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Solving a Solid Transportation Problems Through Fuzzy Ranking

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Communication, Devices, and Computing (ICCDC 2017)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 470))

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Abstract

A solid transportation problem (STP) with imprecise cost coefficients is modeled in this paper. The proposed fuzzy STP (FSTP) is optimized by the Vogel approximation method (VAM). For different types of imprecise operations and comparisons in VAM, fuzzy ranking method is used. The proposed FSTP is also converted to a crisp one using fuzzy expectation (mean value) and then solved using generalized reduced gradient (GRG) method. Finally, a numerical illustration is performed to support the methods, and optimum results by two methods are compared.

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References

  1. H.J. Zimmermann, Description and optimization of fuzzy system. Int. J. Gen. Syst. 2, 209–215 (1976)

    Article  MATH  Google Scholar 

  2. B. Liu, Uncertainty Theory: An Introduction To Its Axiomatic Foundations (Springer, Heidelberg, 2004)

    Book  MATH  Google Scholar 

  3. L. Liu, L. Lin, Fuzzy fixed charge solid transportation problem and its algorithm. Fuzzy Syst. Knowl. Discov. 3, 585–589 (2007)

    Article  Google Scholar 

  4. A.K. Maiti, M. Maiti, Discounted Multi-item Inventory model via Genetic Algorithm with Roulette Wheel Section, arithmetic crossover and uniform mutation in constraints bounded domains. Int. J. Comput. Math. 85(9), 1341–1353 (2008)

    Google Scholar 

  5. L.A. Zadeh, Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Google Scholar 

  6. G. Bortolan, R. Degani, A review of some methods for ranking fuzzy subsets. Fuzzy Sets Syst. 15(1), 1–19 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  7. S.J. Chen, C.L. Hwang, Fuzzy multiple attribute decision making methods, in Fuzzy multiple attribute decision making (Springer, Berlin, Heidelberg, 1992), pp. 289–486

    Google Scholar 

  8. F. Choobineh, H. Li, An index for ordering fuzzy numbers. Fuzzy Sets Syst. 54(3), 287–294 (1993)

    Article  MathSciNet  Google Scholar 

  9. O.P. Dias, Ranking alternatives using fuzzy numbers: a computational approach. Fuzzy Sets Syst. 56(2), 247–251 (1993)

    Article  MathSciNet  Google Scholar 

  10. I. Requena, M. Delgado, J.L. Verdegay, Automatic ranking of fuzzy numbers with the criterion of a decision-maker learnt by an artificial neural network. Fuzzy Sets Syst. 64(1), 1–19 (1994)

    Article  Google Scholar 

  11. E.S. Lee, R.J. Li, Comparison of fuzzy numbers based on the probability measure of fuzzy events. Comput. Math. Appl. 15(10), 887–896 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  12. P.A. Raj, D.N. Kumar, Ranking alternatives with fuzzy weights using maximizing set and minimizing set. Fuzzy Sets Syst. 105(3), 365–375 (1999)

    Article  MATH  Google Scholar 

  13. K. Patra, S.K. Mondal, Risk analysis in diabetes prediction based on a new approach of ranking of generalized trapezoidal fuzzy numbers. Cybern. Syst. 43(8), 623–650 (2012)

    Article  MATH  Google Scholar 

  14. F.L. Hitchcock, The distribution of a product from several sources to numerous localities. J. Math. Phys. 20, 224–230 (1941)

    Google Scholar 

  15. S. Chanas, D. Kuchta, Multi-objective programming in optimization of interval objective functions—a generalized approach. Eur. J. Oper. Res. 94, 594–598 (1996)

    Article  MATH  Google Scholar 

  16. M. Gen, K. Ida, Y.Z. Li, E. Kubota, Solving bicriteria solid transportation problem with fuzzy numbers by a Genetic Algorithm. Comput. Ind. Eng. 29, 537–541 (1995)

    Article  Google Scholar 

  17. A.K. Bit, Fuzzy programming with hyperbolic membership functions for multi-objective capacitated solid transportation problem. J. Fuzzy Math. 13(2), 373–385 (2005)

    MathSciNet  MATH  Google Scholar 

  18. F. Jiménez, J.L. Verdegay, Interval multiobjective solid transportation problem via Genetic Algorithms. Manag. Uncertain. Knowl.-Based Syst. II, 787–792 (1996)

    Google Scholar 

  19. A. Ojha, B. Das, S. Mondal, M. Maiti, A solid transportation problem for an item with fixed charge, vechicle cost and price discounted varying charge using genetic algorithm. App. Soft Comput. 10(1), 100–110 (2010)

    Google Scholar 

  20. E. Shell, Distribution of a product by several properties, Directorate of Management Analysis, in Proceedings of the Second Symposium in Linear Programming, vol. 2, (1995), pp. 615–642

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Midnapore College, Midnapore, India

    Sharmistha Halder(Jana)

  2. Department of Mathematics, Sidho Kanho Birsha University, Purulia, India

    Barun Das

  3. Department of Mathematics, NIT Durgapur, Durgapur, India

    Goutam Panigrahi

  4. Department of Mathematics, Vidyasagar University, Midnapore, India

    Manoranjan Maiti

Authors
  1. Sharmistha Halder(Jana)
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  2. Barun Das
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  3. Goutam Panigrahi
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  4. Manoranjan Maiti
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Corresponding author

Correspondence to Sharmistha Halder(Jana) .

Editor information

Editors and Affiliations

  1. Department of Electronics and Communication Engineering, Haldia Institute of Technology, Haldia, West Bengal, India

    Jaydeb Bhaumik

  2. Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology Kharagpur, Kharagpur, India

    Indrajit Chakrabarti

  3. Department of Electronics and Communication Engineering, Haldia Institute of Technology, Haldia, West Bengal, India

    Bishnu Prasad De

  4. Department of Electronics and Communication Engineering, Haldia Institute of Technology, Haldia, West Bengal, India

    Banibrata Bag

  5. Department of Electronics and Communication Engineering, Haldia Institute of Technology, Haldia, West Bengal, India

    Surajit Mukherjee

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Halder(Jana), S., Das, B., Panigrahi, G., Maiti, M. (2017). Solving a Solid Transportation Problems Through Fuzzy Ranking. In: Bhaumik, J., Chakrabarti, I., De, B.P., Bag, B., Mukherjee, S. (eds) Communication, Devices, and Computing. ICCDC 2017. Lecture Notes in Electrical Engineering, vol 470. Springer, Singapore. https://doi.org/10.1007/978-981-10-8585-7_27

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  • DOI: https://doi.org/10.1007/978-981-10-8585-7_27

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-8584-0

  • Online ISBN: 978-981-10-8585-7

  • eBook Packages: EngineeringEngineering (R0)

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