Research Article
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Year 2019, Volume: 48 Issue: 3, 845 - 858, 15.06.2019

Amin Vahidi

Abstract

References

  • Attari H. and Nasseri S. H. , New Concepts of Feasibility and Efficiency of Solutions in Fuzzy Mathematical Programming Problems, Fuzzy Inf. Eng., vol. 6, no. 2, pp. 203221, Jun. 2014.
  • Azadeh A. , Moghaddam M. ,Khakzad M., and Ebrahimipour V., A flexible neural network- fuzzy mathematical programming algorithm for improvement of oil price es-timation and forecasting, Comput. Ind. Eng., vol. 62, no. 2, pp. 421430, 2012.
  • Azadeh A., Saberi M., Asadzadeh S. M., and Khakestani M., A hybrid fuzzy mathe-matical programming-design of experiment framework for improvement of energy consumption es- timation with small data sets and uncertainty: The cases of USA, Can-ada, Singapore, Pakistan and Iran, Energy, vol. 36, no. 12, pp. 69816992, 2011.
  • Bector C. R. and Chandra S., Fuzzy Mathematical Programming and Fuzzy Matrix Games. Springer, 2005.
  • Bellman R. and Zadeh L. A., Decision Making in a Fuzzy Environment, Manage. Sci., vol. 17, pp. 141164, 1970.
  • BilgenB., Application of fuzzy mathematical programming approach to the produc-tion allocation and distribution supply chain network problem, Expert Syst. Appl., vol. 37, no. 6, pp. 44884495, 2010.
  • Biswas A., and Modak N., A Multiobjective Fuzzy Chance Constrained Programming Model for Land Allocation in Agricultural Sector: A case study, vol. 10. 2017.
  • Carlsson C., and Korhonen P., A Parametric Approach to Fuzzy Linear Programming, Fuzzy Sets Syst., vol. 20, no. 1, pp. 1730, 1986.
  • Chanas S., The Use of Parametric Programming in Fuzzy Linear Programming, Fuzzy Sets Syst., vol. 11, no. 13, pp. 229241, 1983.
  • Cheng C. B,. and Cheng C. J., Available-to-promise based bidding decision by fuzzy mathe- matical programming and genetic algorithm, Comput. Ind. Eng., vol. 61, no. 4, pp. 9931002, 2011.
  • Ebrahimnejad A., Tavana M., Lotfi F. H., Shahverdi R., and Yousefpour M., A three-stage Data Envelopment Analysis model with application to banking industry, Meas-urement, vol. 49, pp. 308319, 2014.
  • Effati S., Pakdaman M., and Ranjbar M., A new fuzzy neural network model for solv-ing fuzzy linear programming problems and its applications, Neural Comput. Appl., vol. 20, no. 8, pp. 12851294, 2011.
  • Ezzati R., Khorram E., and Enayati R., A new algorithm to solve fully fuzzy linear pro- gramming problems using the MOLP problem, Appl. Math. Model., Mar. 2013.
  • Farhadinia B., Sensitivity analysis in interval-valued trapezoidal fuzzy number linear pro- gramming problems, Appl. Math. Model., vol. 38, no. 1, pp. 5062, Jan. 2014.
  • Fazlollahtabar H., Mahdavi I., and Mohajeri A., Applying fuzzy mathematical pro-gramming approach to optimize a multiple supply network in uncertain condition with comparative analysis, Appl. Soft Comput., vol. 13, no. 1, pp. 550562, Jan. 2013.
  • Figueroa-García J. C., Chalco-Cano Y., and Román-Florez H., Distance measures for Inter- val Type-2 fuzzy numbers, Discret. Appl. Math., Dec. 2014.
  • Figueroa-García J. C., Kalenatic D., and Bello C. A. L., An iterative algorithm for fuzzy mixed production planning based on the cumulative membership function, Ingeniería, vol. 16, no. 2, pp. 617, Dec. 2011.
  • Gupta P., Mehlawat M. K., and Saxena A., Asset portfolio optimization using fuzzy math- ematical programming, Inf. Sci. (Ny)., vol. 178, no. 6, pp. 17341755, 2008.
  • Inuiguchi M., and Ichihashi H., Relative modalities and their use in possibilistic linear programming, Fuzzy Sets Syst., vol. 35, no. 3, pp. 303323, 1990.
  • Inuiguchi M., Ichihashi H., and Kume Y., Relationships between modality con-strained programming problems and various fuzzy mathematical programming prob-lems, Fuzzy Sets Syst., vol. 49, no. 3, pp. 243259, 1992.
  • Javadian N., Maali Y., and Mahdavi-Amiri N., Fuzzy linear programming with grades of satisfaction in constraints, Iran. J. Fuzzy Syst., vol. 6, no. 3, pp. 1735, 2009.
  • Kamyad A. V., Hassanzadeh N., and Chaji J., A New Vision on Solving of Fuzzy Linear Programming, in 2009 International Conference on Computational Intelligence and Software Engineering, 2009, pp. 14.
  • Kikuchi S., A method to defuzzify the fuzzy number: transportation problem applica-tion, Fuzzy Sets Syst., vol. 116, no. 1, pp. 39, 2000.
