A Modified Yager’s Ranking Based Approach for Solving Interval Valued Fuzzy Transportation Problems
Keywords:
Fuzzy sets,Trapezoidal fuzzy numbers,Interval numbers, Ranking Methods-Centroid Method and Modified Yeager’s MethodAbstract
This study introduces an integrated framework for addressing transportation problems characterized by interval valued data.In the first stage, interval parameters are transformed into a fuzzy transportation model through a trisection based fuzzification scheme.Subsequently, a newly developed ranking mechanism is employed to defuzzify the fuzzy quantities and obtain equivalent crisp values. The effectiveness and practicality of the proposed approach are demonstrated using numerical examples. Furthermore,a comparative analysis with existing methodologies highlights the robustness and suitability of the proposed method for solving transportation problems under interval uncertainty. The transportation problem (TP) aims to minimize distribution costs while satisfying supply and demand requirements.However, in real world situations,parameters such as costs,supplies and demands are often imprecise.This paper addresses such uncertainty by formulating TP with interval valued trapezoidal fuzzy numbers.A fuzzy linear programming framework is developed,employing a signed distance ranking method for comparing interval-valued fuzzy numbers.To handle interval based transportation problems (IDBTPs),a trisectional approach is introduced,along with a novel incenter ranking technique to obtain crisp solutions.Numerical illustrations demonstrate the applicability and efficiency of the proposed methods.Furthermore, shortcomings of existing approaches for fully fuzzy transportation problems are discussed and new solution strategies based on fuzzy linear programming and classical transportation methods with an improved trapezoidal fuzzy representation are proposed.Comparative analysis confirms the effectiveness of the framework in modeling uncertainty and providing reliable solutions for transportation problems.
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