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1
Content available remote Finite IUML-algebras, Finite Forests and Orthopairs
Aguzzoli S., Ciucci D., Boffa S., Gerla B.
Fundamenta Informaticae
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2018
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Vol. 163, nr 2
139--163
EN
We show that finite IUML-algebras, which are residuated lattices arising from an idempotent uninorm, can be interpreted as algebras of sequences of orthopairs whose main operation is defined starting from the three-valued Sobociński operator between rough sets. Our main tool is the representation of finite IUML-algebras by means of finite forests.
2
Content available remote Rough Set Theory and Digraphs
Chiaselotti G., Ciucci D., Gentile T., Infusino F.
Fundamenta Informaticae
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2017
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Vol. 153, nr 4
291--325
EN
In this paper we apply rough set theory to information tables induced from finite directed graphs without loops and multiples arcs (digraphs). Specifically, we use the adjacency matrix of a digraph as a particular type of information table. In this way, we are able to explore on digraphs the notions of indiscernibility partitions, lower and upper approximations, generalized core, reducts and discernibility matrix. All these ideas will be exemplified on standard digraph families as well on examples from social networks and patterns of flight routes between airports.
3
Content available remote Generalizations of Rough Set Tools Inspired by Graph Theory
Chiaselotti G., Ciucci D., Gentile T., Infusino F.
Fundamenta Informaticae
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2016
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Vol. 148, nr 1/2
207--227
EN
We introduce and study new generalizations of some rough set tools. Namely, the extended core, the generalized discernibility function, the discernibility space and the maximum partitioner. All these concepts where firstly introduced during the application of rough set theory to graphs, here we show that they have an interesting and useful interpretation also in the general setting. Indeed, among other results, we prove that reducts can be computed in incremental polynomial time, we give some conditions in order that a partition coincides with an indiscernibility partition of a given information table and we give the conditions such that a discernibility matrix corresponds to an information table.
4
Content available On exactness, definability and vagueness in partial approximation spaces
Ciucci D., Mihálydeák T., Csajbók Z. E.
Technical Sciences / University of Warmia and Mazury in Olsztyn
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2015
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nr 18(3)
203--212
EN
In this paper, lower/upper, boundary, and negative regions of set approximations, the fundamental concepts of classical rough set theory, have been considered as primitive ones. Assuming that they are independent of each other, a generalized framework for their investigations is outlined. Its main building blocks are base sets and definable sets. Lower/upper approximations, boundaries and negative sets are all considered as definable sets and their mutual interactions are studied. Lastly exact/rough sets are discussed. In generalized framework, four groups of formulae are defined for representing different variants of rough sets. They emphasize distinct features of roughness, and so it may be of highly importance which one is used in practical applications. Some possible choices appeared in authors’ publications are mentioned.
5
Content available remote Structures of Opposition in Fuzzy Rough Sets
Ciucci D., Dubois D., Prade H.
Fundamenta Informaticae
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2015
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Vol. 142, nr 1-4
1--19
EN
The square of opposition is as old as logic. There has been a recent renewal of interest on this topic, due to the emergence of new structures (hexagonal and cubic) extending the square. They apply to a large variety of representation frameworks, all based on the notions of sets and relations. After a reminder about the structures of opposition, and an introduction to their gradual extensions (exemplified on fuzzy sets), the paper more particularly studies fuzzy rough sets and rough fuzzy sets in the setting of gradual structures of opposition.
6
Content available remote Temporal Dynamics in Information Tables
Ciucci D.
Fundamenta Informaticae
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2012
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Vol. 115, nr 1
57-74
EN
An information table can change over time in several different ways: objects enter/exit the system, new attributes are considered, etc. As a consequence rough set instruments also change. At first, we recall a classification of dynamic increase of information with respect to three different factors: objects, attributes, values. Then, the corresponding changes in rough sets are discussed. Results about approximations, positive region and generalized decision are given and algorithms to update reducts and rules provided.
7
Content available remote Orthopairs: A Simple and Widely UsedWay to Model Uncertainty
Ciucci D.
