Modified Approach for Optimization of Real Life Transportation Problem in Neutrosophic Environment

Abstract

To the best of our knowledge, there is only one approach for solving neutrosophic cost minimization transportation problems. Since neutrosophic transportation problems are a new area of research, other researchers may be attracted to extend this approach for solving other types of neutrosophic transportation problems like neutrosophic solid transportation problems, neutrosophic time minimization transportation problems, neutrosophic transshipment problems, and so on. However, after a deep study of the existing approach, it is noticed that a mathematical incorrect assumption has been used in these existing approaches; therefore there is a need to modify these existing approaches. Keeping the same in mind, in this paper, the existing approach is modified. Furthermore, the exact results of some existing transportation problems are obtained by the modified approach.

Solving the Single-Valued Trapezoidal Neutrosophic Transportation Problems through the Novel Dhouib-Matrix-TP1 Heuristic

“…Furthermore, we enrich the DM-TP1 with the defuzzification score function [16] in order to convert the neutrosophic trapezoidal fuzzy parameters to crisp number. us, the score function for the neutrosophic trapezoidal fuzzy number N � 〈(N a , N b , N c , N d ); T N , I N , F N 〉 is defined by equations ( 5) and ( 6).…”

“…Definition 4 (see [16]). For a single-valued neutrosophic number N � 〈(N a , N b , N c , N d ); T N , I N , F N 〉, its score function is defined by M(􏽥 c N ij ) as follows:…”

“…Also, the Travelling Salesman Problem is solved under single-valued triangular neutrosophic parameters in [14]. A real-life TP under neutrosophic domain is solved in [15,16], while the neutrosophic shortest path problem is optimized in [17]. Several operations on neutrosophic matrices are introduced in [18], and an application of the multicriteria group decision in a real-life problem is illustrated.…”

Neutrosophic Assignment Problem via BnB Algorithm

“…Srinivas and Ganesan [14] have applied branch and bound method for unraveling assignment problems. Transportation problems under neutrosophic domain were resolved by Thamaraiselvi et al [15] and Akansha Singh et al [2]. With linguistic variables, Anil and Khot [3] resolved fuzzy assignment problem through BnB method.…”

A commentary on “An improved score function for ranking neutrosophic sets and its application to decision-making process”

“…Later with the time some intriguing extensions of fuzzy sets were developed like-intuitionistic fuzzy set (IFS) [2], interval-valued intuitionistic fuzzy set (IVIFS) [3], Pythagorean fuzzy set (PFS) [24][25][26], interval-valued Pythagorean fuzzy set (IVPFS) [32], neutrosophic set [18][19][20], SVNS [23] and IVNS [22] etc. In this note, a deep study have been made to analyze the ranking order of some of the extensions of fuzzy sets like, IFS [8,9,30], PFS [32], IVPFS [4][5][6][7]11,12,16,17,31], SVNS [1,10,[13][14][15]21] and IVNS [10,13]. After a rigorous study it has been observed that there exist some restrictions in the existing methods [10,13] for comparing SVNS and IVNS.…”