Modifications of the Goguen's intuitionistic 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.

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

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.

Implementation of mamdani fuzzy implication in predicting traffic volume and duration of green lights on an intersection

Traffic congestion at an intersection could be caused by the volume of vehicles that exceed the road capacity, the duration of the green light that is fixed, and so on. The volume of vehicles per unit time at an intersection cannot be known with certainty. Therefore, we need to predict it using fuzzy logic, specifically the Mamdani fuzzy implications. The problems are as follows: how are the input variables to be analyzed with Mamdani fuzzy implications; how are the prediction results, and how is the accuracy based on MAPE. The case study was conducted at two intersections in Semarang City. The tests were carried out using Matlab and manual calculations. The input variables in traffic volume prediction are MC, LV, HV, and time. While the input in the prediction of the duration of the green light is the number of motorcycles and cars. Based on the predictions, there are 74 vehicles (per hour) at the Kaligarang intersection in the east-north direction, there are 111 vehicles at the Kariadi intersection in the south-north direction, and the predictions are good and very accurate (measured by MAPE). The duration of the green light at the Kaligarang intersection on the west approach is 86 seconds, the duration on the Kariadi intersection on the north approach is 81 seconds, and the predictions are good and very accurate.

Some Advances on the Solution of the Generalized Law of Importation for Fuzzy Implication Functions

The law of importation has attracted the interest of many researchers devoted to fuzzy implication functions in the last decades. This property has several important applications, especially in approximate reasoning and image processing. Several generalizations of this property have been proposed. Specifically, one generalization related to the law of migrativity was recently introduced by Baczyński et al. in which two fuzzy implication functions are involved. In this paper, some advances on the solution of this functional equation for the particular case where the involved fuzzy conjunction is a t-norm are presented. Indeed, a complete characterization of all those pairs of fuzzy implication functions with a strict natural fuzzy negation satisfying the generalized law of importation is achieved.

Some new operators for Fermatean fuzzy matrices

In this paper, we define some new operators \([(A \$ B),(A \# B),(A\ast B),(A \rightarrow B) ]\) of Fermatean fuzzy matrices and investigate their algebraic properties. Further, the necessity and possibility operators of Fermatean fuzzy matrices are proved. Finally, we have identified and proved several of these properties, particularly those involving the operator \(A\rightarrow B\) defined as Fermatean fuzzy implication with other operators.

Modifications of Łukasiewicz’s intuitionistic 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.

Lukasiewicz Fuzzy Implication Operator on Pythagorean Fuzzy Tautological Matrices

In this paper, introduced Pythagorean fuzzy tautologial matrices and Pythagorean fuzzy cotautological matrices and some properties of Lukasiwicz implication operator over Pythagorean fuzzy tautologial matrices and Pythagorean fuzzy cotautological matrices are discussed. Also discussed the relation between implication with Lukasiewicz disjunction and conjunction operations of PFCMs and PFCTMs.

A method of constructing fuzzy implications from the FIφ-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.

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

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.