  • Kumar A., Appadoo S. S., and Bector C. R., A note on Generalized fuzzy linear pro- gramming for decision making under uncertainty: Feasibility of fuzzy solutions and solving approach, Inf. Sci. (Ny)., vol. 266, pp. 226227, May 2014.
  • Kumar A., and Kaur J., General Form of Linear Programming Problems with Fuzzy Pa- rameters, J. Appl. Res. Technol., vol. 11, no. 5, pp. 629635, Apr. 2013.
  • Lai Y. J., and Ching-L C.L., Hwang, Fuzzy mathematical programming: methods and applications. Springer Verlag, 1992.
  • Lai Y. J., and Hwang C. L., IFLP-II: A decision support system, Fuzzy Sets Syst., vol. 54, no. 1, pp. 4756, Feb. 1993.
  • León T., Liern V., Ruiz J. L., and Sirvent I., A fuzzy mathematical programming ap-proach to the assessment of efficiency with DEA models, Fuzzy Sets Syst., vol. 139, no. 2, pp. 407419, 2003.
  • Maeda T., Fuzzy linear programming problems as bi-criteria optimization problems, Appl. Math. Comput., vol. 120, no. 13, pp. 109121, 2001.
  • Mitra, K., Gudi D. R., Patwardhan C. S., and Sardar G., Towards resilient supply chains: Uncertainty analysis using fuzzy mathematical programming, Chem. Eng. Res. Des., vol. 87, pp. 967981, 2009.
  • Mula J., Peidro D., and Poler R., The effectiveness of a fuzzy mathematical program-ming approach for supply chain production planning with fuzzy demand, in Interna-tional Journal of Production Economics, 2010, vol. 128, no. 1, pp. 136143.
  • Mula J., Poler R., García-Sabater G. S., and F. C. Lario, Models for production plan-ning under uncertainty: A review, Int. J. Prod. Econ., vol. 103, no. 1, pp. 271285, 2006.
  • Pishvaee M. S., and Razmi J., Environmental supply chain network design using mul- ti-objective fuzzy mathematical programming, Appl. Math. Model., vol. 36, no. 8, pp. 34333446, 2012.
  • Pishvaee M. S., Razmi J., and S. A. Torabi, Robust possibilistic programming for socially responsible supply chain network design: A new approach, Fuzzy Sets Syst., vol. 206, pp. 120, 2012.
  • Rommelfanger H., Fuzzy linear programming and applications, Eur. J. Oper. Res., vol. 92, no. 3, pp. 512527, 1996.
  • Saberi-Najafi H., and Edalatpanah S. A., A note on A new method for solving fully fuzzy linear programming problems, Appl. Math. Model., vol. 37, no. 1415, pp. 78657867, Aug. 2013.
  • Sakawa M., Katagiri H., and Matsui T., Interactive fuzzy random two-level linear program- ming through fractile criterion optimization, Math. Comput. Model., vol. 54, no. 11, pp. 31533163, 2011.
  • Shaocheng T., Interval number and fuzzy number linear programmings, Fuzzy Sets Syst., vol. 66, no. 3, pp. 301306, 1994.
  • Taghizadeh K., Bagherpour M., and Mahdavi I., Application of fuzzy multi-objective linear programming model in a multi-period multi-product production planning prob-lem, Int. J. Comput. Intell. Syst., vol. 4, no. 2, 2011.
  • Vasant P. M., Solving Fuzzy Linear Programming Problems With Modified S-Curve Mem- bership Function, Int. J. Uncertainty, Fuzziness Knowledge-Based Syst., vol. 13, no. 1, pp. 97109, Feb. 2005.
  • Verdegay J. L., Fuzzy mathematical programming, Fuzzy Inf. Decis. Process., vol. 231, p. 237, 1982.
  • Verdegay J. L., A dual approach to solve the fuzzy linear programming problem, Fuzzy Sets Syst., vol. 14, no. 2, pp. 131141, 1984.
  • Wan S.P., and Dong J.Y., Possibility linear programming with trapezoidal fuzzy numbers, Appl. Math. Model., vol. 38, no. 56, pp. 16601672, Mar. 2014.
  • Wan S.P., and Dong J.Y., Interval-valued intuitionistic fuzzy mathematical pro-gramming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees, Inf. Fusion, Feb. 2015.
  • Werners B., An interactive fuzzy programming system, Fuzzy Sets Syst., vol. 23, no. 1, pp. 131147, 1987.
  • Zhang F., Ignatius J., Lim C. P., and Zhao Y., A new method for ranking fuzzy num- bers and its application to group decision making, Appl. Math. Model., vol. 38, no. 4, pp. 15631582, Feb. 2014.
  • Zhu B., and Xu Z., A fuzzy linear programming method for group decision making with additive reciprocal fuzzy preference relations, Fuzzy Sets Syst., vol. 246, pp. 1933, Jul. 2014.
  • Zimmermann H. J., Fuzzy programming and linear programming with several objec-tive functions, Fuzzy Sets Syst., vol. 1, no. 1, pp. 4555, 1978.
  • Zimmermann H. J., Fuzzy Set Theory and Its Applications. 2001.

