A New Intuitionistic Fuzzy Goal Programming Approach to Develop a New Product

Document Type: Research Paper


1 Department of Industrial Engineering, University of Hormozgan, Bandarabbas, Ira

2 Department of Engineering, University of Kurdistan, Sanandaj, Iran


The intuitive fuzzy set theory has attracted many researchers of various fields. Intuitive fuzzy set is a generalization of fuzzy set which offers a new way to express uncertainty by determining the membership and non-membership degree. The intuitive fuzzy set in an ideal planning model in the new product development process, is combined in this study. In this model, considering the threshold values for each ideal by intuitive fuzzy numbers, the allocations for each supplier and the appropriate assembly process in a new product development process at the same time were determined. Besides, the importance of targets including linguistic expressions is determined. Finally, a numerical example explains the fuzzy sets use in a goal programming intuitive model.


Main Subjects

  1. Maffin, D., and Braiden, P., (2001). “Manufacturing and supplier roles in product development”, International Journal of Production Economics., , Vol. 69, No. 2, PP. 205–213.
  2. Herrera-Viedma, E., Chiclana, F., Herrera, F., and Alonso, S. (2007). “A Group decision-making model with incomplete fuzzy preference relations based on additive consistency”, IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B., Vol. 37, No. 1, PP. 176–189.
  3. Deschrijver, G., and Kerre, E. E. (2003). “On the composition of intuitionistic fuzzy relations”, Fuzzy Sets Systems.,  Vol. 136, No. 3, PP. 333–361.
  4. Herrera, F., Martinez, L., and Sánchez, P. J. (2005). “Managing non-homogeneous information in group decision making”, European Journal of Operational Research., Vol. 166, No. 1, PP. 115–132.
  5. Szmidt, E., and Kacprzyk, J. (1998). “Group decision making under intuitionistic fuzzy preference relations”, in Traitement d’information et gestion d’incertitudes dans les syst{è}mes {à} base de connaissances. Conf{é}rence internationale., PP. 172–178.
  6. Szmidt, E., and Kacprzyk, J. (2002). “Using intuitionistic fuzzy sets in group decision making”,  Control and Cybernetics., Vol. 31, PP. 1055–1057.
  7. Xu, Z., and Yager, R. R. (2006). “Some geometric aggregation operators based on intuitionistic fuzzy sets”, International Journal of General Systems., Vol. 35, No. 4, PP. 417–433.
  8. Xu, Z. (2007). “Intuitionistic preference relations and their application in group decision making”, Information Sciences.,Vol. 177, No. 11, PP. 2363–2379.
  9. Atanassov, K. T. (1986). “Intuitionistic fuzzy sets”, Fuzzy sets Systems., Vol. 20, No. 1, PP. 87–96.
  10. Yue, Z. (2014). “TOPSIS-based group decision-making methodology in intuitionistic fuzzy setting”, Information Sciences., No. 277, PP. 141–153.
  11. Chen, T. Y. (2014). “The extended linear assignment method for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets”, APPLIED MATHEMATICAL MODELLING., Vol. 38, No. 7, PP. 2101–2117.
  12. Dowlatshahi, S. (1999). “A modeling approach to logistics in concurrent engineering”, European Journal of Operational Research., Vol. 115, No. 1, PP. 59–76.
  13. Büyüközkan, G., and Feyziog̃lu, O. (2004). “A fuzzy-logic-based decision-making approach for new product development”, International Journal of Production Economics., Vol. 90, No. 1, PP. 27–45.
  14. Ragatz, G. L., Handfield, R. B., and Petersen, K. J. (2002). “Benefits associated with supplier integration into new product development under conditions of technology uncertainty”, Journal of Business Research., Vol. 55, No. 5, PP. 389–400.
  15. Nepal, B., Monplaisir, L., and Singh, N. (2005). “Integrated fuzzy logic-based model for product modularization during concept development phase”, International Journal of Production Economics., Vol. 96, No. 2, PP. 157–174.
  16. Xu, L., Li, Z., Li, S., and Tang, F. (2007). “A decision support system for product design in concurrent engineering” , Decision Support Systems., Vol. 42, No. 4, PP. 2029–2042.
  17. Wang, G., Huang, S. H., and Dismukes, J. P. (2004). “Product-driven supply chain selection using integrated multi-criteria decision-making methodology”, International Journal of Production Economics., Vol. 91, No. 1, PP. 1–15.
  18. Lamghabbar, A., Yacout*, S., and Ouali, M. S., (2004). “Concurrent optimization of the design and manufacturing stages of product development”, International Journal of Production Economics., Vol. 42, No. 21, PP. 4495–4512.
  19. Schniederjans, M. J., and Hong, S. (1996). “Multiobjective concurrent engineering: A goal programming approach”, IEEE Transactions on Engineering Management., Vol. 43, No. 2, PP. 202–209.
  20. Fine, C. H., Golany, B., and Naseraldin, H. (2005). “Modeling tradeoffs in three-dimensional concurrent engineering: a goal programming approach”, Journal of Operations Management., Vol. 23, No. 3, PP. 389–403.
  21. Zadeh, L. A. (1965). “Fuzzy sets”,  Information and Control., Vol. 8, No. 3, PP. 338–353.
  22. Szmidt, E., Kacprzyk, J., and Bujnowski, P. (2014). “How to measure the amount of knowledge conveyed by Atanassov’s intuitionistic fuzzy sets”, Information Sciences.,  Vol. 257, PP. 276–285.
