Innovative Ranking and Conversion Approaches to Handle Impreciseness in Transportation
Pankaj Kumar Srivastava, Dinesh C. S. Bisht and Harish Garg
Pentagonal fuzzy number (PFN) came into existence due to the increasing level of uncertainty in various decision-making problems. Ordering and defuzzification of PFNs have significant practical utility and an improper ranking can mislead the decision maker. The present study aims at two kind of ranking for PFNs. The first one is based on the concept of weighted average while the second one is an extension of the Yager’s ranking. Both the ranking techniques are validated with the help of a set of test data. These ranking techniques are well applied on pentagonal fully fuzzy transportation problem and triangular fuzzy transportation problem (FTP) of type II. For triangular FTP a unique conversion approach is proposed which converts it into a pentagonal FTP. This helps to cope up with increased level of impreciseness due to many affecting factors. To find initial basic feasible solution of FTPs least cost, north-west, Vogel’s approximation and minimum demandsupply are applied and then modified distribution is used to check the optimality of the solution. A comparative study of proposed ranking techniques with existing ranking technique is also done which confirms the applicability of proposed ranking techniques and utility of presented algorithm.
Keywords: Pentagonal fuzzy number, weighted ranking, Yager’s ranking, tripentagonal conversion, fuzzy transportation problem, initial basic feasible solution