On decision evaluation functions in three-way decision spaces derived from overlap and grouping functions
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On decision evaluation functions in three-way decision spaces derived from overlap and grouping functions Zihang Jia1 · Junsheng Qiao1
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Overlap and grouping functions, as two kinds of particular binary aggregation functions, have been continuously discussed in the literature for their vast preponderance in some real applications. Meanwhile, after Hu introduced the notion of three-way decision spaces, the decision evaluation functions in three-way decision spaces constructed from the so-called semi-decision evaluation functions have been investigated consistently. This paper continues to consider this research topic and mainly focuses the decision evaluation functions in three-way decision spaces obtained from overlap and grouping functions. Firstly, based on overlap and grouping functions, we give several methods of constructing semi-decision evaluation functions in semithree-way decision spaces. Secondly, we show some novel semi-decision evaluation functions which are related to fuzzy sets, interval-valued fuzzy sets, fuzzy relations and hesitant fuzzy sets, respectively. Finally, using overlap and grouping functions, we get some ways to construct decision evaluation functions in three-way decision spaces from semi-decision evaluation functions in semi-three-way decision spaces. Keywords (Semi-)three-way decision spaces · Decision evaluation functions · Overlap functions · Grouping functions
1 Introduction 1.1 Short retrospect to overlap and grouping functions In 2009, in order to measure the overlapping degree between two classes, Bustince et al. (2009) introduced the concept of overlap functions. Meanwhile, in 2012, grouping functions were introduced by Bustince et al. (2012) for the pairwise comparison of alternatives in fuzzy preference modeling. Over the decade, these two new binary aggregation functions have met a fast development both in real applications and theory. Communicated by A. Di Nola. This work was supported by the National Natural Science Foundation of China (11901465), the Scientific Research Fund for Young Teachers of Northwest Normal University (NWNU-LKQN-18-28) and the Doctoral Research Fund of Northwest Normal University (6014/0002020202).
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To be precise, in applications, overlap and grouping functions play a key role in miscellaneous respects of practical issues, such as in image processing (Bustince et al. 2010; Jurio et al. 2013), classification (Elkano et al. 2016, 2015; Lucca et al. 2015; Paternain et al. 2016), decision making (Bustince et al. 2012; Elkano et al. 2018) and fuzzy community detection problems (Gómez et al. 2016b). In theory, there exists a vast literature which involve in miscellaneous respects of overlap and grouping functions, for instance, the crucial properties (Qiao and Hu 2018a, 2019; Zhou and Yan 2019), corresponding implications (Dimuro and Bedregal 2015; Dimuro et al. 2014, 2017, 2019), additive and multiplicative generator pairs (Dimuro et al. 2016; Qiao and Hu 2018d), con
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