Research Paper
Intuitionistic fuzzy sets and their variants
Behnam Talaee; Mehrnoosh Sobhani; Bijan Davvaz
Abstract
In this paper, we discuss the structure of intuitionistic fuzzy projec- tive modules and investigate some properties of them. Also we study about intuitionistic fuzzy homomorphisms between intuitionistic fuzzy modules.
We study about exact sequences, products and co-products, func- tors and relating ...
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In this paper, we discuss the structure of intuitionistic fuzzy projec- tive modules and investigate some properties of them. Also we study about intuitionistic fuzzy homomorphisms between intuitionistic fuzzy modules.
We study about exact sequences, products and co-products, func- tors and relating topics in IFR − Mod and investigate the relationship between them, where IFR − Mod is category whose objects are intu- itionidtic fuzzy modules and morphisms are intuitionistic fuzzy homo-
morphisms.
For a commutative ring R and two intuitionistic fuzzy R- modules
A = (μA, νA) ≤IF M, B = (μB, νB) ≤IF N we show that
HomIF −R (A, B) = (α, β) is an intuitionistic fuzzy R-module.
Also for a commutative ring R, if
0⟶𝐴𝑓~→ B 𝑔~→ C is an exact sequence in IFR-Mod, where f˜ is IF split homomorphism, then
we show that HomIF −R(D,-) preserves the sequence, for every D ∈ IFR − Mod.
Research Paper
Neutrosophic sets and their variants
Mohamed Bisher Zeina; mohammad abobala
Abstract
Integers play a basic role in the structures of asymmetric crypto-algorithms. Many famous public key crypto-schemes use the basics of number theory for sharing keys and for the decryption and encryption of messages and multimedia.
As a novel trend in the world of cryptography, non-classical integer systems ...
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Integers play a basic role in the structures of asymmetric crypto-algorithms. Many famous public key crypto-schemes use the basics of number theory for sharing keys and for the decryption and encryption of messages and multimedia.
As a novel trend in the world of cryptography, non-classical integer systems are used for encryption and decryption such as neutrosophic or plithogenic integers.
The objective of this paper is to provide two novel crypto schemes for the encryption and decryption of data and information based on the algebraic properties of 2-cyclic refined integers, where improved versions of the El-Gamal crypto-scheme and RSA algorithm will be established through the view of the algebra of 2-cyclic refined integers.
On the other hand, we illustrate some examples and tables to show the validity and complexity of the novel algorithms.
Research Paper
Picture fuzzy sets and their variants
R. V Jaikumar; R. Sundareswaran; M Shanmugapriya; Said Broumi; Talal Ali Al-Hawary
Abstract
The notion of fuzzy graphs (FGs) and intuitionistic fuzzy graphs (IFGs) is generalized in the picture fuzzy graph (PFG), which is a more common platform for expressing the degree of positive, negative, and neutral membership function. Picture fuzzy soft graphs (PFSGs) are powerful mathematical tools ...
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The notion of fuzzy graphs (FGs) and intuitionistic fuzzy graphs (IFGs) is generalized in the picture fuzzy graph (PFG), which is a more common platform for expressing the degree of positive, negative, and neutral membership function. Picture fuzzy soft graphs (PFSGs) are powerful mathematical tools for modelling the real-world vagueness. The concept of vulnerability parameters of PFSG is provided in this research work by introducing the novel cardinality, domination number, integrity and domination integrity (ÐÏ) of PFSG. Furthermore, a decision-making method for the picture fuzzy soft graph has been presented using domination integrity to suggest an algorithm for determining the ideal location for establishing a diagnosis centre in cities.
Research Paper
Fuzzy sets and their variants
Masresha Wassie Woldie
Abstract
In this study, we attempted to demonstrate the interval-valued fuzzy code by extending the concept of an interval-valued fuzzy set. Further, we discussed the operations of the interval-valued fuzzy code. The interval-valued fuzzy soft code is introduced, and various related properties are investigated ...
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In this study, we attempted to demonstrate the interval-valued fuzzy code by extending the concept of an interval-valued fuzzy set. Further, we discussed the operations of the interval-valued fuzzy code. The interval-valued fuzzy soft code is introduced, and various related properties are investigated in this paper. Finally, we show that the operations of interval-valued fuzzy soft code are discussed. Through this paper, we use the set of integers modulo 2, that is Z_2= {0, 1}.
