Fuzzy sets and their variants
Nivetha Martin; A.Velankanni Ananth; P.K. Sharmila; T. Priya
Abstract
The pandemic has created a wide range of impacts on the livelihood of the people especially in their occupation and income generation. The horrific pandemic impacts have caused the populace to switch their occupations for the sake of their livelihood sustainability. This research works aims in determining ...
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The pandemic has created a wide range of impacts on the livelihood of the people especially in their occupation and income generation. The horrific pandemic impacts have caused the populace to switch their occupations for the sake of their livelihood sustainability. This research works aims in determining the impacts of the occupational shifts especially in case of rural populace. The decision-making method of Fuzzy Cognitive Maps (FCM) is used in combinations with the statistical data collection methods of survey methodology, participatory approach and multi stage purposive sampling. It is observed that a significant percentage of people have shifted from their occupation and the occupational shifts have impacts on the personal, economic, social and health dimensions of the rural populace. The factors under each dimension and their inter associational impacts are also determined using the method of FCM and FCM Expert software. Based on the findings of the research work, it is very evident that the occupational shifts have created a lot of impacts on the livelihood of the rural populace and also each of the person has experienced the impacts more personally. The societal contribution of the research lies in communicating the results and inferences to the concerned administrators so as to facilitate the affected rural populace in getting back to their primary occupation.
Pythagorean fuzzy sets and their variants
Veerappan Chinnadurai; Arul Selvam
Abstract
In this paper, we define the new notion of interval-valued Pythagorean fuzzy ideals in semigroups and established the properties of its with suitable examples. Also, we introduce the concept of interval valued Pythagorean fuzzy sub-semigroup, interval valued Pythagorean fuzzy left (resp. right) ideal, ...
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In this paper, we define the new notion of interval-valued Pythagorean fuzzy ideals in semigroups and established the properties of its with suitable examples. Also, we introduce the concept of interval valued Pythagorean fuzzy sub-semigroup, interval valued Pythagorean fuzzy left (resp. right) ideal, interval valued Pythagorean fuzzy bi-ideal, interval valued Pythagorean fuzzy interior ideal and homomorphism of an interval valued Pythagorean fuzzy ideal in semigroups with suitable illustration. We show that every interval valued Pythagorean fuzzy left (resp. right) ideal is an interval valued Pythagorean fuzzy bi-ideal.
Pythagorean fuzzy sets and their variants
J Marynirmala; D. Sivakumar
Abstract
We present the notion of Pythagorean Fuzzy Weak Bi-Ideals (PFWBI) and interval valued Pythagorean fuzzy weak bi-ideals of Γ-near-rings and studies some of its properties. We present the notion of interval valued Pythagorean fuzzy weak bi-ideal and establish some of its properties. We study interval ...
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We present the notion of Pythagorean Fuzzy Weak Bi-Ideals (PFWBI) and interval valued Pythagorean fuzzy weak bi-ideals of Γ-near-rings and studies some of its properties. We present the notion of interval valued Pythagorean fuzzy weak bi-ideal and establish some of its properties. We study interval valued Pythagorean fuzzy weak bi-ideals of Γ-near-ring using homomorphism.
Intuitionistic fuzzy sets and their variants
Michael Voskoglou; Said Broumi
Abstract
The Intuitionistic Fuzzy Sets (IFSs) are generalizations of Zadeh’s fuzzy sets, in which the elements of the universe have apart from Zadeh’s membership and the degree of non-membership in [0, 1]. This paper studies applications of intuitionistic Fuzzy Sets (FS) to assessment and multi-criteria ...
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The Intuitionistic Fuzzy Sets (IFSs) are generalizations of Zadeh’s fuzzy sets, in which the elements of the universe have apart from Zadeh’s membership and the degree of non-membership in [0, 1]. This paper studies applications of intuitionistic Fuzzy Sets (FS) to assessment and multi-criteria decision making, which are very useful when uncertainty characterizes the grades or parameters respectively assigned to the elements of the universal set. Applications to everyday life situations are also presented illustrating our results.
Fuzzy multisets and their variants
Mahmut Dirik
Abstract
Due to developments in printing technology, the number of counterfeit banknotes is increasing every year. Finding an effective method to detect counterfeit banknotes is an important task in business. Finding a reliable method to detect counterfeit banknotes is a crucial challenge in the world of economic ...
