scholarly journals Some Topological and Modal Operators over the Intuitionistic Fuzzy Sets of Cube Root Type

2019 ◽  
Vol 8 (3) ◽  
pp. 1247-1251
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Cube Root ◽  
Basic Properties ◽  
Modal Operators ◽  
Intuitionistic Fuzzy

In this paper, we defined newly topological operators and modal-like operators and negation over Intuitionistic Fuzzy Sets of Cube Root Type (IFSCRT) are proposed and few theorems are proved. In addition, some of the basic properties of the new operators are discussed

scholarly journals Some Properties of Intuitionistic Fuzzy Soft Rings

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
B. A. Ersoy ◽  
S. Onar ◽  
K. Hila ◽  
B. Davvaz
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Soft Sets ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

Maji et al. introduced the concept of intuitionistic fuzzy soft sets, which is an extension of soft sets and intuitionistic fuzzy sets. In this paper, we apply the concept of intuitionistic fuzzy soft sets to rings. The concept of intuitionistic fuzzy soft rings is introduced and some basic properties of intuitionistic fuzzy soft rings are given. Intersection, union, AND, and OR operations of intuitionistic fuzzy soft rings are defined. Then, the deffinitions of intuitionistic fuzzy soft ideals are proposed and some related results are considered.

scholarly journals On the Most Extended Modal Operator of First Type over Interval-Valued Intuitionistic Fuzzy Sets

Mathematics ◽  
2018 ◽  
Vol 6 (7) ◽  
pp. 123 ◽  
Author(s):  
Krassimir Atanassov
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Modal Operator ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Definition Of ◽  
Interval Valued

The definition of the most extended modal operator of first type over interval-valued intuitionistic fuzzy sets is given, and some of its basic properties are studied.

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 On the Operation ∆ over Intuitionistic Fuzzy Sets

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1518
Author(s):  
Lilija Atanassova ◽  
Piotr Dworniczak
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fuzzy Sets ◽  
Point Theorem ◽  
Intuitionistic Fuzzy Sets ◽  
Geometrical Interpretation ◽  
The Other ◽  
Modal Operators ◽  
Intuitionistic Fuzzy ◽  
The Fixed Point Theorem

Recently, the new operation ∆ was introduced over intuitionistic fuzzy sets and some of its properties were studied. Here, new additional properties of this operations are formulated and checked, providing an analogue to the De Morgan’s Law (Theorem 1), an analogue of the Fixed Point Theorem (Theorem 2), the connections between the operation ∆ on one hand and the classical modal operators over IFS Necessity and Possibility, on the other (Theorems 3 and 4). It is shown that it can be used for a de-i-fuzzification. A geometrical interpretation of the process of constructing the operator ∆ is given.

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