In this paper, we introduce a Sheffer stroke Hilbert algebra by giving definitions of Sheffer stroke and a Hilbert algebra. After it is shown that the axioms of Sheffer stroke Hilbert algebra are independent, it is given some properties of this algebraic structure. Then it is stated the relationship between Sheffer stroke Hilbert algebra and Hilbert algebra by defining a unary operation on Sheffer stroke Hilbert algebra. Also, it is presented deductive system and ideal of this algebraic structure. It is defined an ideal generated by a subset of a Sheffer stroke Hilbert algebra, and it is constructed a new ideal of this algebra by adding an element of this algebra to its ideal.

Kragujevac Journal of Mathematics is a periodical for mathematics. Requirements for acceptance of papers include originality, scientific significance and clarity of presentation.

In this work, we introduce Wajsberg algebras which are equivalent structures to MV-algebras in their implicational version, and then we define new notions and give new solutions to the set-theoretical Yang-Baxter equation by using Wajsberg algebras.

Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough studies have already been done. There are various ways such as fuzzy, intuitionistic and neutrosophic sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. Also, plithogenic sets as a generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets, which is a set whose elements are characterized by many attributes’ values. In this paper, our aim is to demonstrate and review the history of fuzzy, intuitionistic and neutrosophic sets. For this purpose, we divided the paper as: section 1. History of Fuzzy Sets, section 2. History of Intuitionistic Fuzzy Sets and section 3. History of Neutrosophic Theories and Applications, section 4. History of Plithogenic Sets.

The aim of this study is to present (sup-hesitant) fuzzy SUP-subalgebras and fuzzy duplex SUP-sets on Sheffer stroke UP-algebra (in short, SUP-algebra). After defining (sup-hesitant) fuzzy SUP-subalgebras and fuzzy duplex SUP-sets of a SUP-algebra, we give their some properties and analyse whether the intersection or union of these subalgebras is a (sup-hesitant) fuzzy SUP-subalgebra of a SUP-algebra. It is shown that the level sets of (sup-hesitant) fuzzy SUP-subalgebras of a SUP-algebra are its SUP-subalgebras. Also, fuzzy duplex SUP-sets of a SUP-algebra are determined and studied the cases which these sets are SUP-algebras. Finally, the relationships between aforementioned structures are investigated.