4 research outputs found
A Method for Image Reduction Based on a Generalization of Ordered Weighted Averaging Functions
In this paper we propose a special type of aggregation function which
generalizes the notion of Ordered Weighted Averaging Function - OWA. The
resulting functions are called Dynamic Ordered Weighted Averaging Functions ---
DYOWAs. This generalization will be developed in such way that the weight
vectors are variables depending on the input vector. Particularly, this
operators generalize the aggregation functions: Minimum, Maximum, Arithmetic
Mean, Median, etc, which are extensively used in image processing. In this
field of research two problems are considered: The determination of methods to
reduce images and the construction of techniques which provide noise reduction.
The operators described here are able to be used in both cases. In terms of
image reduction we apply the methodology provided by Patermain et al. We use
the noise reduction operators obtained here to treat the images obtained in the
first part of the paper, thus obtaining images with better quality.Comment: 32 pages, 19 figure
Bounded Generalized Mixture Functions
In literature, it is common to find problems which require a way to encode a
finite set of information into a single data; usually means are used for that.
An important generalization of means are the so called Aggregation Functions,
with a noteworthy subclass called OWA functions. There are, however, further
functions which are able to provide such codification which do not satisfy the
definition of aggregation functions; this is the case of pre-aggregation and
mixture functions.
In this paper we investigate two special types of functions: Generalized
Mixture and Bounded Generalized Mixture functions. They generalize both: OWA
and Mixture functions. Both Generalized and Bounded Generalized Mixture
functions are developed in such way that the weight vectors are variables
depending on the input vector. A special generalized mixture operator, H, is
provided and applied in a simple toy example
Nested formulation paradigms for induced ordered weighted averaging aggregation for decisionâmaking and evaluation
Existing extensions to Yager's ordered weighted aver-aging (OWA) operators enlarge the application rangeand to encompass more principles and properties relatedto OWA aggregation. However, these extensions do notprovide a strict and convenient way to model evaluationscenarios with complex or grouped preferences. Basedon earlier studies and recent evolutionary changes inOWA operators, we propose formulation paradigms forinduced OWA aggregation and a related weight functionwith selfâcontained properties that make it possibleto model such complex preferenceâinvolved evaluationproblems in a systematic way. The new formulationshave some recursive forms that provide more waysto apply OWA aggregation and deserve further studyfrom a mathematical perspective. In addition, the newproposal generalizes almost all of the wellâknownextensions to the original OWA operators. We providean example showing the representative use of suchparadigms in decisionâmaking and evaluation problems.This study was partly supported by Scientific Research Startâup Foundation (grant no.184080H202B165), by Jiangsu âs Philosophy and Social Science Fund (grant no. 18EYD005), and also by the Science and Technology Assistance Agency under contract no. APVVâ17â0066. This study was also partially supported by the Spanish Ministry of Science and Technology under project no. TIN2016â77356âP (AEI/FEDER, UE)
The law of O-conditionality for fuzzy implications constructed from overlap and grouping functions
Overlap and grouping functions are special kinds of non necessarily associative aggregation operators proposed for many applications, mainly when the associativity property is not strongly required. The classes of overlap and grouping functions are richer than the classes of t-norms and t-conorms, respectively, concerning some properties like idempotency, homogeneity, and, mainly, the self-closedness feature with respect to the convex sum and the aggregation by generalized composition of overlap/grouping functions. In previous works, we introduced some classes of fuzzy implications derived by overlap and/or grouping functions, namely, the residual implications R-0-implications, the strong implications (G, N)-implications and the Quantum Logic implications QL-implications, for overlap functions O, grouping functions G and fuzzy negations N. Such implications do not necessarily satisfy certain properties, but only weaker versions of these properties, e.g., the exchange principle. However, in general, such properties are not demanded for many applications. In this paper, we analyze the so-called law of O-Conditionality, O(x, 1(x, y)) <= y, for any fuzzy implication I and overlap function O, and, in particular, for Ro-implications, (G, N)-implications, QL-implications and D-implications derived from tuples (O, G, N), the latter also introduced in this paper. We also study the conditional antecedent boundary condition for such fuzzy implications, since we prove that this property, associated to the left ordering property, is important for the analysis of the O-Conditionality. We show that the use of overlap functions to implement de generalized Modus Ponens, as the scheme enabled by the law of O-Conditionality, provides more generality than the laws of T-conditionality and U-conditionality, for t-norms T and uninorms U, respectively.This work was partially supported by the Spanish Ministry of Science and Technology under the project TIN2016-77356-P (AEI/FEDER, UE), and by the Brazilian funding agency CNPQ under Processes 305882/2016-3, 481283/2013-7, 306970/2013-9, 232827/2014-1 and 307681/2012-2