Using Fuzzy and Grey Theory to Improve Green Design in QFD Processes

Using Fuzzy and Grey Theory to Improve Green Design in QFD Processes Chih-Hung Hsu, Tzu-Yuan Lee, Wei-Yin Lu, Jun-Jia Lin, Hai-Fen Lin * Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsin-Chu, 300, Taiwan, R.O.C. * Abstract: The green life cycle design is critical issue for improving bicycle design. Quality function deployment has been successfully applied in a number of fields. However, little study has been done in the integrated approach involving grey relational analysis, fuzzy integral, fuzzy theory of analyzing the necessary quality characteristics for the bicycle design in the design process. The proposed method transforms the process design, usage, package, and abortion in different stages into product s design characteristics applying techniques form grey relational analysis, fuzzy integral, fuzzy theory to insight the voices of customers. Questionnaire is used to get the necessary data in this study. The results showed that the important attributes for consumers. Several important and unimportant technical characteristics and customer attributes were identified and analyzed. The results of this study can provide an effective procedure for improving product s design characteristics, enhancing customer satisfaction and green design for bicycle in the marketplace. Keywords: Green design, Bicycle, Grey theory, Fuzzy theory, Green QFD. 1.Introduction 1.1 Background & Motivation of Study Operation methods and consumer preferences of riding a bike vary depending on differences in geographical locality, national characteristics, and economic development resulting in divergence in the primary purpose of bike products by consumers from different countries. Therefore, this study attempts to explore into consumer needs through survey by questionnaires with the findings for reference by manufacturers of bike products an in-depth understanding of requirements of green design, extent of acceptance, and the willingness to buy. 1.2 Background & Motivation of Study There two purposes for this study attempts to achieve: 1. To understand priorities of importance, satisfaction, and extent of seriousness attached to various factors about the bike by consumers and whether there is significance variation existing among consumers; and 2. To understand what properties valued most by consumers through three types of analysis, respectively, Fuzzy, grey relation analysis, and quality mechanism while providing reference by bike manufacturers in realizing green design for their products. 2. Documentary Research & Discussion 2.1. Fuzzy Prof. L.A. Zadeh from Berkeley University, California, USA, published in a periodical journal Information and Control an article of Fuzzy Sets in 1965 9. Fuzzy has its original meanings of being fluffy, somnolent, blurred; and in Chinese usually translated into blur by free translation, or transliterated. All these translations are usually misleading to the wrong impression that Fuzzy is a blurred theory. In fact, Fuzzy is related to a discipline of science developed to solve those blurred phenomena generally existing in the real world and to express certain fuzzy concepts that prevent precise definition, and it has achieve very impressive results particularly in expressing the fuzziness specific to human language. 8 Fuzzy is indeed a general term for theories of fuzzy sets, fuzzy relation, fuzzy logics, fuzzy control, fuzzy measurement, etc., that is generally referred as fuzzy mathematics by experts in China. 2.2. Grey Relation Analysis ISBN: 978-960-6766-57-2 225 ISSN: 1790-5109