Research Paper
Fermatean fuzzy sets and their variants
Amal Kumar Adak; Manish Kumar Gunjan
Abstract
Stock portfolio problems are one of the most relevant real world problems. In this study, we discuss on portfolio in which risk amount, rate of risk return and expected return rate under Fermatean fuzzy environment. Linear programming problem is used to formulate fermatean fuzzy portfolio. Using the ...
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Stock portfolio problems are one of the most relevant real world problems. In this study, we discuss on portfolio in which risk amount, rate of risk return and expected return rate under Fermatean fuzzy environment. Linear programming problem is used to formulate fermatean fuzzy portfolio. Using the score function, the fermatean fuzzy portfolio is converted to deterministic form. Lingo software is used to solve this converted deterministic portfolio problems. The main features of this model is that investors can select risk coefficicient in order to enhance predicted returns and customize their strategies according to their personal circumstances. An example is offered that illustrates the effectiveness and dependability of the proposed approach.
Research Paper
Fuzzy sets and their variants
Sahabul Alam; Joydeep Kundu; Shivnath Ghosh; Arindam Dey
Abstract
Unmanned aerial vehicles (UAVs) bring both potential and difficulties for emergency applications, including packet loss and changes in network topology. UAVs are also quickly taking up a sizable portion of the airspace, allowing Flying Ad Hoc Networks (FANETs) to conduct effective ad hoc missions. Therefore, ...
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Unmanned aerial vehicles (UAVs) bring both potential and difficulties for emergency applications, including packet loss and changes in network topology. UAVs are also quickly taking up a sizable portion of the airspace, allowing Flying Ad Hoc Networks (FANETs) to conduct effective ad hoc missions. Therefore, building routing protocols for FANETs is difficult due to flight restrictions and changing topology. To solve these problems, a bio-inspired route selection technique is proposed for FANET. A combined trustworthy and bioinspired-based transmission strategy is developed as a result of the growing need for dynamic and adaptable communications in FANETs. The fitness theory is used to assess direct trust and evaluate credibility and activity to estimate indirect trust. In particular, assessing UAVs behaviour are still a crucial problem in this field. It recommends fuzzy logic, one of the most widely utilised techniques for trusted route computing, for this purpose. Fuzzy logic can manage complicated settings by classifying nodes based on various criteria. This method combines geocaching and unicasting, anticipating the location of intermediate UAVs using 3-D estimates. This method guarantees resilience, dependability, and an extended path lifetime, improving FANET performance noticeably. Two primary features of FANETs that shorten the route lifetime must be accommodated for in routing. First of all, the collaborative nature necessitates communication and coordination between the flying nodes, which uses a lot of energy. Second, the flying nodes' highly dynamic mobility pattern in 3D space may cause link disconnection because of their potential dispersion. It employs trusted leader drone selection within the cluster, and safe routing among leaders using ant colony optimization. a fuzzy‐based UAV behaviour analytics is presented for trust management in FANETs. Compared to existing protocols, the simulated results demonstrate improvements in delay, routing overhead in FANET.
Research Paper
Pythagorean fuzzy sets and their variants
SUBHANKAR JANA; Anjali Patel; Juthika Mahanta
Abstract
The fuzzy set is generally used to identify the topological relationship between two vague spatial objects. Indeterminacy can arise at any point in the modelling process, and the fuzzy model is unable to deal with this. Given that the Pythagorean fuzzy is better equipped to deal with such indeterminacies ...
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The fuzzy set is generally used to identify the topological relationship between two vague spatial objects. Indeterminacy can arise at any point in the modelling process, and the fuzzy model is unable to deal with this. Given that the Pythagorean fuzzy is better equipped to deal with such indeterminacies than the fuzzy set, we advocated for the use of Pythagorean fuzzy modelling to determine the topological relation between two spatial objects. This paper contributes to the expanding study of Pythagorean fuzzy topological spaces by introducing core, fringe, outer, regular open set, regular closed set, double connectedness and homeomorphism in Pythagorean fuzzy environment. Using these definitions, the paper proposes an algebraic model, namely the Pythagorean fuzzy 9-intersection matrix, to find topological relations between any two Pythagorean fuzzy sets in a Pythagorean topological space. The inbuilt capability of Pythagorean fuzzy set to handle indeterminacy establishes the proposed model as the potential tool to find topological relations between two indeterminate spatial objects. Ample instances are discussed to nourish the existence of indeterminate spatial objects. Finally, a simple Pythagorean fuzzy region is defined and all possible relations between such two Pythagorean fuzzy regions are examined.