A New Defuzzification Method for Solving Fuzzy Mathematical Programming Problems

Year 2019, Volume: 48 Issue: 3, 845 - 858, 15.06.2019

Amin Vahidi

Abstract

Solving a certain type of Fuzzy mathematical programming (FMP) require several steps and manual intervention in the solution process. Therefore, it reduces the optimality and increases the solving time. In this research, a methodology is pre-sented that, in addition to being applicable to all types of FMPs, increases optimali-ty and reduces the solving time. The proposed method generates improved solutions in less time and requires less monitoring during the problem-solving proce-dure.

Keywords

Linear programming Fuzzy programming Mathematical programming

References

  • Attari H. and Nasseri S. H. , New Concepts of Feasibility and Efficiency of Solutions in Fuzzy Mathematical Programming Problems, Fuzzy Inf. Eng., vol. 6, no. 2, pp. 203221, Jun. 2014.
  • Azadeh A. , Moghaddam M. ,Khakzad M., and Ebrahimipour V., A flexible neural network- fuzzy mathematical programming algorithm for improvement of oil price es-timation and forecasting, Comput. Ind. Eng., vol. 62, no. 2, pp. 421430, 2012.
  • Azadeh A., Saberi M., Asadzadeh S. M., and Khakestani M., A hybrid fuzzy mathe-matical programming-design of experiment framework for improvement of energy consumption es- timation with small data sets and uncertainty: The cases of USA, Can-ada, Singapore, Pakistan and Iran, Energy, vol. 36, no. 12, pp. 69816992, 2011.
  • Bector C. R. and Chandra S., Fuzzy Mathematical Programming and Fuzzy Matrix Games. Springer, 2005.
  • Bellman R. and Zadeh L. A., Decision Making in a Fuzzy Environment, Manage. Sci., vol. 17, pp. 141164, 1970.
  • BilgenB., Application of fuzzy mathematical programming approach to the produc-tion allocation and distribution supply chain network problem, Expert Syst. Appl., vol. 37, no. 6, pp. 44884495, 2010.
  • Biswas A., and Modak N., A Multiobjective Fuzzy Chance Constrained Programming Model for Land Allocation in Agricultural Sector: A case study, vol. 10. 2017.
  • Carlsson C., and Korhonen P., A Parametric Approach to Fuzzy Linear Programming, Fuzzy Sets Syst., vol. 20, no. 1, pp. 1730, 1986.
  • Chanas S., The Use of Parametric Programming in Fuzzy Linear Programming, Fuzzy Sets Syst., vol. 11, no. 13, pp. 229241, 1983.
  • Cheng C. B,. and Cheng C. J., Available-to-promise based bidding decision by fuzzy mathe- matical programming and genetic algorithm, Comput. Ind. Eng., vol. 61, no. 4, pp. 9931002, 2011.
  • Ebrahimnejad A., Tavana M., Lotfi F. H., Shahverdi R., and Yousefpour M., A three-stage Data Envelopment Analysis model with application to banking industry, Meas-urement, vol. 49, pp. 308319, 2014.
  • Effati S., Pakdaman M., and Ranjbar M., A new fuzzy neural network model for solv-ing fuzzy linear programming problems and its applications, Neural Comput. Appl., vol. 20, no. 8, pp. 12851294, 2011.
  • Ezzati R., Khorram E., and Enayati R., A new algorithm to solve fully fuzzy linear pro- gramming problems using the MOLP problem, Appl. Math. Model., Mar. 2013.
  • Farhadinia B., Sensitivity analysis in interval-valued trapezoidal fuzzy number linear pro- gramming problems, Appl. Math. Model., vol. 38, no. 1, pp. 5062, Jan. 2014.
  • Fazlollahtabar H., Mahdavi I., and Mohajeri A., Applying fuzzy mathematical pro-gramming approach to optimize a multiple supply network in uncertain condition with comparative analysis, Appl. Soft Comput., vol. 13, no. 1, pp. 550562, Jan. 2013.
  • Figueroa-García J. C., Chalco-Cano Y., and Román-Florez H., Distance measures for Inter- val Type-2 fuzzy numbers, Discret. Appl. Math., Dec. 2014.
  • Figueroa-García J. C., Kalenatic D., and Bello C. A. L., An iterative algorithm for fuzzy mixed production planning based on the cumulative membership function, Ingeniería, vol. 16, no. 2, pp. 617, Dec. 2011.
  • Gupta P., Mehlawat M. K., and Saxena A., Asset portfolio optimization using fuzzy math- ematical programming, Inf. Sci. (Ny)., vol. 178, no. 6, pp. 17341755, 2008.
  • Inuiguchi M., and Ichihashi H., Relative modalities and their use in possibilistic linear programming, Fuzzy Sets Syst., vol. 35, no. 3, pp. 303323, 1990.
  • Inuiguchi M., Ichihashi H., and Kume Y., Relationships between modality con-strained programming problems and various fuzzy mathematical programming prob-lems, Fuzzy Sets Syst., vol. 49, no. 3, pp. 243259, 1992.
  • Javadian N., Maali Y., and Mahdavi-Amiri N., Fuzzy linear programming with grades of satisfaction in constraints, Iran. J. Fuzzy Syst., vol. 6, no. 3, pp. 1735, 2009.
