Abstract
Since its introduction by Molodstov (Computers & Mathematics with Applications 37(4):19–31 1999), soft set theory has been widely applied in various fields of study. Soft set theory has also been combined with other theories like fuzzy sets theory, rough sets theory, and probability theory. The combination of soft sets and probability theory generates probabilistic soft set theory. However, decision-making based on the probabilistic soft set theory has not been discussed in the literature. In this paper, we propose new algorithms for decision-making based on the probabilistic soft set theory. An example to show the application of these algorithms is given, and its possible extensions and reinterpretations are discussed. Inspired by realistic situations, the notion of dual probabilistic soft sets is proposed, and also, its application in decision-making is investigated.
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Peng and Yang [36] is another recent reference on the applicability of regret theory to an extended model of soft sets with a stochastic component, namely, interval-valued fuzzy soft sets.
Examples in Alcantud [2] show that when dominated alternatives are not eliminated, zero elements can appear at the C comparison matrix. For such reason, we cannot ensure a correct performance of the Perron-Frobenius argument for examples with dominated alternatives.
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Acknowledgments
Part of this research was done while the first author was invited at the Department of Economics and Economic History in Salamanca. Their hospitality is gratefully acknowledged. The authors are thankful to the Editor-in-Chief, Professor John MacIntyre, and the anonymous referees for their time and efforts to review this article.
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Fatimah, F., Rosadi, D., Hakim, R.F. et al. Probabilistic soft sets and dual probabilistic soft sets in decision-making. Neural Comput & Applic 31 (Suppl 1), 397–407 (2019). https://doi.org/10.1007/s00521-017-3011-y
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DOI: https://doi.org/10.1007/s00521-017-3011-y