Document Type : Article

**Authors**

Department of Industrial Engineering and Management Systems, Amirkabir University of Technology, 424 Hafez Ave., Tehran, Iran

**Abstract**

The recognition of membership function by knowledge acquisition from experts is an important factor for many fuzzy mathematical programming models. Thus, the hesitant fuzzy membership function (HFMF) estimation could help users of the mathematical programming approaches to provide a powerful solution in continuous space problems. Therefore, this study proposes a possibilistic programming approach based on Bezier curve mechanism for estimating the HFMF. In the process of possibilistic programming approach, an optimization model is presented to tune the primary parameters of Bezier curve by the goal of minimizing the sum of the squared errors (SSE) between the empirical data and fitted HFMF. After that, the efficiency and applicability of the proposed approach is checked by proposing a novel mathematical model for biomass supply chain network design problem. In this case, the bio-products demand is declared as an imprecise parameter that follows from the estimated HFMF to increase the accuracy of the obtained results by addressing the uncertainty and unreliability of the information. Finally, a computational experiment and validation procedure about the biomass supply chain network design is provided to peruse the verification and validation of the proposed approaches.

**Keywords**

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- Medasani, S., J. Kim, and R. Krishnapuram, ‘‘An overview of membership function generation techniques for pattern recognition’’

Articles in Press, Accepted Manuscript

Available Online from 06 December 2021