Algorithms for single-valued neutrosophic decision making based on TOPSIS and clustering methods with new distance measure

Harish Garg; Nancy; Harish Garg; Nancy

doi:10.3934/math.2020173

AIMS Mathematics

2020, Volume 5, Issue 3: 2671-2693. doi: 10.3934/math.2020173

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Research article

Algorithms for single-valued neutrosophic decision making based on TOPSIS and clustering methods with new distance measure

Harish Garg ^{1
,
,},
Nancy ²

1.
School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University Patiala, Punjab, India
2.
Department of Applied Sciences, Punjab Engineering College (Deemed to be University), Chandigarh, India

Received: 08 December 2019 Accepted: 24 February 2020 Published: 16 March 2020
MSC : 62A86, 90B50, 03E72, 68T35

Single-valued neutrosophic set (SVNS) is an important contrivance for directing the decision-making queries with unknown and indeterminant data by employing a degree of "acceptance", "indeterminacy", and "non-acceptance" in quantitative terms. Under this set, the objective of this paper is to propose some new distance measures to find discrimination between the SVNSs. The basic axioms of the measures have been highlighted and examined their properties. Furthermore, to examine the relevance of proposed measures, an extended TOPSIS ("technique for order preference by similarity to ideal solution") method is introduced to solve the group decision-making problems. Additionally, a new clustering technique is proposed based on the stated measures to classify the objects. The advantages, comparative analysis as well as superiority analysis is given to shows its influence over existing approaches.
- single-valued neutrosophic set,
- information measure,
- TOPSIS,
- clustering algorithm,
- decision-making
Citation: Harish Garg, Nancy. Algorithms for single-valued neutrosophic decision making based on TOPSIS and clustering methods with new distance measure[J]. AIMS Mathematics, 2020, 5(3): 2671-2693. doi: 10.3934/math.2020173

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Abstract

Single-valued neutrosophic set (SVNS) is an important contrivance for directing the decision-making queries with unknown and indeterminant data by employing a degree of "acceptance", "indeterminacy", and "non-acceptance" in quantitative terms. Under this set, the objective of this paper is to propose some new distance measures to find discrimination between the SVNSs. The basic axioms of the measures have been highlighted and examined their properties. Furthermore, to examine the relevance of proposed measures, an extended TOPSIS ("technique for order preference by similarity to ideal solution") method is introduced to solve the group decision-making problems. Additionally, a new clustering technique is proposed based on the stated measures to classify the objects. The advantages, comparative analysis as well as superiority analysis is given to shows its influence over existing approaches.

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