Prof. Julong DENG, a scholar from China teaching at Huazhong University proposed Grey Theory in 1982 1 2, wherein the Grey Relation Analysis, one of two mainstays of the Grey theory series, is related to a method for measuring correlation among discrete sequences. 10 Grey Relation Analysis, one of the Grey theory, is a system applied in processing incomplete message and non-uniqueness and can be also applied in system relation analysis, grey modeling, predication, and decision-making tasks. Having been developed for more than a decade, the Grey Relation Analysis method has been recently applied consecutively by experts in conjunction with other methods to not only correct flaws found in the application of the Grey Relation Analysis method but also improve benefits in the use of Grey Relation Analysis. 2.3. Grey Relation Analysis Yoji Akao 11 believes that the quality mechanism development in its broad sense is related to Quality Development (QD) and a generalized term for quality mechanism in its narrow sense. Quality Development is related to a set of systematic technical method that involves specifying product or service design standards depending on substitutive characteristics converted from customer needs before developing as planned the quality designed to the quality of each mechanical part and service item and the mutual relation among elements or services in the manufacturing process for earlier completion of quality assurance of products or services in meeting customer requirements. 2.4. Green Design Life Cycle Design (LCD) constitutes the central though of green design with the design not only focusing on how to reclaim the exiting refuses, but, and more importantly, on how to foresee possible impacts right in the stage of conceptual development of the product by engineers thus to design the product angling from reduction of impacts upon the environment and minimizing impacts of the product on the ecologic environment. 5 3.Empirical Verification In the survey by questionnaires conducted in this study, sampling was taken at random, and Likert 5-point scale was used as the scoring system to measure the extent of agreement or disagreement, respectively strongly regarded, regarded, neither regarded nor disregarded, disregard, and strongly disregarded ; and in terms of satisfaction, strongly satisfied, satisfied, neither satisfied nor dissatisfied, dissatisfied, and strongly dissatisfied ; and in terms of extent of seriousness, very serious, serious, neither serious nor not serious, not serious, and not serious at all while in each category of scale, scores of 5, 4, 3, 2, and 1 are given in sequence. Valid responses of 320 copies were received as a base for study and analysis. 3.1. Quality House This study employed green quality development and gap 5 in SERVQUAL dimensions (gap between as recognized and as expected) in the construction of a bike quality house. According to documentary research and interviews with professionals, quality elements are classified into seven types of properties and further division into thirty items; and quality characteristics are classified into four aspects that are further converted into fifteen items as shown in Table 1. ISBN: 978-960-6766-57-2 226 ISSN: 1790-5109

VOC Appearance Functionality Reliability Responsiveness Service Popularity Environmental VOE Table 1: Quality House of Bike Mfg. Process Design Use Refuses Functional Design Safety Coefficient Styling 3 9 3.9 3.9 3.4 0.01 Color 9 3 3.7 3.8 3.3 0.09 Fashion 1 3.5 3.7 3.3 0.19 quality sense 9 1 4.1 3.9 3.6 0.19 Front absorber 1 3 1 4.1 4.0 3.9 0.14 Rear absorber 1 3 1 4.0 3.9 3.7 0.11 Speed changing function 77 3 1 4.2 4.0 3.9 0.10 Folding function 9 1 3.0 3.5 3.0 0.50 Easy portability 9 9 3.7 3.7 3.3 0.01 Glove rack 1 2.7 3.2 2.7 0.48 Front warning lamp 9 3.9 3.8 3.6 0.06 Horn or buzzer 3 3.6 3.7 3.4 0.1 Rear warning lamp 9 4.0 4.0 3.7 0.01 Bike-laden tools 1 3.4 3.5 3.1 0.11 Agile gear switching 1 4.2 4.0 4.0 0.19 Agile braking strength 9 4.5 4.2 4.1 0.26 Width of handle 3 3.7 3.7 3.4 0.00 Size of bike 3 1 3.8 3.8 3.4 0.01 Size of rim 1 1 3.6 3.6 3.3 0.08 After sale service 1 4.3 3.9 