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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.  ...  Indicators that reflect the subjective evaluation of well-being or quality of life by inhabitants have to be constructed based on multiple criteria.  ...  ) ( ) ( µ µ µ Definition k-maxitive fuzzy measure [10] : Consider k ∈ {1, 2,..., n}.  ... 
doi:10.1109/fuzzy.2006.1681842 dblp:conf/fuzzIEEE/BotteldoorenVBL06 fatcat:tq2bo3mfbzflpij57gh7iheqpm

Page 1064 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
The second case is that of a symmetric k-order maxitive fuzzy measure, i.e., a fuzzy measure of which the possibilistic Mobius transform vanishes in sets with cardinality greater than k.  ...  The first case is that of a symmetric k-order additive fuzzy measure, i.e., a fuzzy measure for which the MoObius transform vanishes in sets with cardinality greater than k.  ... 

OM3: Ordered maxitive, minitive, and modular aggregation operators – Axiomatic and probabilistic properties in an arity-monotonic setting

Anna Cena, Marek Gagolewski
2015 Fuzzy sets and systems (Print)  
., OM3: Ordered maxitive, minitive, and modular aggregation operators -axiomatic and probabilistic properties in an arity-monotonic setting, Fuzzy Sets and Systems 264, 2015, pp. 138-159,  ...  The recently-introduced OM3 aggregation operators fulfill three appealing properties: they are simultaneously minitive, maxitive, and modular. Among the instances of OM3 operators we find e.g.  ...  ., OM3: Ordered maxitive, minitive, and modular aggregation operators -axiomatic and probabilistic properties in an arity-monotonic setting, Fuzzy Let us investigate the behavior of the expected value  ... 
doi:10.1016/j.fss.2014.04.001 fatcat:gwjchco3wvckdma2d2u7agrvli

Basic generated universal fuzzy measures

R. Mesiar, A. Mesiarová-Zemánková, L'. Valášková
2007 International Journal of Approximate Reasoning  
Special classes and properties of basic generated universal fuzzy measures are discussed, especially the additive, the symmetric and the maxitive case.  ...  The concept of basic generated universal fuzzy measures is introduced.  ...  The idea of universal fuzzy measures is related to the fuzzy measures in the same way as the extended aggregation operators (i.e., aggregation operators without fixed arity, acting on arbitrary finitely  ... 
doi:10.1016/j.ijar.2006.12.012 fatcat:wpv2n2ekvzbqxafr7gdix2sbaa

Bipolar Fuzzy Integrals [article]

Salvatore Greco, Fabio Rindone
2012 arXiv   pre-print
Moreover, we provide an axiomatic characterization of all these three bipolar fuzzy integrals.  ...  maxitive if it is maxitive on such a type of bipolar comonotonic bi-constants, i.e. if fixed K = {1, . . . , k} it holds: k ∈ R with 0 < l 1 < l 2 < . . . < l k ≤ 1 and a sequence {(A i , B i )} i=1,..  ...  As we said, the bipolar fuzzy integrals admit a further generalization if the fuzzy measure (capacity) with respect to which the integrals are calculated can change from a level to another (12; 11) .  ... 
arXiv:1204.5943v1 fatcat:fnkgq4w3orcfrdfvmdv3csxnhq

On aggregation functions based on linguistically quantified propositions and finitely additive set functions

Julien Ah-Pine
2016 Fuzzy sets and systems (Print)  
Our approach is similar to the TOWA function in spirit but instead of using a maxitive measure we propose to rely on a real-valued finitely additive set function.  ...  We study aggregation functions defined as convex combinations of the linguistically quantified propositions "at least k criteria are satisfied".  ...  On the one hand, as already mentioned, TOWA relies on a maxitive measure.  ... 
doi:10.1016/j.fss.2015.06.002 fatcat:j45xujqw2vcatffylmmehhhvva

k -maxitive Sugeno integrals as aggregation models for ordinal preferences

Quentin Brabant, Miguel Couceiro
2018 Fuzzy sets and systems (Print)  
Abstract We consider an order variant of k-additivity, so-called k-maxitivity, and present an axiomatization of the class of k-maxitive Sugeno integrals over distributive lattices.  ...  To cite this version: Quentin Brabant, Miguel Couceiro. k-maxitive Sugeno integrals as aggregation models for ordinal preferences. Fuzzy Sets and Systems, Elsevier, 2018, 343, pp.  ...  This is why a suitable error measure in this context is the pairwise error, which corresponds to the ratio of pairs of elements that are wrongly ordered by the aggregation model.  ... 
doi:10.1016/j.fss.2017.06.005 fatcat:vygv3ixmvvg7djvzo43wmp6xpe

Quasi-continuous histograms

Olivier Strauss
2009 Fuzzy sets and systems (Print)  
We propose a new density estimator based on transferring the counts associated with each cell of the fuzzy partition to any subset of the reference interval.  ...  However, histograms suffer from a high sensitivity to the choice of both reference interval and bin width. This paper addresses this difficulty by means of a fuzzy partition.  ...  This additive way of aggregating the (a k ) k=1,. ..  ... 
doi:10.1016/j.fss.2009.01.013 fatcat:fgi4mfbbcjdslahutdko54ztci