Fundamenta Informaticae
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2011
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Vol. 108, nr 3/4
287-304
EN
The term orthopair is introduced to group under a unique definition different ways used to denote the same concept. Some orthopairmodels dealing with uncertainty are analyzed both from a mathematical and semantical point of view, outlining similarities and differences among them. Finally, lattice operations on orthopairs are studied and a survey on algebraic structures is provided.
8
Content available remote Entropies and Co-Entropies of Coverings with Application to Incomplete Information Systems
Bianucci D., Cattaneo G., Ciucci D.
Fundamenta Informaticae
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2007
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Vol. 75, nr 1-4
77-105
EN
Different generalizations to the case of coverings of the standard approach to entropy applied to partitions of a finite universe X are explored. In the first approach any covering is represented by an identity resolution of fuzzy sets on X and a corresponding probability distribution with associated entropy is defined. A second approach is based on a probability distribution generated by the covering normalizing the standard counting measure. Finally, the extension to a generic covering of the Liang-Xu approach to entropy is investigated, both from the "global" and the "local" point of view. For each of these three possible entropies the complementary entropy (or co-entropy) is defined showing in particular that the Liang-Xu entropy is a co-entropy.
9
Content available remote On the Axioms of Residuated Structures: Independence, Dependencies and Rough Approximations
Ciucci D.
Fundamenta Informaticae
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2006
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Vol. 69, nr 4
359-387
EN
Several residuated algebras are taken into account. The set of axioms defining each structure is reduced with the aim to obtain an independent axiomatization. Further, the relationship among all the algebras is studied and their dependencies outlined. Finally, rough approximation spaces are introduced in residuated lattices with involution and their algebraic structure outlined.
10
Content available remote Algebraic Structures Related to Many Valued Logical Systems. Part 1, Heyting Wajsberg Algebras
Cattaneo G., Ciucci D., Giuntini R., Konig M.
Fundamenta Informaticae
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2004
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Vol. 63, nr 4
331--355
EN
A bottom-up investigation of algebraic structures corresponding to many valued logical systems is made. Particular attention is given to the unit interval as a prototypical model of these kind of structures. At the top level of our construction, Heyting Wajsberg algebras are defined and studied. The peculiarity of this algebra is the presence of two implications as primitive operators. This characteristic is helpful in the study of abstract rough approximations.
11
Content available remote Algebraic Structures Related to Many Valued Logical Systems. Part 2, Equivalence Among some Widespread Structures
Cattaneo G., Ciucci D., Giuntini R., Konig M.
Fundamenta Informaticae
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2004
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Vol. 63, nr 4
357--373
EN
Several algebraic structures (namely HW, BZMVdM, Stonean MV and MVΔ algebras) related to many valued logical systems are considered and their equivalence is proved. Four propositional calculi whose Lindenbaum-Tarski algebra corresponds to the four equivalent algebraic structures are axiomatized and their semantical completeness is given.
12
Content available remote Shadowed Sets and Related Algebraic Structures
Cattaneo G., Ciucci D.
Fundamenta Informaticae
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2003
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Vol. 55, nr 3,4
255-284
EN
BZMVdM algebras are introduced as an abstract environment to describe both shadowed and fuzzy sets. This structure is endowed with two unusual complementations: a fuzzy one \lnot and an intuitionistic one ~ . Further, we show how to define in any BZMVdM algebra the Boolean sub-algebra of exact elements and to give a rough approximation of fuzzy elements through a pair of exact elements using an interior and an exterior mapping. Then, we introduce the weaker notion of pre-BZMVdM algebra. This structure still have as models fuzzy and shadowed sets but with respect to a weaker notion of intuitionistic negation ~ a with a Î [0,1/2). In pre-BZMVdM algebras it is still possible to define an interior and an exterior mapping but, in this case, we have to distinguish between open and closed exact elements. Finally, we see how it is possible to define a-cuts and level fuzzy sets in the pre-BZMVdM algebraic context of fuzzy sets.
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