3.8 0.39 Easy parts replacement 1 4.0 3.8 3.6 0.14 Duration 9 3 4.3 3.9 3.8 0.4 Assembly quality 3 4.3 3.9 3.8 0.34 International leading brand 1 1 1 3.3 3.6 3.0 0.25 Local leading brand 1 1 3.4 3.6 3.0 0.15 Added value 1 1 1 1 1 1 3.4 3.6 3.1 0.14 Parts allowing detailed 3.8 3.7 3.7 0.02 9 1 breakdown for service Parts compatibility 1 1 3 4.1 3.8 3.7 0.32 Impacts of waived parts on 3.9 3.8 3.7 0.08 1 1 1 3 3 3 3 environment and reuse of parts 3.7 3.7 3.7 0.04 1 1 1 3 3 1 and accessories Tire Transmission Chain Extent of Respect Competition Criteria Scores of SERVQAL 1. Relation Matrix: 9 indicates strong relation between two items; 3, medium, and 1, weak. 2. Extent of Respect: averaged scores of extent of respect. 3. Competition criteria: averaged scores of extent of satisfaction. 4. s: extent of impact from accident occurrence under this question is solved by the averaged scores of extent of serious in the questionnaires. 5. SERVQUAL scores: the gap between averaged scores of extent of respect and average scores of extent of satisfaction. 3.2. Fuzzy ISBN: 978-960-6766-57-2 227 ISSN: 1790-5109

This study employed the triangular fuzzy number integral value method to solve fuzzy values of quality characteristics of the product and rankings of those values are shown in Table 2. VOE VOC Appearance Functionality Reliability Responsiveness Service Popularity Environmental Table 2: Development of Fuzzy Green Quality Mechanism Mfg. Process Design Use Refuses Tire Safety Coefficient Functional Design Transmission Chain Styling 0.97 1.39 3.9 3.9 3.4 0.01 Color 9.72 6.77 3.7 3.8 3.3 0.09 Fashion 7.77 3.5 3.7 3.3 0.19 quality sense 23.1 9.11 4.1 3.9 3.6 0.19 Front absorber 7.21 12.8 7.21 4.1 4.0 3.9 0.14 Rear absorber 5.47 9.68 5.47 4.0 3.9 3.7 0.11 Speed changing function 10.1 5.71 4.2 4.0 3.9 0.10 Folding function 45 17.7 3.0 3.5 3.0 0.50 Easy portability 0.64 0.64 3.7 3.7 3.3 0.01 Glove rack 13.9 2.7 3.2 2.7 0.48 Front warning lamp 7.17 3.9 3.8 3.6 0.06 Horn or buzzer 7.28 3.6 3.7 3.4 0.1 Rear warning lamp 1.93 4.0 4.0 3.7 0.01 Bike-laden tools 4.28 3.4 3.5 3.1 0.11 Agile gear switching 10.4 4.2 4.0 4.0 0.19 Agile braking strength 39.3 4.5 4.2 4.1 0.26 Width of handle 0.23 3.7 3.7 3.4 0.00 Size of bike 1.18 0.67 3.8 3.8 3.4 0.01 Size of rim 3.25 3.25 3.6 3.6 3.3 0.08 After sale service 19.6 4.3 3.9 3.8 0.39 Easy parts replacement 6.56 4.0 3.8 3.6 0.14 Duration 50.6 35.3 4.3 3.9 3.8 0.4 Assembly quality 30.3 4.3 3.9 3.8 0.34 International leading brand 8.98 8.98 8.98 3.3 3.6 3.0 0.25 Local leading brand 5.64 5.64 3.4 3.6 3.0 0.15 Added value 5.49 5.49 5.49 5.49 5.49 5.49 3.4 3.6 3.1 0.14 Parts allowing detailed 3.28 1.29 3.8 3.7 3.7 0.02 breakdown for service Parts compatibility 15.1 15.1 4.1 3.8 3.7 0.32 Impacts of waived parts on 3.83 3.83 3.83 6.77 6.77 6.77 6.77 3.9 3.8 3.7 0.08 environment and reuse of parts and accessories 1.84 1.84 1.84 3.26 3.26 1.84 3.7 3.7 3.7 0.04 Total 25.2 99.5 46.9 17.2 36 141 102 5.67 5.67 31.2 20.2 6.77 8.75 18.8 15.4 Sequencing 7 3 4 10 5 1 2 14 14 6 8 13 12 9 11 Extent of Respect Competition Criteria Scores of SERVQAL 3.2.1 Operation of Development If Ã=(a1,a2,a3), and Ẽ=(b1,b2,b3) are related to two triangular fuzzy numbers, then the arithmetic operation methods respectively for addition +, subtraction -, multiplication *, and division are ISBN: 978-960-6766-57-2 228 ISSN: 1790-5109

