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The Symmetric Sugeno Integral
[article]

2008
*
arXiv
*
pre-print

We propose an extension of

arXiv:0804.1760v1
fatcat:beupvo4waranzjconjbn3q7evm
*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. ...##
###
The symmetric Sugeno integral

2003
*
Fuzzy sets and systems (Print)
*

We propose an extension of

doi:10.1016/s0165-0114(02)00499-2
fatcat:nop5ezhylzh2nf5dwalwxf6ufy
*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. ...##
###
Choquet integral with respect to a symmetric fuzzy measure of a function on the real line

2012
*
Annals of Operations Research
*

Acknowledgements Partial support by

doi:10.1007/s10479-012-1166-6
fatcat:spy2gqxabjhx3ltt6o2f6mejz4
*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 ...##
###
Bipolar fuzzy integrals

2013
*
Fuzzy sets and systems (Print)
*

These include

doi:10.1016/j.fss.2012.11.021
fatcat:vbpvp5eebvdwpehojufdlcnd2u
*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] . ...##
###
Fitting Symmetric Fuzzy Measures for Discrete Sugeno Integration
[chapter]

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. ...

##
###
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

2006
*
2006 IEEE International Conference on Fuzzy Systems
*

This paper discusses

doi:10.1109/fuzzy.2006.1681842
dblp:conf/fuzzIEEE/BotteldoorenVBL06
fatcat:tq2bo3mfbzflpij57gh7iheqpm
*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*. ...##
###
Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices
[article]

2009
*
arXiv
*
pre-print

We give several characterizations of discrete

arXiv:0808.2619v3
fatcat:n5rs4ozcbrd3jm6elvowrlqk64
*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*, ...##
###
Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices

2010
*
Fuzzy sets and systems (Print)
*

We discuss several characterizations of discrete

doi:10.1016/j.fss.2009.10.008
fatcat:tfsvw6kwrbacxfgf62yydbffh4
*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*, ...##
###
Fuzzy Measures and Integrals: Recent Developments
[chapter]

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*. ...

##
###
The Bipolar Universal Integral
[chapter]

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] . ...

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

2018
*
arXiv
*
pre-print

In this paper we provide two-sided attainable bounds of Jensen type for

arXiv:1809.08303v1
fatcat:lzmpy5pirrb35oq5lmta26cr5a
*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. ...##
###
Discrete Integrals Based on Comonotonic Modularity

2013
*
Axioms
*

Choquet

doi:10.3390/axioms2030390
fatcat:4whwegtdo5dzhmu7scgnro4b54
*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. ...##
###
Bipolar Fuzzy Integrals
[article]

2012
*
arXiv
*
pre-print

Among them, we remember

arXiv:1204.5943v1
fatcat:fnkgq4w3orcfrdfvmdv3csxnhq
*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) = ...##
###
Explicit Descriptions of Associative Sugeno Integrals
[chapter]

2010
*
Communications in Computer and Information Science
*

In this paper, we investigate these two generalizations in

doi:10.1007/978-3-642-14055-6_48
fatcat:4kebcnmje5g5jiwjsaggpemcde
*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. ...
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