  23. Xu, Z., and Liao, H. (2014). “Intuitionistic fuzzy analytic hierarchy process”, IEEE Transactions onFuzzy Systems., Vol. 22, No. 4, PP. 749–761.
  24. Atanassov, K. T. (2008). “My personal view on intuitionistic fuzzy sets theory,” in Fuzzy Sets and Their Extensions: Representation, Aggregation and Models, PP. 23–43.
  25. Liao, H., and Xu, Z. (2014). “Intuitionistic fuzzy hybrid weighted aggregation operators”, International Journal of Intelligent Systems., Vol. 29, No. 11, PP. 971–993.
  26. Chen, R. Y. (2009). “A problem-solving approach to product design using decision tree induction based on intuitionistic fuzzy”, European Journal of Operational Research., Vol. 196, No. 1, PP. 266–272.
  27. Chen, Y., and Li, B. (2011). “Dynamic multi-attribute decision making model based on triangular intuitionistic fuzzy numbers”, Scientia Iranica., Vol. 18, No. 2, PP. 268–274.
  28. Das, S., and Guha, D. (2016). “A centroid-based ranking method of trapezoidal intuitionistic fuzzy numbers and its application to MCDM problems”, Fuzzy Information and Engineering., Vol. 8, No. 1, PP. 41–74.
  29. Li, K. W., and Wang, Z. (2010). “Notes on multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment”, Journal of Systems Science and Systems Engineering., Vol. 19, No. 4, PP. 504–508.
  30. Xu, Z., and Yager, R. R. (2008). “Dynamic intuitionistic fuzzy multi-attribute decision making”,  International Journal of Approximate Reasoning., Vol. 48, No. 1, PP. 246–262.
  31. Yu, D. (2012). “Group decision making based on generalized intuitionistic fuzzy prioritized geometric operator”,  International Journal of Intelligent Systems., Vol. 27, No. 7, PP. 635–661.
  32. Zavadskas, E. K., Antucheviciene, J., Razavi Hajiagha, S. H., and Hashemi, S. S. (2015). “The interval-valued intuitionistic fuzzy MULTIMOORA method for group decision making in engineering”, Mathematical Problems in Engineering., Vol. 2015, Article ID 560690, 13 pages.
  33. Zhang, X., and Xu, Z. (2012). “A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making”, Fuzzy Optimization and Decision Making., Vol. 11, No. 2, PP. 135–146.
  34. Li, D. F., Wang, Y. C., Liu, S., and Shan, F. (2009). “Fractional programming methodology for multi-attribute group decision-making using IFS”, Applied Soft Computing Journal., Vol. 9, No. 1, PP. 219–225.
  35. Mukherjee, S., and Basu, K. (2011). “Solving intuitionistic fuzzy assignment problem by using similarity measures and score functions”, International Journal of Pure and Applied Sciences and Technology., Vol. 2, No. 1, PP. 1–18.
  36. Jana, B., and Roy, T. K. (2007). “Multi-objective intuitionistic fuzzy linear programming and its application in transportation model”, Notes Intuitionistic Fuzzy Sets, Vol. 13, No. 1, PP. 34–51.
  37. Boran, F. E., Boran, K., and Menlik, T. (2012). “The evaluation of renewable energy technologies for electricity generation in Turkey using intuitionistic fuzzy TOPSIS”, Energy Sources, Part B Economics. Planning, Policy, Vol. 7, No. 1, PP. 81–90.
  38. Ning, X., Lam, K. C., and Lam, M. C. K. (2011). “A decision-making system for construction site layout planning”, Automation in Construction., Vol. 20, No. 4, PP. 459–473.
  39. Chai, J., Liu, J. N. K., and Xu, Z. (2012). “A new rule-based SIR approach to supplier selection under intuitionistic fuzzy environments”, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems., Vol. 20, No. 3, PP. 451–471.
  40. Wang, Y. (2012). “An approach to software selection with triangular intuitionistic fuzzy information”,  International Journal of Computational Intelligence Systems., Vol. 4, No. 2.
  41. Szmidt, E., and Kacprzyk, J. (2001). “Intuitionistic fuzzy sets in some medical applications”, in International Conference on Computational Intelligence, PP. 148–151.
  42. Neog, T. J., and Sut, D. K. (2011). “An application of fuzzy soft sets in medical diagnosis using fuzzy soft complement”, International Journal of Computer Applications., Vol. 33, No. 9.
  43. Gerogiannis, V. C., Fitsilis, P., and Kameas, A. D. (2011). “Using a combined intuitionistic fuzzy set-TOPSIS method for evaluating project and portfolio management information systems”, in Artificial Intelligence Applications and Innovations, PP. 67–81.
  44. Dey, S., and Roy, T. K. (2015). “Intuitionistic Fuzzy Goal Programming Technique for Solving Non-Linear Multi-objective Structural Problem”, Journal of Fuzzy Set Valued Analysis., Vol. 2015, No. 3, PP. 179–193.
  45. Ghosh, P., Roy, T. K., and Majumder, C. (2016). “Optimization of industrial wastewater treatment using intuitionistic fuzzy goal geometric programming problem”, Fuzzy Information and Engineering., Vol. 8, No. 3, PP. 329–343.
  46. Atnassov, K. (1999). “Intuitionistic fuzzy sets: Theory and applications”, Physica-Verlag.
  47. Charnes, A., and Cooper, W. W. (1957). “Management models and industrial applications of linear programming”, Management Science.,Vol. 4, No. 1, PP. 38–91.
  48. Boran, F. E., Genç, S., Kurt, M. and Akay, D. (2009). “A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method”,  Expert Systems with Applications., Vol. 36, No. 8, PP. 11363–11368.