Additive decomposition of fuzzy pre-orders
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Cited by (49)
Axiomatizing logics of fuzzy preferences using graded modalities
2020, Fuzzy Sets and SystemsCitation Excerpt :Two main approaches to representing and handling preferences have been developed: the relational and the logic-based approaches. The most influential reference is the book by Fodor and Roubens [21], that was followed by many other works like, for example [11–14,16]. In this setting, many questions have been discussed, like e.g. the definition of the strict fuzzy order associated to a fuzzy preorder (see for example [6–8,20]).
A hitchhiker's guide to quasi-copulas
2020, Fuzzy Sets and SystemsCitation Excerpt :We start by recalling the definition of a preference structure. For more in-depth results on the role of 2-quasi-copulas in the study of fuzzy preference structures, in particular the important property of transitivity, we refer to [29–32]. Additionally, we have studied how quasi-copulas have been used in the literature to develop bounds on sets of copulas, for example, on the set of copulas with given values on a specific compact set, once again paying special attention to how the results have been developed in the bivariate and in the multivariate case.
Fuzzy levels of preference strength in a graph model with multiple decision makers
2019, Fuzzy Sets and SystemsCitation Excerpt :The concept of fuzzy sets was invented by Zadeh [20–22]. Subsequently, this idea and associated logic were further developed by other researchers [23–26], to name but a few, see [27] and the references contained therein for overviews. In application, fuzzy sets were widely used to express uncertain information in various decision making problems, such as the consensus reaching model involving a group of decision makers [28–30], which is focused on finding a consensus or a collective preference among different experts even there are non-cooperative behaviors.
Weak transitivity of interval-valued fuzzy relations
2014, Knowledge-Based SystemsCitation Excerpt :If a DM provides a preference relation does not possess transitivity (i.e., inconsistency problems exist), the ranking result of alternatives is misleading [25,26,29]. Transitivity of a fuzzy preference relation has been received greatly attention in the past decades [2,3,9–16,18,20,28,29], such as weak transitivity (or called weak stochastic transitivity) [8,15,16,18,31,32,40,41], max–min transitivity [19,25,31,33,37], max-max transitivity [25,31], restricted max–min transitivity (or moderate stochastic transitivity) [8,15,16,25,31–33,37], restricted max-max transitivity (or strong stochastic transitivity) [8,15,16,18,25,31,32], multiplicative consistency [8,25] and additive consistency [8,25]. It should be pointed out that, strictly speaking, additive consistency is not a type of transitivity [17].
Exchangeable copulas
2013, Fuzzy Sets and SystemsCollective transitivity in majorities based on difference in support
2013, Fuzzy Sets and Systems