Q5 Detailed Comments To The Authors:
The paper provides a convincing generalisation of many other decision rules models. However, there are some issues to be addressed here and there:
(NOTED) I believe that \Omega should be finite since the very beginning and overal. In general, be carefull about the finiteness/non-finitenesses of sets. So, also MS(U) should be set of finite multisets, otherwise e.g., in prop.4 mean(X), for X non finite is ill defined.
(NOTED) in E^Pess, E^Pess', what are the first three paprameters exactly?

Q5 Detailed Comments To The Authors:
(IGNORED) 1)The paper does not give experiments or examples. 
(NOTED) 2)The paper lacks the prospect of future work. 
(NOTED) 3)How does the writer argue that his work is better.

Q5 Detailed Comments To The Authors:
Main comments: the contribution deals with an interesting topic, generalizes existing results related to the expected utility representation with non-additive measures and the results seem correct and sound. If I had to nitpick,
(NOTED) I miss a deeper discussion about the role of the function f in the XEU. It is true that the authors discuss its relevance at the beginning of page 6-column 1, but I would suggest to expand this discussion because it would allow the reader to better understand its meaning. 
(Noted) As well, I would appreciate if the authors add a (non-trivial) example in Section 3 showing the generality of the presented framework. 
(NOTED) Finally, I would suggest to thoroughly reviewing the writing. 

Evaluation: Anyway, apart from the comments above, the manuscript perfectly fits with the scope of the conference and I the content is interesting, hence I recommend to accept it. 

Detailed comments (P=page, C=columna, L=line): 
(DONE) Moebius -> M\” obius 
(DONE) monotonic -> monotone 
(DONE) P1,C2,L10: “…work of Halpern and al.”: do you mean Halpern at al? 
(DONE) Please, add reference. 
(DONE) Def 2: monotony -> monotonicity. 
(TODO) Also: shouldn’t you detailed monotone increasing? 
(DONE) Example 1: you may specify that you are using a probability measure, a belief function and a possibility measure. 
(DONE) Def 10, last equation: shouldn’t \succeq be \succeq^v? 
(DONE) Def 12 and 13: I suggest to write \succeq instead of \preceq to be consistent with the previous notation. 
(NOTED) Thm.1: please, add reference. 
(DONE) P4, C1, L24: “monotonic” -> “monotonicity”. 
(DONE) P4, C1, L-8: “regards” -> “regard” 
(DONE) P4, C2, L9: “such as” -> “such that”. 
(DONE) Also, add a final dot at the end of the itemize. 
(NOTED) P4, C2, sentence before def.18: it is unclear; please, rewrite. 
(NOTED) P5, C1, L4-5: unclear sentence; please, rewrite. 
(DONE) Def.21: “such as” -> “such that”. 
(NOTED) P6, C1, paragraphs 1, 2 and 3: I would expand and detail this part to emphasize the relevance of the function f. 
(DONE) P6, C1, L22: “show” -> “shows”.



Q5 Detailed Comments To The Authors:

Because of the generality of the algebraic capacity and its corresponding mass function used in the proposed XEU framework, it can cover a lot of existing decision rules. On one hand, this is indeed a nice result and represents theoretical advance on the endeavor of integrating diverse uncertain formalisms. On the other hand, it is less clear how the work can have impact on the practice of decision-making under uncertainty. 
(NOTED) There is a short remark in the conclusion regarding advantages of the algebraic framework on the computational aspect of the decision rules. However, it need further elaboration on how easily algorithms developed for general algebraic structures can be transferred to more concrete domains.
In addition, the fact that the framework can instantiate a diverse of existing decision rules does not provide much insight on the development of new decision theories. A more insightful direction is perhaps to find new instances of algebraic capacity or mass functions with practical sense and show that the framework can help design meaningful decision rules in those cases.

(NOTED) As there is no guarantee about the unique existence of \boxplus-mass function for a given capacity and as a result, it seems that m_{\mu}^\Boxplus is defined only for commutative group operator \boxplus (Def.19), it is not sure if the restriction is also applied to the definition of XEU since m_{\mu}^\Boxplus explicitly appears in its formulation. If it is the case, then obviously, the applicability of XEU become more restrictive as it excludes many qualitative uncertainty measures. If not, does it mean that XEU may not exist or be not unique for any decision problem and expectation domain?

Below, I list some minor technical issues (or typos) to be clarified.<
(DONE)  Table 1, \Pi violates monotony on {\omega_1} and {\omega1,\omega_3}
(DONE)  Def.10, typo on the expression for GEU: , :\mid
(DONE)  Def.12: as x_1 and x_2 are acts, the RHS should use u(x_1) and u(x_2)
(DONE)  Def.17: W or W^*?
(DONE)  L.2 after Def.18: identity element or neutral element?
(DONE)  Def.23: It seems that B is a subset of U?
(TODO)  Def.24: Is it implicitly assumed that W^*=W and U^*=U in the definition? Answer: NON
(DONE)  L.4, Sec.4.1: do not are not
(NOTED)  Does the \boxplus-decomposability of a capacity imply the uniqueness of its \boxplus-based mass function? Otherwise, the theorem may not hold for all of its \boxplus-based mass functions.
(DONE)  In rewriting U^{Pess}, it seems that the definition of nmax presupposes the existence of the minus operator in the domain \Lambda. When \Lambda is not [0,1], is the restriction reasonable?
(DONE)  In the definition of CEU, x_0\chi seems not defined.
(NOTED)  The section entitled Partial Orderings, L.3: they are?
(NOTED)  Proposition 7: it seems that the definition does not match with the XEU framework as U=\mathbb{R}, W=[0,1], and V=\mathbb{R}^2. According to Def.20, it should be \otimes: \mathbb{R}\times[0,1]\rightarrow\mathbb{R}^2 and {\bf f}:{\cal MS}(\mathbb{R})\rightarrow\mathbb{R}, but arguments of these two operators in the definition do not have correct types. It seems that changing U into \mathbb{R}^2 can partially address the issue (only for the \otimes operator). However, because it is said that DSEU considers real-valued utilit functions, I am not sure if the change complies with the original DSEU.
