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Neural Computing and Applications
Published in: Neural Computing and Applications 1/2019

26-04-2017 | Original Article

Probabilistic soft sets and dual probabilistic soft sets in decision-making

Authors: Fatia Fatimah, Dedi Rosadi, RB. Fajriya Hakim, José Carlos R. Alcantud

Published in: Neural Computing and Applications | Special Issue 1/2019

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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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Footnotes
1
Concerning the determination of weights, Liu et al. [31] and Winkler [41] provide arguments.
 
2
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.
 
3
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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Metadata
Title
Probabilistic soft sets and dual probabilistic soft sets in decision-making
Authors
Fatia Fatimah
Dedi Rosadi
RB. Fajriya Hakim
José Carlos R. Alcantud
Publication date
26-04-2017
Publisher
Springer London
Published in
Neural Computing and Applications / Issue Special Issue 1/2019
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-017-3011-y

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