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.

Intuitionistic fuzzy quasi-interior ideals of semigroups

In this study, it is purposed to introduced the concept of quasi-interior ideal on intuitionistic fuzzy semigroups. The concept introduced is supported with examples and its basic algebraic properties are examined.

Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 2

In the paper, the inequality \frac{\mu^{\frac{1}{\nu}}}{\nu} + \frac{\nu^{\frac{1}{\mu}}}{\mu} \leq \frac{1}{2\mu\nu} - 1 is introduced and proved. The same inequality is valid for \mu = \mu_A(x), \nu = \nu_A(x), where \mu_A and \nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x \in E.

Categorical properties of intuitionistic fuzzy groups

The category theory deals with mathematical structures and relationships between them. Categories now appear in most branches of mathematics and in some areas of theoretical computer science and mathematical physics, and acting as a unifying notion. In this paper, we study the relationship between the category of groups and the category of intuitionistic fuzzy groups. We prove that the category of groups is a subcategory of category of intuitionistic fuzzy groups and that it is not an Abelian category. We establish a function β : Hom(A, B) → [0; 1] × [0; 1] on the set of all intuitionistic fuzzy homomorphisms between intuitionistic fuzzy groups A and B of groups G and H, respectively. We prove that β is a covariant functor from the category of groups to the category of intuitionistic fuzzy groups. Further, we show that the category of intuitionistic fuzzy groups is a top category by establishing a contravariant functor from the category of intuitionistic fuzzy groups to the lattices of all intuitionistic fuzzy groups.

Operation Δ as the tool for the de-i-fuzzification procedure and for the correction of the unconscientious experts' evaluations

In this paper, the Δ operation is discussed as an appropriate tool for the de-i-fuzzification procedure. Some properties of the Δ operation are presented. A known way of the correction of the unconscientious experts’ evaluations in the intuitionistic fuzzy environment is given as the result of the Δ operation.

A new type of intuitionistic fuzzy modal operators over intuitionistic fuzzy pairs

In the paper, two intuitionistic fuzzy modal operators from a new type are introduced over intuitionistic fuzzy pairs. Some of the basic properties of the new operators are formulated and checked.

Intuitionistic fuzzy evaluation of artificial neural network model

In this paper a method that evaluates a trained artificial neural network is presented. The learning type of an artificial neural network is supervised learning which requires labeled input training vectors. Labeled medical data is provided to train the network, where the labels can either be 1 if the person is alive, or 0 if the person has deceased. The data is divided into training and validation vectors. The validation input vectors are used to evaluate the model and the results are summarized by using intuitionistic fuzzy values.

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.

Intuitionistic fuzzy transport equation

In the present paper, we use the generalized differentiability concept to study the intuitionistic fuzzy transport equation. We consider transport equation in the homogeneous and non-homogeneous cases with intuitionistic fuzzy initial condition. To illustrate the results, we will solve an advection equation using the finite difference method.