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 addresses the supplier selection problem, a typical multi‑criteria group decision‑making (MCDM) scenario, where decision makers (DMs) often possess vague, imprecise knowledge about alternatives. Traditional crisp MCDM techniques fail to capture this linguistic uncertainty, prompting the authors to adopt Single‑Valued Neutrosophic Sets (SVNS) as the information carrier. An SVNS element consists of three independent membership degrees: truth (T), indeterminacy (I), and falsity (F), each ranging from 0 to 1. This triadic representation enables a richer modeling of the DM’s hesitation and partial belief compared with fuzzy or intuitionistic fuzzy sets.

The methodological core consists of two parts: (1) aggregation of individual DM assessments and (2) ranking of alternatives using a neutrosophic extension of the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method. For aggregation, the authors employ the Single‑Valued Neutrosophic Weighted Averaging (IFWA) operator. Each DM is assigned a weight (also expressed as an SVNS) reflecting expertise or confidence; the IFWA then produces a single collective SVNS for every alternative‑criterion pair, effectively smoothing conflicts among DMs while preserving the underlying uncertainty.

The neutrosophic TOPSIS proceeds as follows:

• Normalization: All SVNS evaluations are scaled to a common range, preserving the relative ordering of T, I, and F components.
• Weighted aggregation: Criterion weights (SVNS) are applied to the normalized values, yielding a weighted SVNS score for each alternative.
• Ideal and anti‑ideal solutions: The ideal solution is defined as the SVNS with T = 1, I = 0, F = 0 for every criterion, while the anti‑ideal solution has T = 0, I = 1, F = 1.
• Distance measurement: The authors introduce a Euclidean‑type distance for SVNS, computed as √