Abstract
In this paper, we focus on measuring the performance efficiencies of decision making units (DMUs) using dual slack based measure (SBM) model with fuzzy data in data envelopment analysis (DEA). In the conventional dual SBM model, the data and the weights of input and output are found as crisp quantities. However, in real world applications, input-output data and input-output weights may have vague/uncertainty due to various factors such as quality of treatment and medicines, number of medical and non-medical staffs, number of patients, etc. in health sector. To deal with such uncertainty, we can apply fuzzy set theory. In this paper, we propose a SBM model with fuzzy weights in Fuzzy DEA (FDEA) for fuzzy input and fuzzy output. This model is then reduced to a crisp LPP by using expected values of a fuzzy number (FN). Finally, we present an application of the proposed model to the health sector, consisting of two input variables as (i) sum of number of doctors and staff nurses (ii) number of pharmacists and two output variables as (i) number of inpatients (ii) number of outpatients. Both the input variables and output variables are considered as TFNs.
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Acknowledgment
The authors are thankful to the Ministry of Human Resource Development (MHRD), Govt. of India, India for financial support in pursuing this research. The authors are also thankful to Mr. Deen Bandhu, ARO, Chief Medical Office, Meerut, India for providing the valuable data of the hospitals.
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Arya, A., Yadav, S.P. (2017). A Fuzzy Dual SBM Model with Fuzzy Weights: An Application to the Health Sector. In: Deep, K., et al. Proceedings of Sixth International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 546. Springer, Singapore. https://doi.org/10.1007/978-981-10-3322-3_21
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DOI: https://doi.org/10.1007/978-981-10-3322-3_21
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