98 research outputs found
Aggregating fuzzy subgroups and T-vague groups
Fuzzy subgroups and T-vague groups are interesting fuzzy algebraic structures that have been widely studied. While fuzzy subgroups fuzzify the concept of crisp subgroup, T-vague groups can be identified with quotient groups of a group by a normal fuzzy subgroup and there is a close relation between both structures and T-indistinguishability operators (fuzzy equivalence relations).
In this paper the functions that aggregate fuzzy subgroups and T-vague groups will be studied. The functions aggregating T-indistinguishability operators have been characterized [9] and the main result of this paper is that the functions aggregating T-indistinguishability operators coincide with the ones that aggregate fuzzy subgroups and T-vague groups. In particular, quasi-arithmetic means and some OWA operators aggregate them if the t-norm is continuous Archimedean.Peer ReviewedPostprint (author's final draft
A New Approach to the Fuzzification of Convex Structures
A new approach to the fuzzification of convex structures is introduced. It is also called an M-fuzzifying convex structure. In the definition of M-fuzzifying convex structure, each subset can be regarded as a convex set to some degree. An M-fuzzifying convex structure can be characterized by means of its M-fuzzifying closure operator. An M-fuzzifying convex structure and its M-fuzzifying closure operator are one-to-one corresponding. The concepts of M-fuzzifying convexity preserving functions, substructures, disjoint sums, bases, subbases, joins, product, and quotient structures are presented and their fundamental properties are obtained in M-fuzzifying convex structure
Fuzzy closure systems: Motivation, definition and properties
The aim of this paper is to extend closure systems from being crisp sets with certain
fuzzy properties to proper fuzzy sets. The presentation of the paper shows a thorough
discussion on the different alternatives that could be taken to define the desired fuzzy
closure systems. These plausible alternatives are discarded if they are proven impossible
to be in a bijective correspondence with closure operators. Finally, a definition of fuzzy
closure system is established and a one-to-one relation with closure operators is proved.The aim of this paper is to extend closure systems from being crisp sets with certain
fuzzy properties to proper fuzzy sets. The presentation of the paper shows a thorough
discussion on the different alternatives that could be taken to define the desired fuzzy
closure systems. These plausible alternatives are discarded if they are proven impossible
to be in a bijective correspondence with closure operators. Finally, a definition of fuzzy
closure system is established and a one-to-one relation with closure operators is proved. Funding for open access charge: Universidad de Málaga / CBU
Fuzzy Closure Structures as Formal Concepts II
This paper is the natural extension of Fuzzy Closure Structures as Formal
Concepts. In this paper we take into consideration the concept of closure
system which is not dealt with in the previous one. Hence, a connection
must be found between fuzzy ordered sets and a crisp ordered set. This
problem is two-fold, the core of the fuzzy orders can be considered in order
to complete the ensemble, or the crisp order can be fuzzified. Both ways are
studied in the paper. The most interesting result is, similarly to the previous
paper, that closure systems are formal concepts of these Galois connections
as well.Funding for open access charge: Universidad de Málaga / CBUA
This research is partially supported by the State Agency of Research (AEI), the Spanish Ministry of Science, Innovation, and Universities (MCIU), the European Social Fund (FEDER), the Junta de AndalucĂa (JA), and the Universidad de Málaga (UMA) through the FPU19/01467 (MCIU) internship, the project VALID (PID2022-140630NB-I00 funded by MCIN/ AEI/10.13039/501100011033) and the research projects with reference PGC2018-095869-B-I00, PID2021-127870OB-I00, (MCIU/AEI/FEDER, UE) and UMA18-FEDERJA-001 (JA/ UMA/ FEDER, UE)
A Fuzzy Logic Programming Environment for Managing Similarity and Truth Degrees
FASILL (acronym of "Fuzzy Aggregators and Similarity Into a Logic Language")
is a fuzzy logic programming language with implicit/explicit truth degree
annotations, a great variety of connectives and unification by similarity.
FASILL integrates and extends features coming from MALP (Multi-Adjoint Logic
Programming, a fuzzy logic language with explicitly annotated rules) and
Bousi~Prolog (which uses a weak unification algorithm and is well suited for
flexible query answering). Hence, it properly manages similarity and truth
degrees in a single framework combining the expressive benefits of both
languages. This paper presents the main features and implementations details of
FASILL. Along the paper we describe its syntax and operational semantics and we
give clues of the implementation of the lattice module and the similarity
module, two of the main building blocks of the new programming environment
which enriches the FLOPER system developed in our research group.Comment: In Proceedings PROLE 2014, arXiv:1501.0169
Orderings of fuzzy sets based on fuzzy orderings. Part I: the basic approach
The aim of this paper is to present a general framework for comparing
fuzzy sets with respect to a general class of fuzzy orderings. This approach
includes known techniques based on generalizing the crisp linear ordering of
real numbers by means of the extension principle, however, in its general
form, it is applicable to any fuzzy subsets of any kind of universe for which a
fuzzy ordering is known|no matter whether linear or partialPeer Reviewe
Fuzzy closure structures as formal concepts
Galois connections seem to be ubiquitous in mathematics. They have been used to model solutions for both pure and application-oriented problems. Throughout the paper, the general framework is a complete fuzzy lattice over a complete residuated lattice. The existence of three fuzzy Galois connections (two antitone and one isotone) between three specific ordered sets is proved in this paper. The most interesting part is that fuzzy closure systems, fuzzy closure operators and strong fuzzy closure relations are formal concepts of these fuzzy Galois connections.This research is partially supported by the State Agency of Research (AEI), the Spanish Ministry of Science, Innovation and Universities (MCIU), the European Social Fund (FEDER), the Junta de AndalucĂa (JA), and the Universidad de Málaga (UMA) through the FPU19/01467 (MCIU) internship and the research projects with reference PGC2018-095869-B-I00, TIN2017-89023-P, PID2021-127870OB-I00 (MCIU/AEI/FEDER, UE) and UMA18-FEDERJA-001 (JA/ UMA/ FEDER, UE).
Funding for open access charge: Universidad de Málaga / CBU
Controlled Fuzzy Parallel Rewriting
We study a Lindenmayer-like parallel rewriting system to model the growth of filaments (arrays of cells) in which developmental errors may occur. In essence this model is the fuzzy analogue of the derivation-controlled iteration grammar. Under minor assumptions on the family of control languages and on the family of fuzzy languages in the underlying iteration grammar, we show (i) regular control does not provide additional generating power to the model, (ii) the number of fuzzy substitutions in the underlying iteration grammar can be reduced to two, and (iii) the resulting family of fuzzy languages possesses strong closure properties, viz. it is a full hyper-AFFL, i.e., a hyper-algebraically closed full Abstract Family of Fuzzy Languages
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