Determining the importance weights for the design requirements in the house of quality using the fuzzy analytic network approach

Quality function deployment (QFD) has been used to translate customer needs (CNs) and wants into technical design requirements (DRs) in order to increase customer satisfaction. QFD uses the house of quality (HOQ), which is a matrix providing a conceptual map for the design process, as a construct for understanding CNs and establishing priorities of DRs to satisfy them. This article uses the analytic network process (ANP), the general form of the analytic hierarchy process (AHP), to prioritize DRs by taking into account the degree of the interdependence between the CNs and DRs and the inner dependence among them. In addition, because human judgment on the importance of requirements is always imprecise and vague, this work concentrates on a fuzzy ANP approach in which triangular fuzzy numbers are used to improve the quality of the responsiveness to CNs and DRs. A numerical example is presented to show the proposed methodology. © 2004 Wiley Periodicals, Inc.     

Evaluation of design requirements using fuzzy outranking methods

To increase customer satisfaction, quality function deployment is used to translate customer needs into technical design requirements (DRs). Determination of DRs for product development is very important because these requirements are the vital keys to successful products. The methods used to evaluate DRs in the literature can be categorized into multicriteria evaluation methods such as scoring methods, the analytic hierarchy method, analytic network process, and so forth. There are few papers using fuzzy multi‐attribute outranking methods to evaluate DRs. This article aims to compare the results of three different fuzzy outranking methods to evaluate the DRs in the PVC windows industry. A sensitivity analysis is also made by using the software, FOuR. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1229–1250, 2007.     

A new hesitant fuzzy QFD approach: An application to computer workstation selection

Computer workstation selection is a multiple criteria decision making problem that is generally based on vague linguistic assessments, which represent human judgments and their hesitancy. In this paper, a new fuzzy quality function deployment (QFD) approach is used to effectively determine the design requirements (DRs) of a computer workstation. Hesitant fuzzy linguistic term sets (HFLTS) are innovatively employed to capture the hesitancy of the experts in this approach. More precisely, the proposed new QFD approach is the first study that determines the importance of customer requirements (CRs), the relations between CRs and DRs and the correlations among DRs via HFLTS. Additionally, HFLTS based Analytic Hierarchy Process (AHP) and Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) methods are utilized in the computational steps to select the best computer workstation. A real industrial application is carried out to validate the implementation of the proposed approach.     

A new approach to formulate fuzzy regression models

A fuzzy regression model is developed to construct the relationship between the response and explanatory variables in fuzzy environments. To enhance explanatory power and take into account the uncertainty of the formulated model and parameters, a new operator, called the fuzzy product core (FPC), is proposed for the formulation processes to establish fuzzy regression models with fuzzy parameters using fuzzy observations that include fuzzy response and explanatory variables. In addition, the sign of parameters can be determined in the model-building processes. Compared to existing approaches, the proposed approach reduces the amount of unnecessary or unimportant information arising from fuzzy observations and determines the sign of parameters in the models to increase model performance. This improves the weakness of the relevant approaches in which the parameters in the models are fuzzy and must be predetermined in the formulation processes. The proposed approach outperforms existing models in terms of distance, mean similarity, and credibility measures, even when crisp explanatory variables are used.     

A two-phase approach for multi-objective programming problems with fuzzy coefficients

In this study, a two-phase procedure is introduced to solve multi-objective fuzzy linear programming problems. The procedure provides a practical solution approach, which is an integration of fuzzy parametric programming (FPP) and fuzzy linear programming (FLP), for solving real life multiple objective programming problems with all fuzzy coefficients. The interactive concept of the procedure is performed to reach simultaneous optimal solutions for all objective functions for different grades of precision according to the preferences of the decision-maker (DM). The procedure can be also performed to obtain lexicographic optimal and/or additive solutions if it is needed. In the first phase of the procedure, a family of vector optimization models is constructed by using FPP. Then in the second phase, each model is solved by FLP. The solutions are optimal and each one is an alternative decision plan for the DM.     

