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The Symmetric Sugeno Integral [article]

Michel Grabisch
2008 arXiv   pre-print
We propose an extension of the Sugeno integral for negative numbers, in the spirit of the symmetric extension of Choquet integral, also called \Sipos\ integral.  ...  In a second step, we introduce the M\"obius transform on this new structure. Lastly, we define the symmetric Sugeno integral, and show its similarity with the symmetric Choquet integral.  ...  We thank also the anonymous reviewers for their constructive comments.  ... 
arXiv:0804.1760v1 fatcat:beupvo4waranzjconjbn3q7evm

The symmetric Sugeno integral

Michel Grabisch
2003 Fuzzy sets and systems (Print)  
We propose an extension of the Sugeno integral for negative numbers, in the spirit of the symmetric extension of Choquet integral, also calledŠipoš integral.  ...  In a second step, we introduce the Möbius transform on this new structure. Lastly, we define the symmetric Sugeno integral, and show its similarity with the symmetric Choquet integral.  ...  We thank also the anonymous reviewers for their constructive comments.  ... 
doi:10.1016/s0165-0114(02)00499-2 fatcat:nop5ezhylzh2nf5dwalwxf6ufy

Choquet integral with respect to a symmetric fuzzy measure of a function on the real line

Yasuo Narukawa, Vicenç Torra, Michio Sugeno
2012 Annals of Operations Research  
Acknowledgements Partial support by the Spanish MEC (projects ARES-CONSOLIDER INGENIO 2010 CSD2007-00004-and eAEGIS-TSI2007-65406-C03-02) is acknowledged.  ...  $\mu$ $([0,1], \mathcal{B})$ $\mu$ (symmetric) $\lambda(A)=\lambda(B)$ $\mu(A)=\mu(B)$ 3.3.  ...  $a\in \mathcal{F}_{b}([0,1])$ The continuous $OWA$ opemtor (COWA) $COWA_{\mu}( a)=(C)\int ad\mu$ $\mu$ $\mu$ $([0,1], \mathcal{B})$ $([0,1], \mathcal{B})$ $\lambda$ $\lambda(A)<\lambda(B)$ $B'\in \mathcal  ... 
doi:10.1007/s10479-012-1166-6 fatcat:spy2gqxabjhx3ltt6o2f6mejz4

Bipolar fuzzy integrals

Salvatore Greco, Fabio Rindone
2013 Fuzzy sets and systems (Print)  
These include the Choquet integral, the Shilkret integral and the Sugeno integral, among others. Recently, a bipolar Choquet integral was proposed for cases in which the underlying scale is bipolar.  ...  In this paper we propose a bipolar Shilkret integral and a bipolar Sugeno integral. Moreover, we provide an axiomatic characterization of all three bipolar fuzzy integrals.  ...  Pap and Mihailovic extended the notion of a symmetric Sugeno integral [23] .  ... 
doi:10.1016/j.fss.2012.11.021 fatcat:vbpvp5eebvdwpehojufdlcnd2u

Fitting Symmetric Fuzzy Measures for Discrete Sugeno Integration [chapter]

Marek Gągolewski, Simon James
2017 Advances in Intelligent Systems and Computing  
The Sugeno integral has numerous successful applications, including but not limited to the areas of decision making, preference modeling, and bibliometrics.  ...  Despite this, the current state of the development of usable algorithms for numerically fitting the underlying discrete fuzzy measure based on a sample of prototypical values -even in the simplest possible  ...  This study was supported by the National Science Center, Poland, research project 2014/13/D/HS4/01700. Data provided by Scopus.com.  ... 
doi:10.1007/978-3-319-66824-6_10 fatcat:kn73kurtfngdpbnzmpm5eat6ri

Page 7760 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
In this paper the author defines and studies a symmetric Sugeno integral, keeping the ordinal nature of the Sugeno integral and its construction.  ...  based on the preceding two steps. (§5) Finally in 86 he gives alternative definitions and examples of 28 MEASURE AND INTEGRATION 7760 symmetric Sugeno integrals and in the last section surveys related  ... 

Fuzzy Integrals as a Tool for Obtaining an Indicator for Quality of Life

D. Botteldooren, A. Verkeyn, B. De Baets, P. Lercher
2006 2006 IEEE International Conference on Fuzzy Systems  
This paper discusses the choice of fuzzy integrals and analyses the suitability of the approach based on a survey with 2000 people.  ...  Multi-criteria evaluation systems based on fuzzy integrals seem very well suited for this task as they tend to approximate overall quality assessment by inhabitants quite well.  ...  Bipolar discrete Sugeno integral with k-maxitive fuzzy measure Let's start by recalling the definition of the symmetric Sugeno integral.  ... 
doi:10.1109/fuzzy.2006.1681842 dblp:conf/fuzzIEEE/BotteldoorenVBL06 fatcat:tq2bo3mfbzflpij57gh7iheqpm

Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices [article]

