Preference modeling on totally ordered sets by the Sugeno integral

Abstract

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The role of fuzzy sets in decision sciences: Old techniques and new directions

“…Minimum P min) operation is retrieved. These operations have been used in decision under uncertainty (as a substitute to expected utility [44]) and for criteria aggregation with finite value scales [43] The leximin and leximax operations can be extended in order to refine P max and P min. The idea is as follows (Fargier,Sabbadin [45]).…”

The logical encoding of Sugeno integrals

“…If (A(x, )) ≥ then (x) ≥ Let us note that using the results presented in [27] the previous condition is necessary and sufficient. In this paper, we have shown that a Sugeno integral can be modeled by a -base or an N-base in possibilistic logic.…”

“…Hence we just need to identify the fuzzy measures such that [∧ j∈T p j ( ), ] (x) ≥ . In order to calculate these solutions, let us make a brief reminder of the result proved in [27].…”

Fuzzy Measures and Integrals in MCDA

“…). A detailed study of this problem has been done by Rico et al [63] for the Sugeno integral. We mention also the work of Greco et al based on decision rules, which can be found in Chapter 12 of this book (see also [38]).…”