shown as follows 3 4 : Addition: Ã + Ẽ = (a1, a2, a3) + (e1, e2, e3) = (a1 + e1, a2 + e2, a3 + e3) Subtraction: Ã - Ẽ = (a1, a2, a3) - (e1, e2, e3) = (a1 - e3, a2 - e2, a3 - e1) Multiplication: Ã * Ẽ = (a1, a2, a3) * (e1, e2, e3) = (a1 * e1, a2 * e2, a3 * e3) Division: Ã / Ẽ = (a1, a2, a3) / (e1, e2, e3) = (a1 / e3, a2 / e2, a3 / e1) 3.2.2 Triangular Fuzzy Number Figure 1 shows the triangular fuzzy number of linguistic value adopted and its associate functions. Linguistic Value Fuzzy Number Associate Functions 1 1 =(0,2.5,5) x / 2.5, 0 x 2.5 μ (x)= 1 (5 x) / 2.5, 2.5 x 5 3 3 =(2.5,5,7.5) 9 9 =(5,7.5,10) μ (x)= 3 (x - 2.5) / 2.5, 2.5 x 5 (7.5 x) / 2.5, 5 x 7.5 (x 5) / 2.5, 5 x 7.5 μ (x)= 9 (10 x) / 2.5, 7.5 x 10 Fig. 1: Triangular Fuzzy Number & Its Associate Functions 3.2.3 Fuzzy Number Integral Value Formula 1 shows The triangular fuzzy number integral value 6 7 : 3.3. Grey Relation Analysis (1) Quality house must be first digitalized since the greater the better principle applies to digital conversion in performing Grey Relation Analysis, the digits are then standardized to proceed computation of grey relation coefficients before solving the grey relation, and finally the grey relation values are solved and given rankings as shown in Table 3. 1. Standardization: In {P(X);Γ}, sequence xi=( xi(1), xi(2),,xi(k)), Wherein, I=0,, m, k=1,,n, i.e., x0=( x0 (1), x0 (2),,x0 (k)) x1=( x1 (1), x1 (2),,x1 (k)) xm=( xm (1), xm (2),, xm (k)) 2. Solving the difference sequence: (2) 3. Assortment of relation coefficients (3) The parameterζ is referred as an identification coefficient; and is generally designated with a value of 0.5. 4. Solving the Relation: xcompetition Criteria SERVQAL (4) ISBN: 978-960-6766-57-2 229 ISSN: 1790-5109

VOC Appearance Functionality Reliability Responsiveness Service Popularity Environmental VOE Table 3: Development of Grey Relation Green Quality Mechanism Mfg. Process Design Use Refuses Functional Design Safety Coefficient Styling 0.07 0.06 0.06 0.06 0.17 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 3.9 3.9 3.4 0.01 Color 1.18 0.39 0.39 0.39 0.5 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 3.7 3.8 3.3 0.09 Fashion 0.8 0.8 0.8 0.8 0.86 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 3.5 3.7 3.3 0.19 quality sense 0.93 2.8 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 1.01 0.93 0.93 0.93 0.93 4.1 3.9 3.6 0.19 Front absorber 0.74 0.74 0.74 0.8 0.74 0.95 0.8 0.74 0.74 0.74 0.74 0.74 0.74 0.74 0.74 4.1 4.0 3.9 0.14 Rear absorber 0.56 0.56 0.56 0.61 0.56 0.72 0.61 0.56 0.56 0.56 0.56 0.56 0.56 0.56 0.56 4.0 3.9 3.7 0.11 Speed changing function 0.59 0.59 0.59 0.59 0.59 0.75 0.59 0.59 0.59 0.63 0.59 0.59 0.59 0.59 0.59 4.2 4.0 3.9 0.10 Folding function 1.82 1.82 5.46 1.82 1.82 1.97 1.82 1.82 1.82 1.82 1.82 1.82 1.82 1.82 1.82 3.0 3.5 3.0 0.50 Easy portability 0.03 0.03 0.08 0.08 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 3.7 3.7 3.3 0.00 Glove rack 1.43 1.43 1.43 1.43 1.43 1.54 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 2.7 3.2 2.7 0.48 Front warning lamp 0.29 0.29 0.29 0.29 0.29 0.29 0.87 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 3.9 3.8 3.6 0.06 Horn or buzzer 0.42 0.42 0.42 0.42 0.42 0.42 0.54 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 3.6 3.7 3.4 0.1 Rear warning lamp 0.08 0.08 0.08 0.08 0.08 0.08 0.23 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 4.0 4.0 3.7 0.01 Bike-laden tools 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.47 0.44 0.44 0.44 0.44 3.4 3.5 3.1 0.11 Agile gear switching 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.15 1.06 1.06 1.06 1.06 1.06 4.2 4.0 4.0 0.19 Agile braking strength 1.59 1.59 1.59 1.59 1.59 1.59 4.76 1.59 1.59 1.59 1.59 1.59 1.59 1.59 1.59 4.5 4.2 4.1 0.26 Width of handle 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 3.7 3.7 3.4 0.01 Size of bike 0.07 0.07 0.09 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 3.8 3.8 3.4 0.01 Size of rim 0.33 0.33 0.33 0.36 0.33 0.33 0.36 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 3.6 3.6 3.3 0.08 After sale service 2.01 2.01 2.01 2.01 2.01 2.17 2.01 2.01 2.01 2.01 2.01 2.01 2.01 2.01 2.01 4.3 3.9 3.8 0.39 Easy parts replacement 0.67 0.67 0.67 0.67 0.67 0.73 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 4.0 3.8 3.6 0.14 Duration 2.05 6.14 2.05 2.05 2.05 2.63 2.05 2.05 2.05 2.05 2.05 2.05 2.05 2.05 2.05 4.3 3.9 3.8 0.4 Assembly