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 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 Modifications of the Goguen's intuitionistic fuzzy implication

2021 ◽  
Vol 27 (4) ◽  
pp. 20-29
Author(s):  
Janusz Kacprzyk ◽  
◽  
Katarína Čunderlíková ◽  
Nora Angelova ◽  
Krassimir T. Atanassov ◽  
...  
Keyword(s):  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication

On the basis of the Goguen’s intuitionistic fuzzy implication, seven of its modifications are constructed. Some of their basic properties are studied. The negations, generated by these implications are introduced and some of their properties are also described.

scholarly journals Modifications of the Third Zadeh’s intuitionistic fuzzy implication

2021 ◽  
Vol 27 (1) ◽  
pp. 9-23
Author(s):  
Krassimir Atanassov ◽  
◽  
Nora Angelova ◽  
◽  
Keyword(s):  
Basic Properties ◽  
The Third ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication

In [24], G. Klir and B. Yuan named after L. Zadeh the implication p → q = max(1 − p, min(p, q)). In a series of papers, the author introduced two intuitionistic fuzzy forms of Zadeh’s implication and their basic properties have been studied. In the present paper, a new (third) intuitionistic fuzzy form of Zadeh’s implication is given and some of its properties are studied.

scholarly journals On an Intuitionistic Fuzzy Form of the Goguen’s Implication

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 676
Author(s):  
Krassimir Atanassov ◽  
Nora Angelova ◽  
Vassia Atanassova
Keyword(s):  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication

In the present paper we construct a new intuitionistic fuzzy implication, giving intuitionistic fuzzy form to Goguen’s implication. Some of its basic properties are studied and illustrated with examples. Geometrical interpretations of the different forms of the new implication are given. Other forms of the Goguen’s implication are discussed.

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.

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.

scholarly journals Intuitionistic Fuzzy Normed Subrings and Intuitionistic Fuzzy Normed Ideals

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1594
Author(s):  
Nour Abed Alhaleem ◽  
Abd Ghafur Ahmad
Keyword(s):  
Inverse Image ◽  
Ring Homomorphism ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Normed Ring

The main goal of this paper is to introduce the notion of intuitionistic fuzzy normed rings and to establish basic properties related to it. We extend normed rings by incorporating the idea of intuitionistic fuzzy to normed rings, we develop a new structure of fuzzy rings which will be called an intuitionistic fuzzy normed ring. As an extension of intuitionistic fuzzy normed rings, we define the concept of intuitionistic fuzzy normed subrings and intuitionistic fuzzy normed ideals. Some essential operations specially subset, complement, union, intersection and several properties relating to the notion of generalized intuitionistic fuzzy normed rings are identified. Homomorphism and isomorphism of intuitionistic fuzzy normed subrings are characterized. We identify the image and the inverse image of intuitionistic fuzzy normed subrings under ring homomorphism and study their elementary properties. Some properties of intuitionistic fuzzy normed rings and relevant examples are presented.

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