Solving Stochastic Transportation Programming Problems with Fuzzy Information on Probability Distribution Space Using a New Approach

Halgurd Namiq Azeez Azeez; Abdulqader Othman Hamadameen

doi:10.21271/ZJPAS.36.3.7

Authors

Halgurd Namiq Azeez Department of Mathematics, College of Science, Faculty of Science and Health, Koya University, Koya KOY45, Erbil, Kurdistan Region, Iraq. https://orcid.org/0000-0002-6953-1788
Abdulqader Othman Hamadameen Department of Mathematics, College of Science, Faculty of Science and Health, Koya University, Koya KOY45, Erbil, Kurdistan Region, Iraq.

DOI:

https://doi.org/10.21271/ZJPAS.36.3.7

Keywords:

Fuzzy Information, Matrix Minima Cost, Probability Distribution, Alpha-Cut Technique, Ranking Function, Membership Function, Stochastic Transportation Problem, Truth Degrees Technique, Expectation Weighted Summation

Abstract

A study is conducted on solving stochastic transportation linear programming problems with fuzzy uncertainty information on probability distribution space (STLPPFI) model problems. A proposed method utilizes the concepts of alpha-cut technique with truth degrees technique on probability distribution, linear fuzzy membership function (LFMF), linear fuzzy ranking function (LFRF), trapezoidal fuzzy number , triangular fuzzy number and expectation weighted summation (EWS) technique. Those are used to convert STLPPFI into its corresponding equivalent deterministic transportation linear programming problem (DTLPP) via defuzzifying fuzziness on probability distribution and derandomization randomness of problem formulation respectively. Although, matrix minima cost method (MMCM) with modify distribution method (MODI) respectively are used on obtained DTLPP to get optimal solution. In addition, decision maker (DM) manually decides which of resulting solution is a post optimal solution via choosing a solution that has suitable situation to DM. A proposed algorithm along with numerical example on electricity field illustrating the practicability of it. The obtained results with existing methods show the efficiency of strategy proposed solution method based on the analysis that from results performed.

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