•A new generalization of the discrete Choquet integral is proposed.•Fusion functions yielding particular properties are characterized.•Translation invariant generalizations are completely ...described.•New classes of binary aggregation functions are exemplified.
In this paper, we generalize a formula for the discrete Choquet integral by replacing the standard product by a suitable fusion function. For the introduced fusion functions based discrete Choquet-like integrals we discuss and prove several properties and also show that our generalization leads to several new interesting functionals. We provide a complete characterization of the introduced functionals as aggregation functions. For n=2, several new aggregation functions are obtained, and if symmetric capacities are considered, our approach yields new generalizations of OWA operators. If n > 2, the introduced functionals are aggregation functions only if they are Choquet integrals with respect to some distorted capacity.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
In this work we introduce the definition of interval-valued fuzzy implication function with respect to any total order between intervals. We also present different construction methods for such ...functions. We show that the advantage of our definitions and constructions lays on that we can adapt to the interval-valued case any inequality in the fuzzy setting, as the one of the generalized modus ponens. We also introduce a strong equality measure between interval-valued fuzzy sets, in which we take the width of the considered intervals into account, and, finally, we discuss a construction method for this measure using implication functions with respect to total orders.
•We define interval-valued implication functions for every order relation between intervals.•We introduce methods for constructing interval-valued implication functions.•We analyze the importance of preserving the width of the intervals.•We analyze under which conditions the interval-valued GMP holds.•We study strong equality measures built using IV implications with respect to total orders.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The paper introduces a new class of functions from 0,1n to 0,n called d-Choquet integrals. These functions are a generalization of the “standard” Choquet integral obtained by replacing the difference ...in the definition of the usual Choquet integral by a dissimilarity function. In particular, the class of all d-Choquet integrals encompasses the class of all “standard” Choquet integrals but the use of dissimilarities provides higher flexibility and generality. We show that some d-Choquet integrals are aggregation/pre-aggregation/averaging/functions and some of them are not. The conditions under which this happens are stated and other properties of the d-Choquet integrals are studied.
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In this work we consider some classes of functions with relaxed monotonicity conditions generalizing some other given classes of fusion functions. In particular, directionally increasing aggregation ...functions (called also pre-aggregation functions), directionally increasing conjunctors, or directionally increasing implications, etc., generalize the standard classes of aggregation functions, conjunctors, or implication functions, respectively. We analyze different properties of these classes of functions and we discuss a construction method in terms of linear combinations of t-norms.
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5.
On interval fuzzy S-implications Bedregal, B.C.; Dimuro, G.P.; Santiago, R.H.N. ...
Information sciences,
04/2010, Volume:
180, Issue:
8
Journal Article
Peer reviewed
This paper presents an analysis of interval-valued S-implications and interval-valued automorphisms, showing a way to obtain an interval-valued S-implication from two S-implications, such that the ...resulting interval-valued S-implication is said to be
obtainable. Some consequences of that are: (1) the resulting interval-valued S-implication satisfies the correctness property, and (2) some important properties of usual S-implications are preserved by such interval representations. A relation between S-implications and interval-valued S-implications is outlined, showing that the action of an interval-valued automorphism on an interval-valued S-implication produces another interval-valued S-implication.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
When physical quantities
x
i
are numbers, then the corresponding measurement accuracy can be usually represented in interval terms, and interval computations can be used to estimate the resulting ...uncertainty in
y
=
f
(
x
1
,
…
,
x
n
)
.
In some practical problems, we are interested in more complex structures such as functions, operators, etc. Examples: we may be interested in how the material strain depends on the applied stress, or in how a physical quantity such as temperature or velocity of sound depends on a 3-D point.
For many such structures, there are ways to represent uncertainty, but usually, for each new structure, we have to perform a lot of complex analysis from scratch. It is desirable to come up with a general methodology that would automatically produce a natural description of validated uncertainty for all physically interesting situations (or at least for as many such situations as possible). In this paper, we describe the foundations for such a methodology; it turns out that this problem naturally leads to the technique of
domains first introduced by D. Scott in the 1970s.
In addition to general domain techniques, we also describe applications to geospatial and meteorological data.
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Interval Valued QL-Implications Reiser, R. H. S.; Dimuro, G. P.; Bedregal, B. C. ...
Logic, Language, Information and Computation
Book Chapter
Peer reviewed
The aim of this work is to analyze the interval canonical representation for fuzzy QL-implications and automorphisms. Intervals have been used to model the uncertainty of a specialist’s information ...related to truth values in the fuzzy propositional calculus: the basic systems are based on interval fuzzy connectives. Thus, using subsets of the real unit interval as the standard sets of truth degrees and applying continuous t-norms, t-conorms and negation as standard truth interval functions, the standard truth interval function of an QL-implication can be obtained. Interesting results on the analysis of interval canonical representation for fuzzy QL-implications and automorphisms are presented. In addition, commutative diagrams are used in order to understand how an interval automorphism acts on interval QL-implications, generating other interval fuzzy QL-implications.
On Interval Fuzzy Numbers Dimuro, G. P.
2011 Workshop-School on Theoretical Computer Science,
2011-Aug.
Conference Proceeding
Interval fuzzy sets allow us to deal not only with vagueness (lack of sharp class boundaries), but also with uncertainty (lack of information). The aim of this tutorial is to present some basic ...concepts about interval fuzzy numbers. Several concepts related to fuzzy sets are extended to the interval approach. We present an algebraic and ordered structure of interval fuzzy numbers, where the arithmetic operations are defined in terms of interval cuts, allowing the analysis of the properties of the operations based on the properties of the interval arithmetic operations.
This work introduces a tessellation-based model for the declivity analysis of geographic regions. The analysis of the relief declivity, which is embedded in the rules of the model, categorizes each ...tessellation cell, with respect to the whole considered region, according to the (positive, negative, null) sign of the declivity of the cell. Such information is represented in the states assumed by the cells of the model. The overall configuration of such cells allows the division of the region into subregions of cells belonging to a same category, that is, presenting the same declivity sign. In order to control the errors coming from the discretization of the region into tessellation cells, or resulting from numerical computations, interval techniques are used. The implementation of the model is naturally parallel since the analysis is performed on the basis of local rules. An immediate application is in geophysics, where an adequate subdivision of geographic areas into segments presenting similar topographic characteristics is often convenient.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The aim of this paper is to introduce the notion of interval additive generators of interval t-norms as interval representations of additive generators of t-norms, considering both the correctness ...and the optimality criteria, in order to provide a more systematic methodology for the selection of interval t-norms in the various applications. We prove that interval additive generators satisfy the main properties of punctual additive generators discussed in the literature.
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