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Reduced soft matrices and generalized products with applications in decision making

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Abstract

A soft matrix multiplication of matrices in different types was not possible so far. In this study, we generalize the soft matrix products And, And–Not, Or, Or–Not defined in Çağman and Enginoğlu (Comput Math Appl 59:3308–3314, 2010) so as to multiply soft matrices in different types. Furthermore, these generalizations allow us to multiply soft matrices more than two soft matrices. Therefore, we can solve decision making problems with multiple decision makers using a single product. These new operations make the process of solving decision making problems faster, easier and more convenient. Then we construct some effective decision making methods called soft distributive max–min (max–max, min–min, min–max) decision making methods. We also provided Scilab codes to demonstrate our methods.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100, Yozgat, Turkey

    Akın Osman Atagün, Hüseyin Kamacı & Onur Oktay

Authors
  1. Akın Osman Atagün
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  2. Hüseyin Kamacı
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  3. Onur Oktay
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Correspondence to Akın Osman Atagün.

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The authors declare that there is no conflict of interests regarding the publication of this paper.

Appendix

Appendix

Scilab Algorithms: We give following algorithms since one of the generalized products which \(\curlyvee \), \(\overset{-}{\curlywedge }\) and \(\underset{-}{\curlyvee }\) we can use for decision problems.

figure c

We give following algorithms since one of the decision making methods (SDmMDM), (SDmmDM) and (SDMMDM) we can use for decision problems.

figure d

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Atagün, A.O., Kamacı, H. & Oktay, O. Reduced soft matrices and generalized products with applications in decision making. Neural Comput & Applic 29, 445–456 (2018). https://doi.org/10.1007/s00521-016-2542-y

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