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    Neutrosophic N -structures on strong Sheffer stroke non-associative MV-algebras
    (University of New Mexico, 2021) Oner T.; Katican T.; Rezaei A.
    The aim of the study is to examine a neutrosophic N -subalgebra, a neutrosophic N -filter, level sets of these neutrosophic N -structures and their properties on a strong Sheffer stroke non-associative MV-algebra. We show that the level set of neutrosophic N -subalgebras on this algebra is its strong Sheffer stroke nonassociative MV-subalgebra and vice versa. Then it is proved that the family of all neutrosophic N -subalgebras of a strong Sheffer stroke non-associative MV-algebra forms a complete distributive lattice. By defining a neutrosophic N -filter of a strong Sheffer stroke non-associative MV-algebra, it is presented that every neutro-sophic N -filter of a strong Sheffer stroke non-associative MV-algebra is its neutrosophic N -subalgebra but the inverse is generally not true, and some properties © 2021. All Rights Reserved.
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    Neutrosophic N?structures on Sheffer stroke BCH-algebras
    (University of New Mexico, 2022) Oner T.; Katican T.; Rezaei A.
    The aim of the study is to introduce a neutrosophic N?subalgebra and neutrosophic N?ideal of a Sheffer stroke BCH-algebras. We prove that the level-set of a neutrosophic N?subalgebra (neutrosophic N?ideal) of a Sheffer stroke BCH-algebra is its subalgebra (ideal) and vice versa. Then it is shown that the family of all neutrosophic N?subalgebras of a Sheffer stroke BCH-algebra forms a complete distributive modular lattice. Also, we state that every neutrosophic N?ideal of a Sheffer stroke BCH-algebra is its neutrosophic N?subalgebra but the inverse is generally not true. We examine relationships between neutrosophic N?ideals of Sheffer stroke BCH-algebras by means of a surjective homomorphism between these algebras. Finally, certain subsets of a Sheffer stroke BCH-algebra are defined by means of N?functions on this algebraic structure and some properties are investigated. © 2022
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    A note on translation of bipolar-valued fuzzy sets in Sheffer stroke MTL-algebras
    (CRC Press, 2024) Oner T.; Senturk I.; Rezaei A.
    When constructing a mathematical model, it is crucial to simplify the expression as much as possible by using the least number of axioms or operations. Tarski tackled this issue in his study of Abelian groups, where he found that a single axiom characterizes them based on the divisor operator [1]. © 2024 selection and editorial matter, Said Broumi, D. Nagarajan, Michael Gr. Voskoglou and S. A. Edalatpanah; individual chapters, the contributors.
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    A short history of fuzzy, intuitionistic fuzzy, neutrosophic and plithogenic sets
    (American Scientific Publishing Group (ASPG), 2022) Rezaei A.; Oner T.; Katican T.; Smarandache F.; Gandotra N.
    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. © 2022, American Scientific Publishing Group (ASPG). All rights reserved.