Bipolar fuzzy integrals

Salvatore Greco, Fabio Rindone
2013 Fuzzy sets and systems (Print)  
Moreover, we provide an axiomatic characterization of all three bipolar fuzzy integrals.  ...  Theorem 3. [19] An aggregation function G ∶ I n → I is idempotent, comonotone maxitive and stable with respect to the minimum if and only if there exists a measure ν on N with a scale I such that, for  ...  In Section 2 we present preliminaries and list some properties of an aggregation function useful in the characterization of the bipolar fuzzy integrals considered here.  ... 
doi:10.1016/j.fss.2012.11.021 fatcat:vbpvp5eebvdwpehojufdlcnd2u

THE USE OF THE DISCRETE SUGENO INTEGRAL IN DECISION-MAKING: A SURVERY

D. DUBOIS, J. L. MARICHAL, H. PRADE, M. ROUBENS, R. SABBADIN
2001 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
An overview of the use of the discrete Sugeno integral as either an aggregation tool or a utility function is presented in the qualitative framework of two decision paradigms: multi-criteria decision-making  ...  Important particular cases of Sugeno integrals such as prioritized minimum and maximum operators, their ordered versions, and Boolean max-min functions are studied.  ...  Acknowledgements The paper was prepared during a one-month visit of Jean-Luc Marichal at the "Institut de Recherche en Informatique de Toulouse" (University Paul Sabatier, Toulouse), in the framework of  ... 
doi:10.1142/s0218488501001058 fatcat:rqc2mjok5fhgfe22onwvm6tjee

Axiomatisation of Discrete Fuzzy Integrals with Respect to Possibility and Necessity Measures [chapter]

D. Dubois, A. Rico
2016 Lecture Notes in Computer Science  
This additional axiom enforces the maxitivity or the minitivity of the capacity and essentially assumes that the decisionmaker preferences only reflect the plausibility ordering between states of nature  ...  Necessity (resp. possibility) measures are very simple representations of epistemic uncertainty due to incomplete knowledge.  ...  The definition of discrete fuzzy integrals is based on a monotonic set function named capacity or fuzzy measure.  ... 
doi:10.1007/978-3-319-45656-0_8 fatcat:u2klt2lq5bhfdjvee6cd4d3lhu

An Approach to Consensus Reaching in Multiperson Decision Making Problems with Incomplete Information

Sergio Alonso, Enrique Herrera-Viedma, Francisco Chiclana, Francisco Herrera
2005 European Society for Fuzzy Logic and Technology  
These rules are based on consistency and consensus measures.  ...  In this paper we present a Consensus Reaching Process for MPDM where the information given by the experts is based on incomplete fuzzy preference relations.  ...  In order to model such situations, we define the concept of an incomplete fuzzy preference relation: Definition 2.  ... 
dblp:conf/eusflat/AlonsoHCH05 fatcat:ntiuyntvsvcctmo4wgq44u2sbe

Congruences and the discrete Sugeno integrals on bounded distributive lattices

Radomír Halaš, Radko Mesiar, Jozef Pócs
2016 Information Sciences  
We study compatible aggregation functions on a general bounded distributive lattice L, where the compatibility is related to the congruences on L.  ...  As a by-product, a new proof of an earlier result of G. Grätzer is obtained. Moreover, our results yield a new characterization of discrete Sugeno integrals on bounded distributive lattices.  ...  As a typical example, recall Goguen's introduction of L-fuzzy sets [8] and several of related particular concepts based on particular bounded lattices, such as fuzzy type-2 sets proposed by Zadeh [23  ... 
doi:10.1016/j.ins.2016.06.017 fatcat:kwlb5do3bfaw5pkxgv732askm4

A Learning Procedure to Estimate Missing Values in Fuzzy Preference Relations Based on Additive Consistency [chapter]

Sergio Alonso, Francisco Chiclana, Francisco Herrera, Enrique Herrera-Viedma
2004 Lecture Notes in Computer Science  
In decision-making, information is usually provided by means of fuzzy preference relations.  ...  We also define an expert consistency measure, based on additive consistency property.  ...  In particular, in this paper we use the additive consistency property [4] to define a consistency measure of the expert's information. In order to do this, the paper is set out as follows.  ... 
doi:10.1007/978-3-540-27774-3_22 fatcat:ioakoudugranniiimeeggjpu34

Non-additive interval-valued F-transform

O. Strauss
2015 Fuzzy sets and systems (Print)  
This article proposes a new interval-valued fuzzy transform. Its construction is based on a possibilistic interpretation of the partition on which the fuzzy transform is built.  ...  In the experimental section, we illustrate some properties of the proposed transform while highlighting interesting features of the obtained framework.  ...  Within this framework, the fuzzy subset E that generates the fuzzy partition {C k } k∈Θp is considered as a maxitive kernel [13] .  ... 
doi:10.1016/j.fss.2014.08.006 fatcat:nkbgzpblwjgbbmz3bkwl3btjli
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