A Multi-criteria neutrosophic group decision making metod based TOPSIS for supplier selection

The process of multiple criteria decision making (MCDM) is of determining the best choice among all of the probable alternatives. The problem of supplier selection on which decision maker has usually vague and imprecise knowledge is a typical example of multi criteria group decision-making problem. The conventional crisp techniques has not much effective for solving MCDM problems because of imprecise or fuzziness nature of the linguistic assessments. To find the exact values for MCDM problems is both difficult and impossible in more cases in real world. So, it is more reasonable to consider the values of alternatives according to the criteria as single valued neutrosophic sets (SVNS). This paper deal with the technique for order preference by similarity to ideal solution (TOPSIS) approach and extend the TOPSIS method to MCDM problem with single valued neutrosophic information. The value of each alternative and the weight of each criterion are characterized by single valued neutrosophic numbers. Here, the importance of criteria and alternatives is identified by aggregating individual opinions of decision makers (DMs) via single valued neutrosophic weighted averaging (IFWA) operator. The proposed method is, easy use, precise and practical for solving MCDM problem with single valued neutrosophic data. Finally, to show the applicability of the developed method, a numerical experiment for supplier choice is given as an application of single valued neutrosophic TOPSIS method at end of this paper.

💡 Research Summary

The paper proposes a novel multi‑criteria group decision‑making (MCDM) framework for supplier selection that integrates single‑valued neutrosophic sets (SVNS) with the well‑known TOPSIS technique. Recognizing that traditional crisp or fuzzy approaches cannot fully capture the inherent vagueness, indeterminacy, and incompleteness of expert judgments, the authors adopt SVNS, which represents each evaluation by three independent components: truth‑membership (T), indeterminacy‑membership (I), and falsity‑membership (F), all ranging between 0 and 1.

Key methodological contributions include: (1) definition of basic SVNS arithmetic (addition, multiplication, scalar exponentiation); (2) introduction of a single‑valued neutrosophic weighted averaging (IFWA) operator that aggregates the opinions of multiple decision makers into a collective SVNS decision matrix; (3) a score function that converts an SVNS into a scalar by rewarding truth, penalizing falsity, and optionally discounting indeterminacy; (4) construction of the positive ideal solution (PIS) and negative ideal solution (NIS) directly in SVNS space by taking component‑wise extrema; (5) computation of Euclidean distances between each alternative and the PIS/NIS, followed by the usual TOPSIS relative closeness index C_i = d_i^−/(d_i^+ + d_i^−).

The authors illustrate the full procedure with a numerical example involving three decision makers, four potential suppliers, and five evaluation criteria. Linguistic assessments (e.g., “very important”, “good”) are first mapped to SVNS values, then aggregated via IFWA, scored, and finally ranked using the SVNS‑TOPSIS distance calculations. The resulting ranking is compared with a conventional fuzzy TOPSIS approach, showing that the neutrosophic model provides a more nuanced differentiation when indeterminacy is significant.

The paper also discusses practical aspects such as the determination of decision‑maker weights (derived from their own SVNS evaluations) and the visualization of alternatives relative to PIS and NIS. Limitations are acknowledged: the weight‑determination process is subjective, the sensitivity of the score function to the choice of I‑penalty is not explored, and validation is limited to a single case study. Future research directions suggested include systematic sensitivity analysis, extension to dynamic or real‑time decision environments, and integration with other multi‑objective optimization techniques. Overall, the study offers a comprehensive and mathematically coherent extension of TOPSIS to neutrosophic environments, promising enhanced handling of uncertainty in complex supplier selection problems.