Solving epistemic uncertainty based optimization problem with crisp coefficients

Diptiranjan Behera ()
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Diptiranjan Behera: The University of the West Indies

International Journal of System Assurance Engineering and Management, 2024, vol. 15, issue 6, No 10, 2130-2140

Abstract: Abstract Optimization problem such as linear programming problem under epistemic uncertainty for instance fuzzy has been studied in this paper. Here, coefficients are assumed as crisp however, decision variables and the right-hand side vector of the constraints are presumed as uncertain in nature for the considered problem. Using the concept of fuzzy centre and fuzzy arithmetic a new method for the solution has been developed. First, solution of fuzzy centre for $$r=0$$ r = 0 has been obtained. And then as the upper bound of the solution can be expressed in term of fuzzy centre and lower bound, then using this an equivalent crisp system is solved to obtain the lower bound of the solution. Next again using the solution of lower bound and centre upper bound has been computed. Similarly lower and upper bounds for $$r=1$$ r = 1 have been obtained. Finally using these solutions fuzzy feasible optimal solution can be obtained. Various example problem has been solved using the proposed method and obtained results are compared with the existing results to show the advantage and validation.

Keywords: Fuzzy linear programming problem; Fuzzy set; Fuzzy number; $$r$$ r -cut; Fuzzy centre; Fuzzy decision variables (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13198-023-02226-2

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