  • Kamyad A. V., Hassanzadeh N., and Chaji J., A New Vision on Solving of Fuzzy Linear Programming, in 2009 International Conference on Computational Intelligence and Software Engineering, 2009, pp. 14.
  • Kikuchi S., A method to defuzzify the fuzzy number: transportation problem applica-tion, Fuzzy Sets Syst., vol. 116, no. 1, pp. 39, 2000.
  • Kumar A., Appadoo S. S., and Bector C. R., A note on Generalized fuzzy linear pro- gramming for decision making under uncertainty: Feasibility of fuzzy solutions and solving approach, Inf. Sci. (Ny)., vol. 266, pp. 226227, May 2014.
  • Kumar A., and Kaur J., General Form of Linear Programming Problems with Fuzzy Pa- rameters, J. Appl. Res. Technol., vol. 11, no. 5, pp. 629635, Apr. 2013.
  • Lai Y. J., and Ching-L C.L., Hwang, Fuzzy mathematical programming: methods and applications. Springer Verlag, 1992.
  • Lai Y. J., and Hwang C. L., IFLP-II: A decision support system, Fuzzy Sets Syst., vol. 54, no. 1, pp. 4756, Feb. 1993.
  • León T., Liern V., Ruiz J. L., and Sirvent I., A fuzzy mathematical programming ap-proach to the assessment of efficiency with DEA models, Fuzzy Sets Syst., vol. 139, no. 2, pp. 407419, 2003.
  • Maeda T., Fuzzy linear programming problems as bi-criteria optimization problems, Appl. Math. Comput., vol. 120, no. 13, pp. 109121, 2001.
  • Mitra, K., Gudi D. R., Patwardhan C. S., and Sardar G., Towards resilient supply chains: Uncertainty analysis using fuzzy mathematical programming, Chem. Eng. Res. Des., vol. 87, pp. 967981, 2009.
  • Mula J., Peidro D., and Poler R., The effectiveness of a fuzzy mathematical program-ming approach for supply chain production planning with fuzzy demand, in Interna-tional Journal of Production Economics, 2010, vol. 128, no. 1, pp. 136143.
  • Mula J., Poler R., García-Sabater G. S., and F. C. Lario, Models for production plan-ning under uncertainty: A review, Int. J. Prod. Econ., vol. 103, no. 1, pp. 271285, 2006.
  • Pishvaee M. S., and Razmi J., Environmental supply chain network design using mul- ti-objective fuzzy mathematical programming, Appl. Math. Model., vol. 36, no. 8, pp. 34333446, 2012.
  • Pishvaee M. S., Razmi J., and S. A. Torabi, Robust possibilistic programming for socially responsible supply chain network design: A new approach, Fuzzy Sets Syst., vol. 206, pp. 120, 2012.
  • Rommelfanger H., Fuzzy linear programming and applications, Eur. J. Oper. Res., vol. 92, no. 3, pp. 512527, 1996.
  • Saberi-Najafi H., and Edalatpanah S. A., A note on A new method for solving fully fuzzy linear programming problems, Appl. Math. Model., vol. 37, no. 1415, pp. 78657867, Aug. 2013.
  • Sakawa M., Katagiri H., and Matsui T., Interactive fuzzy random two-level linear program- ming through fractile criterion optimization, Math. Comput. Model., vol. 54, no. 11, pp. 31533163, 2011.
  • Shaocheng T., Interval number and fuzzy number linear programmings, Fuzzy Sets Syst., vol. 66, no. 3, pp. 301306, 1994.
  • Taghizadeh K., Bagherpour M., and Mahdavi I., Application of fuzzy multi-objective linear programming model in a multi-period multi-product production planning prob-lem, Int. J. Comput. Intell. Syst., vol. 4, no. 2, 2011.
  • Vasant P. M., Solving Fuzzy Linear Programming Problems With Modified S-Curve Mem- bership Function, Int. J. Uncertainty, Fuzziness Knowledge-Based Syst., vol. 13, no. 1, pp. 97109, Feb. 2005.
  • Verdegay J. L., Fuzzy mathematical programming, Fuzzy Inf. Decis. Process., vol. 231, p. 237, 1982.
  • Verdegay J. L., A dual approach to solve the fuzzy linear programming problem, Fuzzy Sets Syst., vol. 14, no. 2, pp. 131141, 1984.
  • Wan S.P., and Dong J.Y., Possibility linear programming with trapezoidal fuzzy numbers, Appl. Math. Model., vol. 38, no. 56, pp. 16601672, Mar. 2014.
  • Wan S.P., and Dong J.Y., Interval-valued intuitionistic fuzzy mathematical pro-gramming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees, Inf. Fusion, Feb. 2015.
  • Werners B., An interactive fuzzy programming system, Fuzzy Sets Syst., vol. 23, no. 1, pp. 131147, 1987.
  • Zhang F., Ignatius J., Lim C. P., and Zhao Y., A new method for ranking fuzzy num- bers and its application to group decision making, Appl. Math. Model., vol. 38, no. 4, pp. 15631582, Feb. 2014.
  • Zhu B., and Xu Z., A fuzzy linear programming method for group decision making with additive reciprocal fuzzy preference relations, Fuzzy Sets Syst., vol. 246, pp. 1933, Jul. 2014.
  • Zimmermann H. J., Fuzzy programming and linear programming with several objec-tive functions, Fuzzy Sets Syst., vol. 1, no. 1, pp. 4555, 1978.
  • Zimmermann H. J., Fuzzy Set Theory and Its Applications. 2001.
There are 49 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Amin Vahidi This is me 0000-0001-6598-4491