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Due to developments in printing technology, the number of counterfeit banknotes is increasing every year. Finding an effective method to detect counterfeit banknotes is an important task in business. Finding a reliable method to detect counterfeit banknotes is a crucial challenge in the world of economic transactions. Due to technological development, counterfeit banknotes may pass through the counterfeit banknote detection system based on physical and chemical properties undetected. In this study, an intelligent counterfeit banknote detection system based on a Genetic Fuzzy System (GFS) is proposed to detect counterfeit banknotes efficiently. GFS is a hybrid system that uses a network architecture to fine-tune the membership functions of a fuzzy inference system. The learning algorithms Fuzzy Classification, Genetic Fuzzy Classification, ANFIS Classification, and Genetic ANFIS Classification were applied to the dataset in the UCI machine learning repository to detect the authenticity of banknotes. The developed model was evaluated based on Accuracy (ACC), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Error Mean, Error STD, and confusion matrix. The experimental results and statistical analysis showed that the classification performance of the proposed model was evaluated as follows: Fuzzy = 97.64%, GA_Fuzzy = 98.60%, ANFIS = 80.83%, GA_ANFIS = 97.72% accuracy (ACC). This shows the significant potential of the proposed GFS models for fraud detection.
Pythagorean fuzzy sets and their variants
V. S. Subha; P. Dhanalakshmi
Abstract
In this paper, we expose cosine, jaccard and dice similarity measures and rough interval Pythagorean mean operator. Some of the important properties of the defined similarity measures have been established. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, ...
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In this paper, we expose cosine, jaccard and dice similarity measures and rough interval Pythagorean mean operator. Some of the important properties of the defined similarity measures have been established. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed strategies.
Neutrosophic sets and their variants
Vakkas Uluçay; Necmiye Merve Şahin; Nisa İrem Toz; Enver Bozkurt
Abstract
Different frameworks can be chosen to solve Multi-Criteria Decision-Making (MCDM) problems emerging in business, cyber environment, economy, health care, engineering and other areas. Uncertainty, vagueness and non-rigid boundaries of the initial information are frequently noticed when dealing with the ...
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Different frameworks can be chosen to solve Multi-Criteria Decision-Making (MCDM) problems emerging in business, cyber environment, economy, health care, engineering and other areas. Uncertainty, vagueness and non-rigid boundaries of the initial information are frequently noticed when dealing with the practicalities of the MCDM tasks. Single-valued neutrosophic sets are considered as the effective tool to express uncertainty of the information, however in some cases it lacks the desirable generality and flexibility. The Q-single-valued neutrosophic sets were recently proposed to deal with this situation. Then, we develop a VIKOR method based on the Q-single-valued neutrosophic sets for novel MCDM method. In the decision-making framework, the proposed method is not only a way to solve the problem of MCDM, but also contains an important mathematical idea as a different solution approach. By applying this method to the real-life problem of cyber warfare, demonstrated the flexibility, effectiveness and feasibility of the proposed VIKOR method and compare the obtained results with the results of other existing methods.
Hypersoft sets and their variants
Florentin Smarandache
Abstract
In this paper we define the Soft Set Product as a product of many soft sets and afterwards we extend it to the HyperSoft Set. Similarly, the IndetermSoft Product is extended to the IndetermHyperSoft Set. We also present several applications of the Soft Set Product to Fuzzy (and fuzzy-extensions) ...
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In this paper we define the Soft Set Product as a product of many soft sets and afterwards we extend it to the HyperSoft Set. Similarly, the IndetermSoft Product is extended to the IndetermHyperSoft Set. We also present several applications of the Soft Set Product to Fuzzy (and fuzzy-extensions) Soft Set Product and to IndetermSoft Set and IndetermHyperSoft Set.
Spherical fuzzy sets
Chinnadurai Veerappan; Shakila Venkatesan
Abstract
In this paper we introduce the concept of the spherical interval-valued fuzzy bi-ideal of gamma near-ring R and its some results. The union and intersection of the spherical interval-valued fuzzy bi-ideal of gamma near-ring R is also a spherical interval-valued fuzzy bi-ideal of gamma near-ring R . Further ...
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In this paper we introduce the concept of the spherical interval-valued fuzzy bi-ideal of gamma near-ring R and its some results. The union and intersection of the spherical interval-valued fuzzy bi-ideal of gamma near-ring R is also a spherical interval-valued fuzzy bi-ideal of gamma near-ring R . Further we discuss about the relationship between bi-ideal and spherical interval-valued fuzzy bi-ideal of gamma near-ring R.
Hesitant fuzzy sets and their variants
Madineh Farnam; Majid Darehmiraki
Abstract
Complex nature of the current market is often caused by uncertainties, data uncertainties, their manner of use, and differences in managers' viewpoints. To overcome these problems, Hesitant Fuzzy Sets (HFSs) can be useful as the extension of fuzzy set theory, in which the degree of membership of an element ...
