Fuzzy implications based on semicopulas (original) (raw)
Related papers
On two construction methods of copulas from fuzzy implication functions
Progress in Artificial Intelligence, 2015
Copulas have been deeply investigated because of their applications in many fields. From the theoretical point of view, a key point in this research lies in the search of new construction methods of parametrized families of copulas. This paper presents some construction methods based on fuzzy implication functions by reversing the construction methods of fuzzy implication functions from copulas presented by P. Grzegorzewski in some recent papers. Specifically, the PSI and SSI-construction methods of copulas are proposed which provide copulas from a given fuzzy implication function. In addition, the analysis of these construction methods of copulas lead to the characterization of the intersection of the probabilistic S and survival S-implications with (S, N) and R-implications.
Fuzzy Sets and Systems, 2017
Since their introduction in 2012 and 2013 by P. Grzegorzewski, probabilistic S-implications and survival S-implications have attracted the efforts of some researchers due to the connection that they represent between probability theory and fuzzy logic. In this paper, the characterizations of these two families of fuzzy implication functions are presented jointly with the characterization of the material implications derived from co-copulas and the classical negation. Even more, it is proved that the three families are actually the same. Thus every result concerning one of these families can be straightforwardly rewritten in terms of the other two families.
Communications in Computer and Information Science, 2014
Recently, Grzegorzewski [5-7] introduced two new families of fuzzy implication functions called probabilistic implications and probabilistic S-implications. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In the same article [7] author gives a motivation to his idea and indicates some interesting connections between new families of implications and the dependence structure of the underlying environment. In this paper the laws of contraposition and the law of importation are studied for these families of fuzzy implications.
A Method of Generating Fuzzy Implications with Specific Properties
Symmetry
In this paper we introduce a new method of generating fuzzy implications via known fuzzy implications. We focus on the case of generating fuzzy implications via a fuzzy connective and at least one known fuzzy implication. We present some basic desirable properties of fuzzy implications that are invariant via this method. Furthermore, we suggest some ways of preservation or violation of these properties, based in this method. We show how we can generate not greater or not weaker fuzzy implications with specific properties. Finally, two subclasses of any fuzzy implication arise, the so called T and S subclasses.
On a new class of fuzzy implications: h-Implications and generalizations
Information Sciences, 2011
A new class of fuzzy implications called the h-implications is introduced. They are implications generated from an additive generator of a representable uninorm in a similar way of Yager's f-and g-implications which are generated from additive generators of continuous Archimedean t-norms and t-conorms. Basic properties of these implications are studied in detail. Modifications and generalizations of the initial definition are presented and their properties studied and compared between them. One of the modifications, called (h, e)-implications, is another example of a fuzzy implication satisfying the exchange principle but not the law of importation for any t-norm, in fact for any function
Constructing implication functions from fuzzy negations
Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology, 2013
A class of implication functions is constructed from fuzzy negations. The interest of this new class lies in its simplicity and in the fact that when N is Idsymmetrical, the corresponding implication agrees with the residuum of a commutative semicopula.
Fuzzy implication functions constructed from general overlap functions and fuzzy negations
arXiv (Cornell University), 2021
Fuzzy implication functions have been widely investigated, both in theoretical and practical fields. The aim of this work is to continue previous works related to fuzzy implications constructed by means of non necessarily associative aggregation functions. In order to obtain a more general and flexible context, we extend the class of implications derived by fuzzy negations and t-norms, replacing the latter by general overlap functions. We also investigate their properties, characterization and intersections with other classes of fuzzy implication functions.
On dependencies and independencies of fuzzy implication axioms
Fuzzy Sets and Systems, 2010
A fuzzy implication, commonly defined as a two-place operation on the unit interval, is an extension of the classical binary implication. It plays important roles in both mathematical and applied sides of fuzzy set theory. Besides the basic axioms, there are many potential fuzzy implication axioms, among which eight are widely used in the literature. Different fuzzy implications satisfying different subgroups of these eight axioms can be found. However, certain interrelationships exist between these eight axioms. But the results remain incomplete. This paper aims to lay bare the interrelationships between these eight axioms. The result is instrumental to propose a classification of fuzzy implications.