A classification of barycentrically associative polynomial functions

We describe the class of polynomial functions which are barycentrically associative over an infinite commutative integral domain

Strongly barycentrically associative and preassociative functions

We study the property of strong barycentric associativity, a stronger version of barycentric associativity for functions with indefinite arities. We introduce and discuss the more general property of strong barycentric preassociativity, a generalization of strong barycentric associativity which does not involve any composition of functions. We also provide a generalization of Kolmogoroff-Nagumo's characterization of the quasi-arithmetic mean functions to strongly barycentrically preassociative functions.Comment: arXiv admin note: text overlap with arXiv:1406.434

Preassociative aggregation functions

The classical property of associativity is very often considered in aggregation function theory and fuzzy logic. In this paper we provide axiomatizations of various classes of preassociative functions, where preassociativity is a generalization of associativity recently introduced by the authors. These axiomatizations are based on existing characterizations of some noteworthy classes of associative operations, such as the class of Acz\'elian semigroups and the class of t-norms.Comment: arXiv admin note: text overlap with arXiv:1309.730

Preferenciastruktúrák döntési modellekben = Preference structures in decision models

A kutatási eredmények vagy magukra a preferenciákra, vagy az ezek alapját képező műveletekre vonatkoznak. Igazoltuk, hogy a ]-1,1[ intervallum az ún. szimmetrikus minimummal és maximummal van (jól definiált értelemben) a legközelebb egy gyűrűhöz. Egy asszociatív, részben kompenzatív aggregációs műveletcsaládon (uninormák) belül jellemeztük azokat a reprezentálható tagokat, amelyek két polinom hányadosaként állnak elő. Egy függvényegyenlet megoldásának segítségével jellemeztük és meg tudtuk konstruálni az összes folytonos ún. migratív t-normát. Megmutattuk, hogy fuzzy preferenciastruktúrák konstrukciója csak az indifferencia generátor választásán múlik. Karakterizáltuk azokat az eseteket, amikor az indifferencia generátor i) kommutatív kvázi-kopula, ii) Frank-féle t-normák lexikografikus összege, iii) speciális Frank-féle t-norma. Meghatároztuk azokat a folytonos De Morgan hármasok, amelyekre a konjunktív és diszjunktív fuzzifikált normálformák különbsége nemnegatív, illetve amikor e különbség független az eredeti Boole függvénytől. Értékelőfüggvényeken, tartalmazási reláción, illetve fuzzy ekvivalencia-relációk és hagyományos lineáris rendezések dekompozícióján alapuló reprezentációs eredményeket kaptunk fuzzy gyenge rendezésekre, amelyek egyúttal konstrukciós eljárásokat is adnak. Meghatároztunk egy általános keretet, amelyben preferenciastruktúrák értelmes és nem-triviális módon felépíthetők, és amelynek az eddig ismert struktúrák (additív, maxitív) speciális esetei. | The main results are either on the preferences or on the underlying aggregation operations. We proved that the interval ]-1,1[ equipped with the symmetric minimum and maximum is (in a well-defined sense) the closest one to a ring structure. Within the class of associative partially compensative operations (uninorms) we charaterized those members that are quotients of two polynomials. We could characterize and construct all continuous migrative t-norms by solving a functional equation. We proved that the construction of fuzzy preference structures is based only on the indifference generator. We characterized cases when the indifference generator is i) a commutative quasi-copula, ii) an ordinal sum of Frank t-norms, iii) a particular Frank t-norm. We determined those continuous De Morgan triplets for which the difference of conjunctive and disjunctive fuzzified normal forms is non-negative, and also those ones when this difference is independent of the original Boolean function. We obtained fundamental representation results for fuzzy weak orders, where each one also provides a construction method: (i) score function-based representations, (ii) inclusion-based representations, (iii) representations by decomposition into crisp linear orders and fuzzy equivalence relations. We determined a general framework in which preference structures can be built up in a meaningful and non-trivial way, and the known structures (additive, maxitive) are particular cases

A Variance-Based Consensus Degree in Group Decision Making Problems

The variance is a well-known statistical measure and is frequently used for the calculation of variability. This concept can be used to obtain the degree of agreement in groups that have to make decisions. In this study, we propose the use of a variance derivative as an alternative for the calculation of the degree of consensus for Group Decision Making problems with fuzzy preference relations. As revealed by a subsequent comparative study, the values obtained by this new method are comparable to the values obtained by means of frequently used methods that employ distance functions and aggregation operators, while it turns out to be a simpler application method

Invariant copulas

summary:Copulas which are invariant with respect to the construction of the corresponding survival copula and other related dualities are studied. A full characterization of invariant associative copulas is given

Consensus image method for unknown noise removal

Noise removal has been, and it is nowadays, an important task in computer vision. Usually, it is a previous task preceding other tasks, as segmentation or reconstruction. However, for most existing denoising algorithms the noise model has to be known in advance. In this paper, we introduce a new approach based on consensus to deal with unknown noise models. To do this, different filtered images are obtained, then combined using multifuzzy sets and averaging aggregation functions. The final decision is made by using a penalty function to deliver the compromised image. Results show that this approach is consistent and provides a good compromise between filters.This work is supported by the European Commission under Contract No. 238819 (MIBISOC Marie Curie ITN). H. Bustince was supported by Project TIN 2010-15055 of the Spanish Ministry of Science