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A PRE-SUBADDITIVE FUZZY MEASURE MODEL AND ITS THEORETICAL INTERPRETATION

Year 2020, Volume: 10 Issue: 1, 270 - 278, 01.01.2020

Abstract

In this paper a particular set function which depends on densities of singletons with interdependence coecients and which provides redundancy among singletons is considered. The Mobius representation of this function is obtained. Then a necessary and sucient condition is presented to attain a fuzzy measure from this set function.

References

  • Bellman, R.E. and Zadeh, L.A., (1970), Decision-making in a fuzzy environment. Management Science, 17 (4):141-164.
  • Chateauneuf, A. and Jaffray, J.Y., (1989), Some characterizations of lower probabilities and other monotone capacities through the use of M¨obius inversion, Mathematical Social Sciences, 17:263-283.
  • Chen,T.Y, Wang, J.C. and Tzeng, G.H., (2000), Identification of general fuzzy measures by genetic algorithms based on partial information. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 30: 517-528.
  • Chen, T.Y. and Wang,J.C., (2001), Identification of λ-fuzzy measures using sampling design and genetic algorithms, Fuzzy Sets and Systems, 123(3): 321-341.
  • Choquet, G., (1953), Theory of capacities. Annales de L’Institut Fourier 5(1):131-295.
  • Combarro, E.F. and Miranda, P., (2006), Identification of fuzzy measures from sample data with genetic algorithms. Computers and Operations Research, 33: 3046-3066.
  • Grabisch, M., (1995), Fuzzy integral in multicriteria decision making. Fuzzy Sets and Systems, 69 (3): 279-298.
  • Grabisch, M., (1996),The application of fuzzy integrals in multi criteria decision making. European Journal of Operational Research, 89 (3): 445-456.
  • Grabisch, M., (1995), A new algorithm for identifying fuzzy measures and its application to pattern recognation, Int. Joint Conf. of the 4th IEEE International Conference Fuzzy Systems and the 2nd International Fuzzy Engineering Symposium, March 1995, Yokohama, Japan, 145-150.
  • Grabisch, M., (1997), k-Order additive discrete fuzzy measures and their represantation. Fuzzy Sets and Systems, 92 (2): 167-189.
  • Grabisch, M., (1997), k-order additive discrete fuzzy measures and their representation, Fuzzy Sets and Systems, 92:167-189.
  • Grabisch, M. and Roubens, M., (1996), Equivalent representations of a set function with application to decision making. In 6th IEEE Int. Conf. on Fuzzy Systems, Barcelona, Spain.
  • Ishii, K. and Sugeno M., (1985), A model of human evaluation process using fuzzy measure. Interna- tional Journal of Man-Machine Studies, 22 (1): 19-38.
  • Kuo, Y.C., Lu, S.T., Tzeng, G.H., Lin, Y.C. and Huang, Y.S., (2013), Using fuzzy integral approach to enhance site selection assessment: A Case Study of the Optoelectronics Industry. First International Conference on Information Technology and Quantitative Management, Procedia Computer Science, 17:306-313.
  • Larbani M., Huang C., and Tzeng G., (2011), A novel method for fuzzy measure identification, International Journal of Fuzzy Systems, 13, (1).
  • Lee, K.M.L. and Leekwang, H., (1995), Identification of λ-fuzzy measure by genetic algorithms, Fuzzy Sets and Systems, 75: 301-309.
  • Liginlal, D. and T. Ow., (2005), On policy capturing with fuzzy measures. European Journal of Operational Research, 167: 461-474.
  • Mikenina, L. and Zimmermann, H.J., (1999), Improved feature selection and classification by the 2-additive fuzzy measure Fuzzy Sets and Systems, 107: 195-218.
  • Miranda, P. and Grabisch, M., (1999), Optimization issues for fuzzy measures International Journal of Uncertainty, Fuzziness, and Knowledge Based Systems, 7 (6): 545-560.
  • Miranda, P., Combarro, E.F. and Gil, P., (2006), Extreme points of some families of non-additive measures, European Journal of Operational Research 174: 1865-1884.
  • Murillo, J., Guillaume, S., Tapia, E. and Bulacio, P., (2013), Revised HLMS: A useful algorithm for fuzzy measure identification. Information Fusion 14: 532-540.
  • Sekita,Y., (1976), A consideration of identifying fuzzy measures. Osaka University Economy, 25(4): 133-138.
  • Shee, D.Y., Tzeng, G.H. and Tang, T. I., (2003), AHP, Fuzzy measure and fuzzy integral approaches for the appraisal of information service providers in Taiwan. Journal of Global Information Technology Management, 6 (1): 8-30.
  • Sugeno, M., (1974), Theory of fuzzy integrals and its applications. PhD Dissertation. Tokyo Institute of Technology, Tokyo, Japan.
  • Torra, V. and Narukawa, Y., (2007), Fuzzy measures and integrals in evaluation of strategies. Infor- mation Sciences, 177 (21): 4686-4695.
  • Tzeng, G.H. and Huang, J.J., (2011), Multiple attribute decision making, methods and applications. CRC Press, taylor and Francis Group, Boca Raton, FL.
  • Ozcelik, G., Unver M. and Temel Gencer C., (2016), Evaluation of the global warming impacts using a hybrid method based on fuzzy techniques: A case study in Turkey. Gazi Journal of Science, 29 (4), 883-894.
  • Wang, J.C. and Chen, T.Y., (2005), Experimental analysis of λ-fuzzy measure identification by evo- lutionary algorithms, International Journal of Fuzzy Systems, 7(1): 1-10.
  • Wierzchon, S.T., (1983), An algorithm for identification of fuzzy measure, Fuzzy Sets and Systems, 9: 69-78.
  • Yager, R.R., (2016), Modeling multi-criteria objective functions using fuzzy measures. Information Fusion, 29: 105-111.
Year 2020, Volume: 10 Issue: 1, 270 - 278, 01.01.2020

