scholarly journals A Study of GD′- Implications, a New Hyper Class of Fuzzy Implications

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1925
Author(s):  
Dimitrios S. Grammatikopoulos ◽  
Basil Papadopoulos
Keyword(s):  
Necessary Conditions ◽  
Basic Properties ◽  
Fuzzy Implications ◽  
Fuzzy Implication ◽  
Identity Principle ◽  
Exchange Principle

In this paper, we introduce and study the GD′-operations, which are a hyper class of the known D′-operations. GD′-operations are in fact D′-operations, that are generated not only from the same fuzzy negation. Similar with D′-operations, they are not always fuzzy implications. Nevertheless, some sufficient, but not necessary conditions for a GD′-operation to be a fuzzy implication, will be proved. A study for the satisfaction, or the violation of the basic properties of fuzzy implications, such as the left neutrality property, the exchange principle, the identity principle and the ordering property will also be made. This study also completes the study of the basic properties of D′-implications. At the end, surprisingly an unexpected new result for the connection of the QL-operations and D-operations will be presented.

scholarly journals Modifications of Łukasiewicz’s intuitionistic fuzzy implication

2021 ◽  
Vol 27 (3) ◽  
pp. 32-39
Author(s):  
Alžbeta Michalíková ◽  
◽  
Eulalia Szmidt ◽  
Peter Vassilev ◽  
◽  
...  
Keyword(s):  
Basic Properties ◽  
Fuzzy Implications ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication

In [6], G. Klir and B. Yuan named after J. Łukasiewicz the implication p \rightarrow q = min(1, p+q). In a series of papers, 198 different intuitionistic fuzzy implications have been introduced, and their basic properties have been studied. Here we introduce six new implications which are modifications of Łukasiewicz’s intuitionistic fuzzy implication, and we describe and prove some of their properties.

scholarly journals A Method of Generating Fuzzy Implications from n Increasing Functions and n + 1 Negations

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 886
Author(s):  
Maria N. Rapti ◽  
Basil K. Papadopoulos
Keyword(s):  
Artificial Intelligence ◽  
Fuzzy Implications ◽  
Fuzzy Implication ◽  
New Construction ◽  
Novel Method ◽  
Increasing Functions ◽  
Increasing Function ◽  
Important Form ◽  
And Robotics ◽  
Exchange Principle

In this paper, we introduce a new construction method of a fuzzy implication from n increasing functions g i : [ 0 , 1 ] → [ 0 , ∞ ) ,   ( g ( 0 ) = 0 ) ( i = 1 , 2 , … , n ,   n   ∈ ℕ ) and n + 1 fuzzy negations N i ( i = 1 , 2 , … , n + 1 ,   n   ∈ ℕ ). Imagine that there are plenty of combinations between n increasing functions g i and n + 1 fuzzy negations N i in order to produce new fuzzy implications. This method allows us to use at least two fuzzy negations N i and one increasing function g in order to generate a new fuzzy implication. Choosing the appropriate negations, we can prove that some basic properties such as the exchange principle (EP), the ordering property (OP), and the law of contraposition with respect to N are satisfied. The worth of generating new implications is valuable in the sciences such as artificial intelligence and robotics. In this paper, we have found a novel method of generating families of implications. Therefore, we would like to believe that we have added to the literature one more source from which we could choose the most appropriate implication concerning a specific application. It should be emphasized that this production is based on a generalization of an important form of Yager’s implications.

scholarly journals Modal Type of Weak Intuitionistic Fuzzy Implications Generated by the Operation Δ

2021 ◽  
Vol 21 (4) ◽  
pp. 137-144
Author(s):  
Piotr Dworniczak ◽  
Lilija Atanassova ◽  
Nora Angelova
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Basic Properties ◽  
Fuzzy Implications ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication ◽  
Modal Type

Abstract In 2020 L. Atanassova has been introduced the new operation Δ over intuitionistic fuzzy sets and over intuitionistic fuzzy pairs. Some of its properties have been studied in 2021 from L. Atanassova and P. Dworniczak. In 2021 L. Atanassova and P. Dworniczak generated an intuitionistic fuzzy implication by the operation Δ, and it has been introduced and some of its basic properties have been described. Here, eight modal type of intuitionistic fuzzy implications are generated by the first one and some of their properties are discussed.

scholarly journals Third Zadeh’s Intuitionistic Fuzzy Implication

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 619
Author(s):  
Krassimir Atanassov
Keyword(s):  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication

George Klir and Bo Yuan named after Lotfi Zadeh the implication p→q=max(1−p,min(p,q)) (also Early Zadeh implication). In a series of papers, the author introduced two intuitionistic fuzzy forms of Zadeh’s implication and studied their basic properties. In the present paper, a new (third) intuitionistic fuzzy form of Zadeh’s implication is proposed and some of its properties are studied.