Publication Date June 15, 2019
Published in Issue Year 2019 Volume: 48 Issue: 3

Cite

APA Vahidi, A. (2019). A New Defuzzification Method for Solving Fuzzy Mathematical Programming Problems. Hacettepe Journal of Mathematics and Statistics, 48(3), 845-858.
AMA Vahidi A. A New Defuzzification Method for Solving Fuzzy Mathematical Programming Problems. Hacettepe Journal of Mathematics and Statistics. June 2019;48(3):845-858.
Chicago Vahidi, Amin. “A New Defuzzification Method for Solving Fuzzy Mathematical Programming Problems”. Hacettepe Journal of Mathematics and Statistics 48, no. 3 (June 2019): 845-58.
EndNote Vahidi A (June 1, 2019) A New Defuzzification Method for Solving Fuzzy Mathematical Programming Problems. Hacettepe Journal of Mathematics and Statistics 48 3 845–858.
IEEE A. Vahidi, “A New Defuzzification Method for Solving Fuzzy Mathematical Programming Problems”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 3, pp. 845–858, 2019.
ISNAD Vahidi, Amin. “A New Defuzzification Method for Solving Fuzzy Mathematical Programming Problems”. Hacettepe Journal of Mathematics and Statistics 48/3 (June 2019), 845-858.
JAMA Vahidi A. A New Defuzzification Method for Solving Fuzzy Mathematical Programming Problems. Hacettepe Journal of Mathematics and Statistics. 2019;48:845–858.
MLA Vahidi, Amin. “A New Defuzzification Method for Solving Fuzzy Mathematical Programming Problems”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 3, 2019, pp. 845-58.
Vancouver Vahidi A. A New Defuzzification Method for Solving Fuzzy Mathematical Programming Problems. Hacettepe Journal of Mathematics and Statistics. 2019;48(3):845-58.

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