Generator of Fuzzy Implications

Daniilidou, Athina; Konguetsof, Avrilia; Souliotis, Georgios; Papadopoulos, Basil

doi:10.3390/a16120569

Cited by 1 publication

(1 citation statement)

References 48 publications

(84 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We know that we can generate fuzzy implications from aggregation functions and fuzzy negations [7][8][9][10][11][12][13][14][15]. Other methods of generating fuzzy implications can be achieved using additive generating functions or by some initial implications [16][17][18][19][20][21][22]. Thus, fuzzy implications are useful in fuzzy relational equations and fuzzy mathematical morphology, fuzzy measures and image processing [23], data mining [24], and computing with words and fuzzy partitions.…”

Section: Introductionmentioning

confidence: 99%

Two Extensions of the Sugeno Class and a Novel Constructed Method of Strong Fuzzy Negation for the Generation of Non-Symmetric Fuzzy Implications

Rapti,

Konguetsof,

Papadopoulos

2024

Symmetry

View full text Add to dashboard Cite

In this paper, we present two new classes of fuzzy negations. They are an extension of a well-known class of fuzzy negations, the Sugeno Class. We use it as a base for our work for the first two construction methods. The first method generates rational fuzzy negations, where we use a second-degree polynomial with two parameters. We investigate which of these two conditions must be satisfied to be a fuzzy negation. In the second method, we use an increasing function instead of the parameter δ of the Sugeno class. In this method, using an arbitrary increasing function with specific conditions, fuzzy negations are produced, not just rational ones. Moreover, we compare the equilibrium points of the produced fuzzy negation of the first method and the Sugeno class. We use the equilibrium point to present a novel method which produces strong fuzzy negations by using two decreasing functions which satisfy specific conditions. We also investigate the convexity of the new fuzzy negation. We give some conditions that coefficients of fuzzy negation of the first method must satisfy in order to be convex. We present some examples of the new fuzzy negations, and we use them to generate new non-symmetric fuzzy implications by using well-known production methods of non-symmetric fuzzy implications. We use convex fuzzy negations as decreasing functions to construct an Archimedean copula. Finally, we investigate the quadratic form of the copula and the conditions that the coefficients of the first method and the increasing function of the second method must satisfy in order to generate new copulas of this form.

show abstract