Intelligent Solution for Transportation Problems Using Complete Ordering of Single Valued Neutrosophic Numbers

Abstract

TheTransportation Problem (TP) is extensively studied in operations research due to its nu merous real-world applications. However, real-world scenarios often involve uncertainty, making it difficult to determine costs, supply, and demand accurately. Fuzzy Numbers are commonly used to address this uncertainty but have limitations. These limitations arise from the inherent uncertainties in human thought patterns, which vary due to different val ues assigned to the three basic degrees of human thought—membership, non-membership, and indeterminacy—termed by Florentin. To better describe uncertainty in real-life situa tions, modern science uses Single Valued Neutrosophic Numbers (SVNS), which assign all three degree functions to any value, providing a more comprehensive mathematical model. Despite their extensive applicability in many Multi-Criteria Decision Making (MCDM) sit uations, ranking SVNS’s remain a significant challenge. Therefore, in this thesis we have f irstly defined a comprehensive ranking model for Single Valued Trapezoidal Neutrosophic Numbers (Normalized/Non-Normalized/ Uniform and Non Uniform Spread) based on four ranking functions/measures involving three existential levels namely- the Basic member ship (involving only membership function)-the Possible membership (a simple compliment of non- membershipfunction)–the Biggest membership (a combination of membership and indeterminacy function) and last but most important a Parametric combination of Possible membership and the Biggest membership. Next, we have employed the last ranking func tion– the parametric combination of Possible membership and the Biggest membership to ix build a Generalized Single Valued Trapezoidal Transportation Problem. In particular, we have utilized generalized trapezoidal data (normailized,/non-normalized/ with Uniform and Non Uniform Spread) to study three different types of transportation problems involving Crip and Single Valued Neutrosophic (triangular and trapezoidal) data for supply, demand, and cell costs. The thesis extends the principles of Least Cost Method (LCM), the North West Corner Method (NWCM), Vogel’s Approximation Method (VAM), and the Modified Distribution Method (MODI) to solve the Transportation Problem within a Single valued Neutrosophic environment. In this thesis, all the above modified solution models for TP incorporates generalized single valued trapezoidal neutrosophic data in different scenarios. Thus they provides the decision maker a flexible intelligence based environment which is capable of accommodating all different types of human mind behaviors (including the three basic behaviors of being optimist, pessimist and neutral ) due to the presence of logical op erations of fuzzy conjunctions and disjunctions that can be modelled by any pair of fuzzy t-norms and their conforms.