Research Paper
Neutrosophic sets and their variants
Rajeshwari S; Hema R; Florentin Smarandache
Abstract
This paper is mainly intended to verify whether the basic laws of set theory are applicable in the Neutrosophic soft set. The laws that have been examined in this paper for NSS include Commutative law, Associative law, Distributive law, Involution law, Idempotent law, Negation law (law of contradiction ...
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This paper is mainly intended to verify whether the basic laws of set theory are applicable in the Neutrosophic soft set. The laws that have been examined in this paper for NSS include Commutative law, Associative law, Distributive law, Involution law, Idempotent law, Negation law (law of contradiction and law of excluded middle), it has also been illustrated with sufficient examples. In addition, extending that to the hypersoft set, we have proved if H is a Neutrosophic hypersoft Subgroup (NHSSG) of a group G and N is a normal subgroup of G, then HN is a Neutrosophic hypersoft Subgroup (NHSSG) of G.
Keywords: Neutrosophic Set: Neutrosophic Soft Set: Complement set: Neutrosophic hypersoft set
Research Paper
Fuzzy sets and their variants
MHALLA ANIS
Abstract
The scope of the presented work is devoted to the monitoring of transport railway networks. These systems have robustness to temporal perturbations. The major paper's contribution is a fuzzy filtering of sensor signals incorporating robustness parameters. This novel concept combines a conventional ...
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The scope of the presented work is devoted to the monitoring of transport railway networks. These systems have robustness to temporal perturbations. The major paper's contribution is a fuzzy filtering of sensor signals incorporating robustness parameters. This novel concept combines a conventional sensor signal filter mechanism and fuzzy logic principles. The strengths of these two techniques are leveraged to prevent control freezing and the fuzzy systems' ability to handle inaccurate information by employing fuzzy rules. Lastly, to prove the efficiency and the accuracy of the newly developed approach, an example is shown. The findings reveal that the fuzzy logic allows to maintain the travel process in a degraded mode, while ensuring the traffic quality and customers safety through the incorporation of expert knowledge.
Review Paper
Other
Lama Razouk
Abstract
The objective of this paper is to create a strong background of many algebraic structures dealing with Weak Fuzzy Complex elements. So that, we build a special transformation function that has an important role in working with variables from a Real number set instead of a Weak Fuzzy Complex set. We study ...
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The objective of this paper is to create a strong background of many algebraic structures dealing with Weak Fuzzy Complex elements. So that, we build a special transformation function that has an important role in working with variables from a Real number set instead of a Weak Fuzzy Complex set. We study its algebraic properties and models. Also, we define the Weak Fuzzy Complex function, its canonical formula and its main establishments. Therefore, we show the formulas of some famous functions and relations in Weak Fuzzy Complex variables.
On the other hand, differentiability, integrability and continuity of Weak Fuzzy Complex functions in one variable will be presented in terms of theorems, as well, many related examples will be illustrated to clarify the validity of our work.
Research Paper
Neutrosophic sets and their variants
Abhishek Singh; Hemant Kulkarni; Florentin Smarandache; Gajendra K. Vishwakarma
Abstract
In this article, we introduce a novel approach by presenting separate ratio and regression estimators in the context of neutrosophic stratified sampling for the very first time, incorporating auxiliary variables. We have conducted a thorough analysis to estimate these newly proposed estimators' ...
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In this article, we introduce a novel approach by presenting separate ratio and regression estimators in the context of neutrosophic stratified sampling for the very first time, incorporating auxiliary variables. We have conducted a thorough analysis to estimate these newly proposed estimators' bias and mean square error (MSE) up to the first-order approximation. Theoretically using efficiency comparison criteria, our findings demonstrate the superior performance of these estimators compared to traditional unbiased estimators. Also, numerically based on real-life and artificial data, we have shown the supremacy of the neutrosophic stratified sampling over neutrosophic simple random sampling along with the supremacy of our proposed neutrosophic separate stratified estimators over neutrosophic stratified unbiased estimator. Moreover, our research highlights the enhanced reliability of neutrosophic stratified estimators when contrasted with classical stratified estimators.