Construction of house of quality for new product planning: A 2-tuple fuzzy linguistic approach

A house of quality (HOQ) diagram is used to analyze the critical factors involved in the quality function deployment (QFD) processes for the new product planning (NPP). The principal tasks of the QFD acting process comprise describing and scoring customer requirements (CRs); determining design requirements (DRs), the relationship between CRs and DRs, the correlations among CRs, and the correlations among DRs. Finally, the DRs can be scored by these assessments in NPP. This study proposes various methods of scoring the requirements of current and potential customers to reflect the knowledge and preference differences among different customers regarding CRs. The CR scores provided by different customers can be assessed by using linguistic, numerical, and interval values, or can be assessed using linguistic label sets with different granularity. A 2-tuple fuzzy linguistic computational approach is adopted to aggregate the CR importance scores obtained from customers by using various methods. In addition, to accurately rate the DRs, a modified relationship between CRs and DRs is proposed. The proposed HOQ construction model is practical because it prevents the loss of information during the QFD process for NPP. An example is used to demonstrate the applicability of the proposed model.     

Fuzzy cognitive map based quality function deployment approach for dishwasher machine selection

The traditional quality function deployment (QFD) approach deals with the weights of customer requirements (CRs), relationships among CRs and design requirements (DRs), correlation among DRs by using crisp values. This paper uses fuzzy numbers to improve the drawbacks of the traditional QFD method because fuzzy numbers enable to make consistent decisions in uncertain environment to decision makers. The existing papers handle a simple multiplication operation to calculate the correlation among CRs and the correlation among DRs. This study proposes fuzzy cognitive map (FCM) approach to calculate these correlations so that FCM is a successful method to handle the interactions among criteria. This paper contributes to the literature by integrating QFD approach and fuzzy cognitive map approach. The weights of DRs are defined in the result of the proposed QFD approach. These weights are used to evaluate the dishwasher machine alternatives in intuitionistic fuzzy VIKOR method. Intuitionistic fuzzy number (IFS) ensures to handle more information than type-1 fuzzy number to describe the fuzziness and the uncertainty of the real life world. Finally, the proposed approach has been implemented to a dishwasher machine selection in order to test its validity.     

A fuzzy decision support system for digital camera selection based on user preferences

Mobile phones have been the most rapidly spreading development in the field of communication and information technologies over the past decades. Nowadays, digital cameras have taken their place. The wide product range in the market, each with numerous heterogeneous technical attributes, complicates the selection of the most convenient camera for end-users. The aim of this work is to provide end-users with a decision support framework for selecting the best digital camera according to their preferences. End-users and photography experts use subjective assessments when determining their requirements and making their evaluations. The proposed decision support tool is built on the basis of fuzzy set theory. The imprecision of the subjective assessments are transformed to fuzzy triangular numbers. The fuzzy analytic hierarchy process (FAHP) and fuzzy compromise programming methodologies are applied in order to determine the relative weights of sub-criteria and criteria and to rank the digital camera alternatives, respectively.     

Piecewise regression for fuzzy input–output data with automatic change-point detection by quadratic programming

To handle the large variation issues in fuzzy input–output data, the proposed quadratic programming (QP) method uses a piecewise approach to simultaneously generate the possibility and necessity models, as well as the change-points. According to Tanaka and Lee [H. Tanaka, H. Lee, Interval regression analysis by quadratic programming approach, IEEE Transactions on Fuzzy Systems 6 (1998) 473–481], the QP approach gives more diversely spread coefficients than linear programming (LP) does. However, their approach only deals with crisp input and fuzzy output data. Moreover, their method is weak in handling fluctuating data. So far, no method has been developed to cope with the large variation problems in fuzzy input–output data. Hence, we propose a piecewise regression for fuzzy input–output data with a QP approach. There are three advantages in our method. First, the QP technique gives a more diversely spread coefficient than does a linear programming technique. Second, the piecewise approach is used to detect the change-points in the estimated model automatically, and handle the large variation data such as outliers well. Third, the possibility and necessity models with better fitness in data processing are obtained at the same time. Two examples are presented to demonstrate the merits of the proposed method.     

Single machine scheduling problems under position-dependent fuzzy learning effect with fuzzy processing times

In this paper, we consider single machine scheduling problems under position-dependent fuzzy learning effect with fuzzy processing times. We study three objectives which are to minimize makespan, total completion time and total weighted completion time. Furthermore, we show that these three problems are polynomially solvable under position-dependent fuzzy learning effects with fuzzy processing times. In order to model the uncertainty of fuzzy model parameters such as processing time and learning effect, we use an approach called likelihood profile that depends on the possibility and necessity measures of fuzzy parameters. For three objective functions, we build Fuzzy Mixed Integer Nonlinear Programming (FMINP) models using dependent chance constrained programming techniques for the same predetermined confidence levels. Furthermore, we present polynomially solvable algorithms for different confidence levels for these problems.     