Miguel Couceiro, Jean-Luc Marichal
2009 arXiv   pre-print
We give several characterizations of discrete Sugeno integrals over bounded distributive lattices, as particular cases of lattice polynomial functions, that is, functions which can be represented in the  ...  We also consider the subclass of term functions as well as the classes of symmetric polynomial functions and weighted minimum and maximum functions, and present their characterizations, accordingly.  ...  Some noteworthy subclasses of Sugeno integrals were also considered, namely those of • term functions, which were shown to constitute weakly conservative Sugeno integrals, • symmetric Sugeno integrals,  ... 
arXiv:0808.2619v3 fatcat:n5rs4ozcbrd3jm6elvowrlqk64

Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices

Miguel Couceiro, Jean-Luc Marichal
2010 Fuzzy sets and systems (Print)  
We discuss several characterizations of discrete Sugeno integrals over bounded distributive lattices as particular cases of lattice polynomial functions, that is, functions which can be represented in  ...  We also consider the subclass of term functions as well as the classes of symmetric polynomial functions and weighted infimum and supremum functions, and present their characterizations, accordingly.  ...  Some noteworthy subclasses of Sugeno integrals were also considered, namely those of • term functions, which were shown to constitute weakly conservative Sugeno integrals, • symmetric Sugeno integrals,  ... 
doi:10.1016/j.fss.2009.10.008 fatcat:tfsvw6kwrbacxfgf62yydbffh4

Fuzzy Measures and Integrals: Recent Developments [chapter]

Michel Grabisch
2015 Studies in Fuzziness and Soft Computing  
the extension of the Choquet integral for nonmeasurable functions, and the notion of universal integral.  ...  This paper surveys the basic notions and most important results around fuzzy measures and integrals, as proposed independently by Choquet and Sugeno, as well as recent developments.  ...  The Choquet and Sugeno integrals The term "fuzzy integral" has been introduced by Sugeno [7] in 1974, and is now most commonly called the Sugeno integral.  ... 
doi:10.1007/978-3-319-19683-1_8 fatcat:m2wvkev62rdwvnvm7fwgk3twba

The Bipolar Universal Integral [chapter]

Salvatore Greco, Radko Mesiar, Fabio Rindone
2012 Communications in Computer and Information Science  
The concept of universal integral, recently proposed, generalizes the Choquet, Shilkret and Sugeno integrals.  ...  In this paper we propose the bipolar universal integral generalizing the Choquet, Shilkret and Sugeno bipolar integrals.  ...  The universal integral generalizes the Choquet integral [2] , the Sugeno integral [18] and the Shilkret integral [17] .  ... 
doi:10.1007/978-3-642-31718-7_38 fatcat:sprfbfbp5rc3dompcxml4omfsa

Sharp bounds of Jensen type for the generalized Sugeno integral [article]

Michał Boczek, Marek Kałuszka
2018 arXiv   pre-print
In this paper we provide two-sided attainable bounds of Jensen type for the generalized Sugeno integral of any measurable function.  ...  As a by-product, we obtain sharp inequalities for symmetric integral of Grabisch. To the best of our knowledge, the results in the real-valued functions context are presented for the first time here.  ...  Acknowledgements The authors would like to thank the referees for their comments which led to improvements in the paper.  ... 
arXiv:1809.08303v1 fatcat:lzmpy5pirrb35oq5lmta26cr5a

Discrete Integrals Based on Comonotonic Modularity

Miguel Couceiro, Jean-Luc Marichal
2013 Axioms  
Choquet integrals and symmetric signed Choquet integrals as well as natural extensions of Sugeno integrals.  ...  It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions.  ...  Acknowledgments This research is partly supported by the internal research project F1R-MTH-PUL-12RDO2 of the University of Luxembourg.  ... 
doi:10.3390/axioms2030390 fatcat:4whwegtdo5dzhmu7scgnro4b54

Bipolar Fuzzy Integrals [article]

Salvatore Greco, Fabio Rindone
2012 arXiv   pre-print
Among them, we remember the Choquet integral, the Shilkret integral and the Sugeno integral.  ...  Recently, the bipolar Choquet integral has been proposed for the case in which the underlying scale is bipolar. In this paper we propose the bipolar Shilkret integral and the bipolar Sugeno integral.  ...  Suppose that µ ∶ 2 N → [0, 1], is a capacity and x ∈ [−1, 1] n is a vector evaluated on each criterion on the symmetric scale [−1, 1], the symmetric Sugeno integral (5) of x is defined aš Su (x , µ) =  ... 
arXiv:1204.5943v1 fatcat:fnkgq4w3orcfrdfvmdv3csxnhq

Explicit Descriptions of Associative Sugeno Integrals [chapter]

Miguel Couceiro, Jean-Luc Marichal
2010 Communications in Computer and Information Science  
In this paper, we investigate these two generalizations in the case of Sugeno integrals over bounded distributive lattices and present explicit descriptions of the corresponding associative functions.  ...  We also show that, in this case, both generalizations of associativity are essentially the same.  ...  We say that a function g: L * → L is a Sugeno integral if every g n , n ≥ 1, is a Sugeno integral. The following theorem yields a description of associative Sugeno integrals g: L * → L.  ... 
doi:10.1007/978-3-642-14055-6_48 fatcat:4kebcnmje5g5jiwjsaggpemcde
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