Abstract

References

  • Bellman, R.E. and Zadeh, L.A., (1970), Decision-making in a fuzzy environment. Management Science, 17 (4):141-164.
  • Chateauneuf, A. and Jaffray, J.Y., (1989), Some characterizations of lower probabilities and other monotone capacities through the use of M¨obius inversion, Mathematical Social Sciences, 17:263-283.
  • Chen,T.Y, Wang, J.C. and Tzeng, G.H., (2000), Identification of general fuzzy measures by genetic algorithms based on partial information. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 30: 517-528.
  • Chen, T.Y. and Wang,J.C., (2001), Identification of λ-fuzzy measures using sampling design and genetic algorithms, Fuzzy Sets and Systems, 123(3): 321-341.
  • Choquet, G., (1953), Theory of capacities. Annales de L’Institut Fourier 5(1):131-295.
  • Combarro, E.F. and Miranda, P., (2006), Identification of fuzzy measures from sample data with genetic algorithms. Computers and Operations Research, 33: 3046-3066.
  • Grabisch, M., (1995), Fuzzy integral in multicriteria decision making. Fuzzy Sets and Systems, 69 (3): 279-298.
  • Grabisch, M., (1996),The application of fuzzy integrals in multi criteria decision making. European Journal of Operational Research, 89 (3): 445-456.
  • Grabisch, M., (1995), A new algorithm for identifying fuzzy measures and its application to pattern recognation, Int. Joint Conf. of the 4th IEEE International Conference Fuzzy Systems and the 2nd International Fuzzy Engineering Symposium, March 1995, Yokohama, Japan, 145-150.
  • Grabisch, M., (1997), k-Order additive discrete fuzzy measures and their represantation. Fuzzy Sets and Systems, 92 (2): 167-189.
  • Grabisch, M., (1997), k-order additive discrete fuzzy measures and their representation, Fuzzy Sets and Systems, 92:167-189.
  • Grabisch, M. and Roubens, M., (1996), Equivalent representations of a set function with application to decision making. In 6th IEEE Int. Conf. on Fuzzy Systems, Barcelona, Spain.
  • Ishii, K. and Sugeno M., (1985), A model of human evaluation process using fuzzy measure. Interna- tional Journal of Man-Machine Studies, 22 (1): 19-38.
  • Kuo, Y.C., Lu, S.T., Tzeng, G.H., Lin, Y.C. and Huang, Y.S., (2013), Using fuzzy integral approach to enhance site selection assessment: A Case Study of the Optoelectronics Industry. First International Conference on Information Technology and Quantitative Management, Procedia Computer Science, 17:306-313.
  • Larbani M., Huang C., and Tzeng G., (2011), A novel method for fuzzy measure identification, International Journal of Fuzzy Systems, 13, (1).
  • Lee, K.M.L. and Leekwang, H., (1995), Identification of λ-fuzzy measure by genetic algorithms, Fuzzy Sets and Systems, 75: 301-309.
  • Liginlal, D. and T. Ow., (2005), On policy capturing with fuzzy measures. European Journal of Operational Research, 167: 461-474.
  • Mikenina, L. and Zimmermann, H.J., (1999), Improved feature selection and classification by the 2-additive fuzzy measure Fuzzy Sets and Systems, 107: 195-218.
  • Miranda, P. and Grabisch, M., (1999), Optimization issues for fuzzy measures International Journal of Uncertainty, Fuzziness, and Knowledge Based Systems, 7 (6): 545-560.
  • Miranda, P., Combarro, E.F. and Gil, P., (2006), Extreme points of some families of non-additive measures, European Journal of Operational Research 174: 1865-1884.
  • Murillo, J., Guillaume, S., Tapia, E. and Bulacio, P., (2013), Revised HLMS: A useful algorithm for fuzzy measure identification. Information Fusion 14: 532-540.
  • Sekita,Y., (1976), A consideration of identifying fuzzy measures. Osaka University Economy, 25(4): 133-138.
  • Shee, D.Y., Tzeng, G.H. and Tang, T. I., (2003), AHP, Fuzzy measure and fuzzy integral approaches for the appraisal of information service providers in Taiwan. Journal of Global Information Technology Management, 6 (1): 8-30.
  • Sugeno, M., (1974), Theory of fuzzy integrals and its applications. PhD Dissertation. Tokyo Institute of Technology, Tokyo, Japan.
  • Torra, V. and Narukawa, Y., (2007), Fuzzy measures and integrals in evaluation of strategies. Infor- mation Sciences, 177 (21): 4686-4695.
  • Tzeng, G.H. and Huang, J.J., (2011), Multiple attribute decision making, methods and applications. CRC Press, taylor and Francis Group, Boca Raton, FL.
  • Ozcelik, G., Unver M. and Temel Gencer C., (2016), Evaluation of the global warming impacts using a hybrid method based on fuzzy techniques: A case study in Turkey. Gazi Journal of Science, 29 (4), 883-894.
  • Wang, J.C. and Chen, T.Y., (2005), Experimental analysis of λ-fuzzy measure identification by evo- lutionary algorithms, International Journal of Fuzzy Systems, 7(1): 1-10.
  • Wierzchon, S.T., (1983), An algorithm for identification of fuzzy measure, Fuzzy Sets and Systems, 9: 69-78.
  • Yager, R.R., (2016), Modeling multi-criteria objective functions using fuzzy measures. Information Fusion, 29: 105-111.
There are 30 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

M. Unver This is me

G. Ozcelik This is me

M. Olgun This is me

Publication Date January 1, 2020
Published in Issue Year 2020 Volume: 10 Issue: 1

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