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A gamma type-2 defuzzification method for solving a solid transportation problem considering carbon emission

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Abstract

This paper intends to develop a multi-objective solid transportation problem considering carbon emission, where the parameters are of gamma type-2 fuzzy in nature. This paper proposed the defuzzification process for gamma type-2 fuzzy variable using critical value (CV ) and nearest interval approximation method. A chance constraint programming problem is generated using the CV based reduction method to convert the fuzzy problem to its equivalent crisp form. Applying the \(\alpha \)-cut based interval approximation method, a deterministic problem is developed. Some real life data are used to minimize the cost and carbon emission. LINGO standard optimization solver has been used to solve the multi-objective problem using weighted sum method and intuitionistic fuzzy programming technique. The Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithm are implemented to generate efficient optimal solution by converting the multi-objective problem to a single objective problem using penalty cost for carbon emission. After solving the problem, analysis on some particular cases has been presented. The sensitivity analysis has been shown to different credibility levels of cost, emission, source, demand, conveyance to find total cost, emission and transported amount in each level. A comparison study on the performance of three algorithms (LINGO, GA and PSO) is presented. At the end, some graphs have been plotted which shows the effect of emission with different emission parameters.

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Acknowledgments

Dr. Bera acknowledges the financial assistance from Department of Science and Technology, New Delhi under the Research Project (F.No. SR/S4/MS:761/12).

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Authors and Affiliations

  1. School of Management, National Institute of Technology Agartala, Jirania, West Tripura, 799046, India

    Dipanjana Sengupta

  2. Department of Mathematics, National Institute of Technology Agartala, Jirania, West Tripura, 799046, India

    Amrit Das & Uttam Kumar Bera

Authors
  1. Dipanjana Sengupta
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  2. Amrit Das
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  3. Uttam Kumar Bera
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Correspondence to Uttam Kumar Bera.

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Sengupta, D., Das, A. & Bera, U.K. A gamma type-2 defuzzification method for solving a solid transportation problem considering carbon emission. Appl Intell 48, 3995–4022 (2018). https://doi.org/10.1007/s10489-018-1173-7

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