scholarly journals Flags of holomorphic foliations

2011 ◽  
Vol 83 (3) ◽  
pp. 775-786 ◽  
Author(s):  
Rogério S. Mol
Keyword(s):  
Finite Number ◽  
Complex Manifold ◽  
Necessary Conditions ◽  
Holomorphic Foliations ◽  
Lower Dimension ◽  
Higher Dimension ◽  
Basic Properties ◽  
Codimension One ◽  
Tangent Sheaf ◽  
Polar Classes

A flag of holomorphic foliations on a complex manifold M is an object consisting of a finite number of singular holomorphic foliations on M of growing dimensions such that the tangent sheaf of a fixed foliation is a subsheaf of the tangent sheaf of any of the foliations of higher dimension. We study some basic properties oft hese objects and, in <img src="/img/revistas/aabc/2011nahead/aop2411pcn.jpg" align="absmiddle" />, n > 3, we establish some necessary conditions for a foliation, we find bounds of lower dimension to leave invariant foliations of codimension one. Finally, still in <img src="/img/revistas/aabc/2011nahead/aop2411pcn.jpg" align="absmiddle" /> involving the degrees of polar classes of foliations in a flag.

A method of constructing fuzzy implications from the FIφ-construction

2021 ◽  
pp. 1-14
Author(s):  
Yifan Zhao ◽  
Kai Li
Keyword(s):  
Specific Property ◽  
New Method ◽  
Aggregation Function ◽  
Fuzzy Implications ◽  
Construction Methods ◽  
Fuzzy Implication ◽  
New Construction

In the recent years, several new construction methods of fuzzy implications have been proposed. However, these construction methods actually care about that the new implication could preserve more properties. In this paper, we introduce a new method for constructing fuzzy implications based on an aggregation function with F (1,  0) =1, a fuzzy implication I and a non-decreasing function φ, called FIφ-construction. Specifically, some logical properties of fuzzy implications preserved by this construction are studied. Moreover, it is studied how to use the FIφ-construction to produce a new implication satisfying a specific property. Furthermore, we produce two new subclasses of fuzzy implications such as UIφ-implications and GpIφ-implications by this method and discuss some additional properties. Finally, we provide a way to generate fuzzy subsethood measures by means of FIφ-implications.

CONTRAPOSITIVE SYMMETRY OF DISTRIBUTIVE FUZZY IMPLICATIONS

2002 ◽  
Vol 10 (supp01) ◽  
pp. 135-147 ◽  
Author(s):  
MICHAŁ BACZYŃSKI
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Strong Negation ◽  
Fuzzy Implications ◽  
Fuzzy Implication

Recently, we have examined the solutions of the system of the functional equations I(x, T(y, z)) = T(I(x, y), I(x, z)), I(x, I(y, z)) = I(T(x, y), z), where T : [0, 1]2 → [0, 1] is a strict t-norm and I : [0, 1]2 → [0, 1] is a non-continuous fuzzy implication. In this paper we continue these investigations for contrapositive implications, i.e. functions which satisfy the functional equation I(x, y) = I(N(y), N(x)), with a strong negation N : [0, 1] → [0, 1]. We show also the bounds for two classes of fuzzy implications which are connected with our investigations.

A new class of fuzzy implications. Axioms of fuzzy implication revisited

1998 ◽  
Vol 100 (1-3) ◽  
pp. 267-272 ◽  
Author(s):  
I. Burhan Türkşen ◽  
Vladik Kreinovich ◽  
Ronald R. Yager
Keyword(s):  
New Class ◽  
Fuzzy Implications ◽  
Fuzzy Implication

On the Ordering Property and Law of Importation in Fuzzy Logic

2010 ◽  
Vol 1 (3) ◽  
pp. 17-30
Author(s):  
Huiwen Deng ◽  
Huan Jiang
Keyword(s):  
Fuzzy Logic ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Fuzzy Implications ◽  
Fuzzy Implication ◽  
The Law ◽  
Necessary And Sufficient ◽  
Triple I Method

In this paper, the authors investigate the ordering property (OP), , together with the general form of the law of importation(LI), i.e., , whereis a t-norm andis a fuzzy implication for the four main classes of fuzzy implications. The authors give necessary and sufficient conditions under which both (OP) and (LI) holds for S-, R-implications and some specific families of QL-, D-implications. Following this, the paper proposes the sufficient condition under which the equivalence between CRI and triple I method for FMP can be established. Moreover, this conclusion can be viewed as a unified triple I method, a generalized form of the known results proposed by Wang and Pei.

scholarly journals Generating Fuzzy Implications by Ordinal Sums

2016 ◽  
Vol 66 (1) ◽  
pp. 39-50 ◽  
Author(s):  
Paweł Drygaś ◽  
Anna Król
Keyword(s):  
Fuzzy Implications ◽  
Fuzzy Implication

Abstract This paper deals with ordinal sums of fuzzy implications. Some of the known constructions are recalled and new ways of generating fuzzy implications from given ones are proposed. Sufficient properties of fuzzy implications as summands for obtaining a fuzzy implication as a result are presented.

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