A fuzzy QFD approach to determine supply chain management strategies in the dairy industry

The aim of this study is to identify the crucial logistics requirements and supply chain management (SCM) strategies for the dairy industry. For product or service development, quality function deployment (QFD) is a useful approach to maximize customer satisfaction. The determination of design requirements and supply chain management strategies are important issues during QFD processes for product or service design. For this reason, a fuzzy QFD methodology is proposed in this study to determine these aspects and to improve customer satisfaction. Qualitative information is converted firstly into quantitative parameters, and then this data is combined with other quantitative data to parameterize two multi-objective mathematical programming models. In the first model, the most important logistic requirements for the company are determined based on total technical importance, total cost, total feasibility and total value increment objectives, and in the second model, based on these objectives, appropriate supply chain management strategies are determined. Finally, a case study from the Turkish dairy industry is given to illustrate the proposed approach.     

GSETSK: a generic self-evolving TSK fuzzy neural network with a novel Hebbian-based rule reduction approach

Takagi–Sugeno–Kang (TSK) fuzzy systems have been widely applied for solving function approximation and regression-centric problems. Existing dynamic TSK models proposed in the literature can be broadly classified into two classes. Class I TSK models are essentially fuzzy systems that are limited to time-invariant environments. Class II TSK models are generally evolving systems that can learn in time-variant environments. This paper attempts to address the issues of achieving compact, up-to-date fuzzy rule bases and interpretable knowledge bases in TSK models. It proposes a novel rule pruning method which is simple, computationally efficient and biologically plausible. This rule pruning algorithm applies a gradual forgetting approach and adopts the Hebbian learning mechanism behind the long-term potentiation phenomenon in the brain. It also proposes a merging approach which is used to improve the interpretability of the knowledge bases. This approach can prevent derived fuzzy sets from expanding too many times to protect their semantic meanings. These two approaches are incorporated into a generic self-evolving Takagi–Sugeno–Kang fuzzy framework (GSETSK) which adopts an online data-driven incremental-learning-based approach.Extensive experiments were conducted to evaluate the performance of the proposed GSETSK against other established evolving TSK systems. GSETSK has also been tested on real world dataset using the high-way traffic flow density and Dow Jones index time series. The results are encouraging. GSETSK demonstrates its fast learning ability in time-variant environments. In addition, GSETSK derives an up-to-date and better interpretable fuzzy rule base while maintaining a high level of modeling accuracy at the same time.     

A multi-item transportation problem with fuzzy tolerance

This paper presents the recently introduced modified subgradient method for optimization and its effectiveness in a fuzzy transportation model. Here a multi-item balanced transportation problem (MIBTP) is formulated where unit transportation costs are imprecise. Also available spaces and budgets at destinations are limited but imprecise. The objective is to find a shipment schedule for the items that minimizes the total cost subjected to imprecise warehouse and budget constraints at destinations. The proposed model is reduced to a multi-objective optimization problem using tolerances, then to a crisp single-objective one using fuzzy non-linear programming (FNLP) technique and Zimmermann's method. The above fuzzy MIBTP is also reduced to another form of deterministic one using modified sub-gradient method (MSM). These two crisp optimization problems are solved by Genetic Algorithm (GA). As an extension, fuzzy multi-item balanced solid transportation problems (STPs) with and without restrictions on some routes and items are formulated and reduced to deterministic ones following FNLP and Zimmermann's methods. These models are also solved by GA. Models are illustrated numerically, optimum results of fuzzy MIBTP from two deductions are compared. Results are also presented for different GA parameters.     

Notes on “Possibilistic programming approach for fuzzy multidimensional analysis of preference in group decision making”

The aim of this note is to point out and correct some errors in the definitions, notations operations and possibilistic programming model introduced by Sadi-Nezhad and Akhtari (2008) and hereby develop two correct possibilistic programming models for fuzzy multidimensional analysis of preference in the fuzzy multiattribute group decision making problems with both the fuzzy weight vector and the fuzzy positive ideal solution (PIS) unknown a priori.     

Duality theory in fuzzy mathematical programming problems with fuzzy coefficients

In this paper, the notions of subgradient, subdifferential, and differential with respect to convex fuzzy mappings are investigated, which provides the basis for the fuzzy extremum problem theory. We consider the problems of minimizing or maximizing a convex fuzzy mapping over a convex set and develop the necessary and/or sufficient optimality conditions. Furthermore, the concept of saddle-points and minimax theorems under fuzzy environment is discussed. The results obtained are used to formulate the Lagrangian dual of fuzzy programming. Under certain fuzzy convexity assumptions, KKT conditions for fuzzy programming are derived, and the “perturbed” convex fuzzy programming is considered. Finally, these results are applied to fuzzy linear programming and fuzzy quadratic programming.     

