculate the weights of experts objectively. Finally, a product-service system design is provided to illustrate the effectiveness of the proposed QFD approach. The result shows that the manufacturer should pay more attention to “Meantime before failure”, “Warning feature” and “Quality of product manual”. Feedback from domain experts indicates that the integrated approach being proposed in this paper is more suitable for assessing and prioritizing ECs in QFD.     

A fuzzy AHP approach to the determination of importance weights of customer requirements in quality function deployment

Quality function deployment (QFD) is an important tool in product planning that could contribute to increase in customer satisfaction and shorten product design and development time. During the QFD process, determination of the importance weights of customer requirements is a crucial and essential step. The analytic hierarchy process (AHP) has been used in weighting the importance. However, due to the vagueness and uncertainty existing in the importance attributed to judgement of customer requirements, the crisp pairwise comparison in the conventional AHP seems to be insufficient and imprecise to capture the degree of importance of customer requirements. In this paper, fuzzy number is introduced in the pairwise comparison of AHP. An AHP based on fuzzy scales is proposed to determine the importance weights of customer requirements. The new approach can improve the imprecise ranking of customer requirements which is based on the conventional AHP. Finally, an example of bicycle splashguard design is used to illustrate the proposed approach.