With the advent of neutrosophic set theory, it is now possible to quantify the neutral viewpoint on any situation in real life, which can be expressed as an indeterminacy membership function. This advancement has significantly enhanced the optimization process across various research domains. Neutrosophic optimization utilizes the optimization of three membership functions: truth, indeterminacy, and falsity, which represent marginal evaluations of objective functions in practical scenarios. These evaluations can be expressed through either linear or nonlinear membership functions. In this chapter, we explore three different forms of membership functions to solve a neutrosophic Multi-Objective Transportation Problem (MOTP). An existing numerical problem is solved using these different membership functions, and the results are compared. The findings reveal that, regardless of the membership function’s structure, the solution for a given MOTP remains consistent.

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Neutrosophic Linear Programming Approach to Multi-objective Transportation Problem with Linear, Hyperbolic and Exponential Membership Functions

  • Abdul Quddoos,
  • Seema Bano,
  • Md. Gulzar ull Hasan,
  • Md. Izhar Khan

摘要

With the advent of neutrosophic set theory, it is now possible to quantify the neutral viewpoint on any situation in real life, which can be expressed as an indeterminacy membership function. This advancement has significantly enhanced the optimization process across various research domains. Neutrosophic optimization utilizes the optimization of three membership functions: truth, indeterminacy, and falsity, which represent marginal evaluations of objective functions in practical scenarios. These evaluations can be expressed through either linear or nonlinear membership functions. In this chapter, we explore three different forms of membership functions to solve a neutrosophic Multi-Objective Transportation Problem (MOTP). An existing numerical problem is solved using these different membership functions, and the results are compared. The findings reveal that, regardless of the membership function’s structure, the solution for a given MOTP remains consistent.