quality 1.76 1.76 1.76 1.76 1.76 1.76 2.26 1.76 1.76 1.76 1.76 1.76 1.76 1.76 1.76 4.3 3.9 3.8 0.34 International leading brand 1 1 0.92 0.92 1 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 3.3 3.6 3.0 0.25 Local leading brand 0.58 0.62 0.58 0.58 0.62 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 3.4 3.6 3.0 0.15 Added value 0.61 0.61 0.56 0.56 0.61 0.56 0.56 0.56 0.56 0.56 0.56 0.56 0.61 0.61 0.61 3.4 3.6 3.1 0.14 Parts allowing detailed 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.4 0.14 3.8 3.7 3.7 0.02 breakdown for service Parts compatibility 1.55 1.55 1.55 1.55 1.55 1.68 1.55 1.55 1.55 1.68 1.55 1.55 1.55 1.99 1.55 4.1 3.8 3.7 0.32 Impacts of waived parts on 0.39 0.42 0.39 0.39 0.39 0.39 0.39 0.42 0.42 0.39 0.5 0.5 0.39 0.5 0.5 3.9 3.8 3.7 0.08 environment and reuse of parts 0.19 0.2 0.19 0.19 0.19 0.19 0.19 0.2 0.2 0.19 0.19 0.19 0.24 0.24 0.2 3.7 3.7 3.7 0.04 and accessories Total 23.4 28.6 26.2 22.6 22.9 24.2 27.1 22.5 22.5 22.7 22.7 22.6 22.5 23.4 22.6 Sequencing 5 1 3 10 7 4 2 14 14 8 9 12 13 6 11 Tire Transmission Chain Extent of Respect Competition Criteria Scores of SERVQAL ISBN: 978-960-6766-57-2 230 ISSN: 1790-5109

4.Conclusion Comparison among three ranking methods, respectively, Fuzzy, Grey Relation Analysis, and Development of Quality Mechanism is listed in Table 5 below Table 5: Comparison among Three Ranking Methods Transmission Chain Outer tube Safety Coefficient Functional Design Fuzzy Ranking 7 3 4 10 5 1 2 14 14 6 8 13 12 9 11 Grey Relation Analysis Ranking 5 1 3 10 7 4 2 14 14 8 9 12 13 6 11 As observed from Table 5, it is found that the ranking variance is very significant between a former ranking and a latter ranking after having performed mutual comparison among results of three types of computations. In the rankings of Fuzzy, the highest extent of satisfaction falls on the item of Functional Design, followed by Safety Coefficient,,, and Overall Styling in sequence; with the rankings of Grey Relation Analysis, the item of s has the highest extent of satisfaction, followed by Safety Coefficient, and in sequence; Among those findings described above, Fuzzy is function oriented; and Grey Relation Analysis, quality oriented. Therefore, to achieve the optimal results, manufacturers may carry out their efforts on product improvement by priority in terms of the orientation that is highest respected, and those quality characteristics that are least and most satisfied. Acknowledgment The study was supported by the National Science Council, NSC 96-2815-C-164-001-E, Taiwan. The author would like to thank the anonymous reviewers for comments on a previous draft of this article. References 1. Deng, G. L. (2000)., Multiple Ggrey Planning, University Press, China. 2. Deng, J. L. (1988). Properties of relational space for grey system, In Essential Topics on Grey System Theory and Applications, pp.1-13. Beijing: China Ocean. 3. Dubois, D. and Prade, H. (1980)., Fuzzy Set and System: Theory and Applications, Academic Press, New York. 4. Dubois, D. and Prade, H. (1983)., Ranking Fuzzy Numbers in the Setting of Possibility Theory, Information Sciences, No.30, pp.183-224. 5. Guo, C. J. (2002)., Green Design, Industrial Magazine, No.2, pp.45-54. 6. Liou, T. S. and Kang, B. Z. (2003)., Evaluation of the Quality of Work Life Using Fuzzy Linguistic Terms, Quality Magazine, No.8, pp.49-55. 7. Liou, T. S. and Wang, M. J. (1992)., Ranking Fuzzy Numbers with Integral Value, Fuzzy Sets and System, No.50, pp.247-255. 8. Sun, Z. Y. and Yang, Y. K. (1994)., Fuzzy control, Quan Hua, Taipei. 9. Wang, W. G. (2001)., Fuzzy, Quan Hua, Taipei. 10. Wen, K. L., Huang, Y. N., Zhang, W. Z., Zhang, T. Z., You, M. L., and Lai, J. R. (2003)., Grey Relational Analysis Fuzzy, Gao Li, Taipei. 11. Yoji, A. (1991)., Quality Function Deployment, China Productivity Center, Taipei. ISBN: 978-960-6766-57-2 231 ISSN: 1790-5109