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.     

A GP-AHP method for solving group decision-making fuzzy AHP problems

The analytic hierarchy process (AHP) elicits a corresponding priority vector interpreting the preferred information from the decision-maker(s), based on the pairwise comparison values of a set of objects. Since pairwise comparison values are the judgments obtained from an appropriate semantic scale, in practice the decision-maker(s) usually give some or all pair-to-pair comparison values with an uncertainty degree rather than precise ratings. By employing the property of goal programming (GP) to treat a fuzzy AHP problem, this paper incorporates an absolute term linearization technique and a fuzzy rating expression into a GP-AHP model for solving group decision-making fuzzy AHP problems. In contrast to current fuzzy AHP methods, the GP-AHP method developed herein can concurrently tackle the pairwise comparison involving triangular, general concave and concave–convex mixed fuzzy estimates under a group decision-making environment.

Scope and purpose

Many real world decision problems involve multiple criteria in qualitative domains. As expected, such problems will be increasingly modeled as multiple criteria decision-making problems, which involve scoring on subjective/qualitative domains. This results in a class of significant problems for which an evaluation framework, which handles occurrences of seeming intransitivity and inconsistency will be required. Another interesting issue of group decision-making analysis is how to deal with disagreements between two or more different rankings within an alternative set. These phenomena are likely to appear in qualitative/subjective domains where the decision-making environment is ambiguous and vague. Therefore, this study proposes a GP-AHP model that is sufficiently robust to permit conflict and imprecision. Numerical examples demonstrate the effectiveness and applicability of the proposed models in deriving the most promising priority vector from a fuzzy AHP problem within a group decision-making environment.     

Multi-objective inventory models of deteriorating items with some constraints in a fuzzy environment

In this paper, multi-item inventory models of deteriorating items with stock-dependent demand are developed in a fuzzy environment. Here, the objectives of maximizing the profit and minimizing the wastage cost are fuzzy in nature. Total average cost, warehouse space, inventory costs, purchasing and selling prices are also assumed to be vague and imprecise. The impreciseness in the above objective and constraint goals have been expressed by fuzzy linear membership functions and that in inventory costs and prices by triangular fuzzy numbers (TFN). Models have been solved by the fuzzy non-linear programming (FNLP) method based on Zimmerman [Zimmermann, H.-J., Fuzzy linear programming with several objective functions. Fuzzy Sets and Systems, 1978, 1, 46-55] and Lee and Li [Lee, E. S. and Li, R. J., Fuzzy multiple objective programming and compromise programming with Pareto optima. Fuzzy Sets and Systems, 1993, 53, 275-288]. These are illustrated with numerical examples and results of one model are compared with those obtained by the fuzzy additive goal programming (FAGP) [Tiwari, R. N., Dharmar, S. and Rao, J. R., Fuzzy goal programming: an additive model. Fuzzy Sets and Systems, 1987, 24, 27-34] method.     

A fuzzy bi-criteria transportation problem

In this paper, a fuzzy bi-criteria transportation problem is studied. Here, the model concentrates on two criteria: total delivery time and total profit of transportation. The delivery times on links are fuzzy intervals with increasing linear membership functions, whereas the total delivery time on the network is a fuzzy interval with a decreasing linear membership function. On the other hand, the transporting profits on links are fuzzy intervals with decreasing linear membership functions and the total profit of transportation is a fuzzy number with an increasing linear membership function. Supplies and demands are deterministic numbers. A nonlinear programming model considers the problem using the max–min criterion suggested by Bellman and Zadeh. We show that the problem can be simplified into two bi-level programming problems, which are solved very conveniently. A proposed efficient algorithm based on parametric linear programming solves the bi-level problems. To explain the algorithm two illustrative examples are provided, systematically.     

Interval analysis using least squares support vector fuzzy regression

A least squares support vector fuzzy regression model(LS-SVFR) is proposed to estimate uncertain and imprecise data by applying the fuzzy set principle to weight vectors.This model only requires a set of linear equations to obtain the weight vector and the bias term,which is different from the solution of a complicated quadratic programming problem in existing support vector fuzzy regression models.Besides,the proposed LS-SVFR is a model-free method in which the underlying model function doesn’t need to be predefined.Numerical examples and fault detection application are applied to demonstrate the effectiveness and applicability of the proposed model.