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The Approach of Induced Generalized Neutrosophic Cubic Shapley Choquet Integral Aggregation Operators via the CODAS Method to Solve Distance‐Based Multicriteria Decision‐Making Problems

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  • Majid Khan
  • Muhammad Gulistan
  • Mohammed M. Al-Shamiri

Abstract

This study aims to define a conjecture that can handle complex frames of work more efficiently that occurs in daily life problems. In decision‐making theory inter‐relation of criteria, weights and choice decision‐making method subject to the given circumstances which are an important component for appropriate decisions. For this, we define neutrosophic cubic Shapley–Choquet integral (NCSCI) measure; combinative distance‐based assessment selection (CODAS) is accomplished over NCSCI and is implemented over a numerical example of a company foreign investment model as an application in decision‐making (DM) theory. The neutrosophic cubic set (NCS) is a hybrid of the neutrosophic set (NS) and interval neutrosophic set (INS), which provides a better plate form to handle inconsistent and vague data more conveniently. The novel CODAS method is based on Shapley–Choquet integral and Minkowski distance which contain more information measures than usual criteria weights and distances. The weights of criteria are measured by Shapley–Choquet integral and distance is evaluated by Minkowski distance. The Choquet integral considers the interaction among the criteria, and Shapley considers the overall weight criteria. Motivated by these characteristics NCSCI, we defined two aggregation operators’ induced‐generalized neutrosophic cubic Shapley–Choquet integral arithmetic (IGNCSCIA) and operators’ induced‐generalized neutrosophic cubic Shapley–Choquet integral geometric (IGNCSCIG) operators. To find the distance between two NC values, Minkowski distance is defined to evaluate neutrosophic cubic combinative distance‐based assessment selection (NCCODAS). To examine the feasibility of the proposed method, an example of company investment in a foreign country is considered. To check, the validity of the method, the comparative analysis of the proposed method with other methods is conducted.

Suggested Citation

  • Majid Khan & Muhammad Gulistan & Mohammed M. Al-Shamiri, 2022. "The Approach of Induced Generalized Neutrosophic Cubic Shapley Choquet Integral Aggregation Operators via the CODAS Method to Solve Distance‐Based Multicriteria Decision‐Making Problems," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4898699
    DOI: 10.1155/2022/4898699
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    References listed on IDEAS

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    1. Young Bae Jun & Florentin Smarandache & Chang Su Kim, 2017. "Neutrosophic Cubic Sets," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 41-54, March.
    2. Yangyang Jiao & Lu Wang & Jianxia Liu & Gang Ma, 2020. "Multi-criteria decision making based on induced generalized interval neutrosophic Choquet integral," PLOS ONE, Public Library of Science, vol. 15(12), pages 1-25, December.
    3. Juan-juan Peng & Chao Tian & Zhi-qiang Zhang & Hai-yu Song & Jian-qiang Wang, 2019. "Single-Valued Neutrosophic Power Shapley Choquet Average Operators and Their Applications to Multi-Criteria Decision-Making," Mathematics, MDPI, vol. 7(11), pages 1-27, November.
    4. Khaleed Alhazaymeh & Muhammad Gulistan & Majid Khan & Seifedine Kadry, 2019. "Neutrosophic Cubic Einstein Hybrid Geometric Aggregation Operators with Application in Prioritization Using Multiple Attribute Decision-Making Method," Mathematics, MDPI, vol. 7(4), pages 1-16, April.
    5. Mehdi Keshavarz Ghorabaee & Maghsoud Amiri & Edmundas Kazimieras Zavadskas & Reyhaneh Hooshmand & Jurgita Antuchevičienė, 2017. "Fuzzy extension of the CODAS method for multi-criteria market segment evaluation," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 18(1), pages 1-19, January.
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