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Complex nature of the current market is often caused by uncertainties, data uncertainties, their manner of use, and differences in managers' viewpoints. To overcome these problems, Hesitant Fuzzy Sets (HFSs) can be useful as the extension of fuzzy set theory, in which the degree of membership of an element can be a set of possible values and provide greater flexibility in design and, thus, model performance. The power of this application becomes clear when different decision-makers tend to independently record their views. In most real-world situations, there are several goals for managers to achieve the desired performance. Therefore, in this study, a description of the solution of the Hesitant Fuzzy Linear Programming (HFLP) problem for solving hesitant fuzzy multi-objective problems is considered. In the following, the multi-objective and three-level supply chain management problem is modeled with the hesitant fuzzy approach. Then, with an example, the flexibility of the model responses is evaluated by the proposed method. The hesitant fuzzy model presented in this study can be extended to other supply chain management problems.
Neutrosophic sets and their variants
Mohanasundari Mohan; Mohana Krishnaswamy
Abstract
Abstract Quadripartitioned single valued neutrosophic (QSVN) set is a powerful structure where we have four components Truth-T, Falsity-F, Unknown-U and Contradiction-C. And also it generalizes the concept of fuzzy, initutionstic and single valued neutrosophic set. In this paper we have proposed the ...
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Abstract Quadripartitioned single valued neutrosophic (QSVN) set is a powerful structure where we have four components Truth-T, Falsity-F, Unknown-U and Contradiction-C. And also it generalizes the concept of fuzzy, initutionstic and single valued neutrosophic set. In this paper we have proposed the concept of K-algebras on QSVN, level subset of QSVN and studied some of the results. In addition to this we have also investigated the characteristics of QSVN Ksubalgebras under homomorphism.
Fuzzy sets and their variants
Abouzar Sheikhi; Mohammad Javad Ebadi
Abstract
In this paper, we present a novel method for solving Fractional Transportation Problems (FTPs) with fuzzy numbers using a ranking function. The proposed method introduces a transformation technique that converts an FTP with fuzzy numbers into an FTP with crisp numbers by employing the robust ranking ...
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In this paper, we present a novel method for solving Fractional Transportation Problems (FTPs) with fuzzy numbers using a ranking function. The proposed method introduces a transformation technique that converts an FTP with fuzzy numbers into an FTP with crisp numbers by employing the robust ranking technique. Subsequently, we formulate two transportation problems, one for maximization and another for minimization, based on the given FTP. The optimal solution for the original FTP is then derived by leveraging the solutions obtained for the formulated transportation problems. By optimizing these single-objective transport problems, our method provides decision-makers with the ability to make satisfactory managerial decisions and evaluate economic operations when confronted with logistic problems involving fractional transportation. To demonstrate the effectiveness of the proposed approach, we present several illustrative examples that showcase its practical application and efficiency.
Fuzzy sets and their variants
Leonce Leandry; Innocent Sosoma; David Koloseni
Abstract
Currently fuzzy set theory has a wide range to model real life problems with incomplete or vague information which perfectly suits the reality and its application is theatrically increasing. This work explored the basic fuzzy operations with the Gaussian Membership using the α-cut method. As it ...
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Currently fuzzy set theory has a wide range to model real life problems with incomplete or vague information which perfectly suits the reality and its application is theatrically increasing. This work explored the basic fuzzy operations with the Gaussian Membership using the α-cut method. As it is known that, the Gaussian membership function has a great role in modelling the fuzzy problems this is what impelled to explore its operation which can further be used in analysis of fuzzy problems. Primarily the basic operations which has been discussed here are addition, subtraction, multiplication, division, reciprocal, exponential, logarithmic and nth power.
Picture fuzzy sets and their variants
Hasan Mohammad Kamrul; Ali Md. Yasin; Sultana Abeda; Mitra Nirmal Kanti
Abstract
Picture fuzzy set is the generalization of fuzzy set and intuitionistic fuzzy set. It is useful for handling uncertainty by considering the positive membership, neutral membership and negative membership degrees independently for each element of a universal set. The main objective of this article is ...
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Picture fuzzy set is the generalization of fuzzy set and intuitionistic fuzzy set. It is useful for handling uncertainty by considering the positive membership, neutral membership and negative membership degrees independently for each element of a universal set. The main objective of this article is to develop some picture fuzzy mean operators, including Picture Fuzzy Harmonic Mean (PFHM), Picture Fuzzy Weighted Harmonic Mean (PFWHM), Picture Fuzzy Arithmetic Mean (PFAM), Picture Fuzzy Weighted Arithmetic Mean (PFWAM), Picture Fuzzy Geometric Mean (PFGM) and Picture Fuzzy Weighted Geometric Mean (PFWGM), to aggregate the picture fuzzy sets. Moreover, we discuss some relevant properties of these operators. Furthermore, we apply these mean operators to make decisions with practical examples. Finally, to show the efficiency and the validity of the proposed operators, we compare our results with the results of existing methods and concluded from the comparison that our proposed methods are more effective and reliable.
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.
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.
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.
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}.
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.
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.
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.
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
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.
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.
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.