A short history of fuzzy; intuitionistic fuzzy; neutrosophic and plithogenic sets

American Journal of Business and Operations Research |

Hyers-Ulam-Rassias Stability for Functional Equation in Neutrosophic Normed Spaces

In Neutrosophic Normed spaces, we investigate a unique quadratic function and a unique additive quadratic function of the Hyers-Ulam-Rassias stability for the functional equation which is said to be a functional equation associated with inner products space.

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American Journal of Business and Operations Research |

Hyers-Ulam-Rassias Stability for Functional Equation in Neutrosophic Normed Spaces

In Neutrosophic Normed spaces, we investigate a unique quadratic function and a unique additive quadratic function of the Hyers-Ulam-Rassias stability for the functional equation which is said to be a functional equation associated with inner products space

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Journal of Neutrosophic and Fuzzy Systems | 2021

On Imperfect Duplets In Some Refined Neutrosophic Rings

This paper solves the imperfect duplets problem in refined neutrosophic rings, where it presents the necessary and sufficient conditions for a pair  to be an imperfect duplet in any refined neutrosophic ring. Also, this work introduces a full description of the structure of imperfect duplets in numerical refined neutrosophic rings such as refined neutrosophic ring of integers  , refined neutrosophic ring of rationales , and refined neutrosophic ring or real numbers. 

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Katy D. Ahmad mail -

Mikail Bal mail -

Arwa A. Hajjari mail -

Rozina Ali mail

link https://doi.org/10.54216/JNFS.010203

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Vol. Volume 1 / Iss. Issue 2

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Journal of Neutrosophic and Fuzzy Systems | 2021

On The Symbolic Turiyam Rings

In this paper, we define for the first time the concept of symbolic Turiyam ring as a direct application of Turiyam symbolic set and as a new generalization of neutrosophic rings. Also, we study many of essential properties and related concepts of these rings such as AH-ideals and subrings.   On the other hand, we illustrate many examples to clarify the validity of our work.

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Prem Kumar Singh mail -

Katy D. Ahmad mail -

Mikail Bal mail -

Malath Aswad mail

link https://doi.org/10.54216/JNFS.010204

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Vol. Volume 1 / Iss. Issue 2

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Journal of Neutrosophic and Fuzzy Systems | 2021

Novel Applications Of Neutrosophic AH-Isometries To The Group Of Units Problem In Neutrosophic Rings and Refined Neutrosophic Rings

The Objective of this paper is to study the group of units problem in two different kinds of neutrosophic structures (neutrosophic rings and refined neutrosophic rings), where we use the concept of AH-isometry to classify neutrosophic rings\refined neutrosophic rings as direct products of classical rings with itself. Also, this classification will lead to the algebraic structure of the corresponding group of units.

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Katy D. Ahmad mail -

Mikail Bal mail -

Arwa A. Hajjari mail -

Rozina Ali mail

link https://doi.org/10.54216/JNFS.010205

Volume & Issue

Vol. Volume 1 / Iss. Issue 2

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International Journal of Neutrosophic Science | 2022

A Short Note on Some Novel Applications of Semi Module Homomorphisms

In this paper, we study the algebraic relationships between n- refined neutrosophic modules by using semi-module homomorphisms. On the other hand, this work shows the relationship between neutrosophic geometrical AH-isometry and semi-module isomorphisms. 

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Mohammad Abobala mail -

Mikail Bal mail -

Malath Aswad mail

link https://doi.org/10.54216/IJNS.180101

Volume & Issue

Vol. Volume 18 / Iss. Issue 1

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International Journal of Neutrosophic Science | 2022

A Study of Some Neutrosophic Clean Rings

The objective of this paper is to introduce a necessary and sufficient condition for a neutrosophic ring to be clean. This work proves the equivalence between case of classical clean ring R and the corresponding neutrosophic ring R(I), refined neutrosophic ring R(I_1,I_2 ), and n-refined neutrosophic ring R_n (I).

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Mohammad Abobala mail -

Mikail Bal mail -

Ahmed Hatip mail

link https://doi.org/10.54216/IJNS.180102

Volume & Issue

Vol. Volume 18 / Iss. Issue 1

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International Journal of Neutrosophic Science |

A short history of fuzzy; intuitionistic fuzzy; neutrosophic and plithogenic sets

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.

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International Journal of Neutrosophic Science |

A short history of fuzzy; intuitionistic fuzzy; neutrosophic and plithogenic sets

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.

groups

link

Volume & Issue

Details open_in_new

International Journal of Neutrosophic Science |

A short history of fuzzy; intuitionistic fuzzy; neutrosophic and plithogenic sets

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.

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