Research Paper
Fuzzy multisets and their variants
Mahdi Mollaei
Abstract
This paper, considers the fuzzy topological subsets, fuzzy topological spaces and introduces a novel concept of fuzzy Hausdorff space and fuzzy manifold space in this regards. Based on these concepts, we present a concept of fuzzy metric Hausdorff spaces and fuzzy metric manifold spaces via the notations ...
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This paper, considers the fuzzy topological subsets, fuzzy topological spaces and introduces a novel concept of fuzzy Hausdorff space and fuzzy manifold space in this regards. Based on these concepts, we present a concept of fuzzy metric Hausdorff spaces and fuzzy metric manifold spaces via the notations of KM-fuzzy metric spaces.This study, generalises the concept of fuzzy metric space to union and product of fuzzy metric spaces in classical logic and in this regard investigates the some product of fuzzy metric fuzzy manifold spaces. We apply the notation of valued-level subsets and make a relation between of topological space, Husdorff space, manifold space and fuzzy topological space, fuzzy Husdorff space and fuzzy manifold space. In final, we extended the fuzzy topological space, fuzzy Husdorff space and fuzzy manifold space to fuzzy metric topological space, fuzzy metric Husdorff space and fuzzy metric manifold spaceIndeed, this study analyses the notation of fuzzy metric manifold based on valued-level subset.
Research Paper
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 study 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 study 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. The use of Gaussian Membership function add more realist compartment to investigate each elements behavior and its predication outputs. Graphical analysis has been done for each operation depicting the results of the corresponding operation to the original membership function(s). Primarily the basic operations which has been discussed here are addition, subtraction, multiplication, division, reciprocal, exponential, logarithmic and nth power.The sightseen operations can further be used in analysis of fuzzy sets with Gaussian Membership and using the alpha-cut method to make things easier for the calculations of all the basic operations. Therefore, we propose this approach to be used when analyzing the fuzzy problem with Gaussian Membership
Research Paper
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.
Research Paper
Picture fuzzy sets and their variants
Mohammad Kamrul Hasan; Md. Yasin Ali; Abeda Sultana; Nirmal Kanti Mitra
Abstract
Picture fuzzy set is the generalization of fuzzy set and intuitionistic fuzzy set. It is useful for handling uncertainty by considering positive membership, neutral membership and the 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 positive membership, neutral membership and the 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 decision 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.
Research Paper
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.
Research Paper
Fuzzy sets and their variants
besma belhadj
Abstract
Under the additional assumption that the errors are normally distributed, the ordinary least squares method is the maximum likelihood estimator. In this paper, we propose, for a simple regression, an estimation method alternative to the ordinary least squares method based on a so-called Gaussian membership ...
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Under the additional assumption that the errors are normally distributed, the ordinary least squares method is the maximum likelihood estimator. In this paper, we propose, for a simple regression, an estimation method alternative to the ordinary least squares method based on a so-called Gaussian membership function, one that checks the validity of the verbal explanation suggested by the observer. The fuzzy estimation approach demonstrated here is based on a suitable framework for a natural behavior observed in nature. An application based on a group of MENA countries in 2015 is presented to estimate the Employment Poverty relationship.
Under the additional assumption that the errors are normally distributed, the ordinary least squares method is the maximum likelihood estimator. In this paper, we propose, for a simple regression, an estimation method alternative to the ordinary least squares method based on a so-called Gaussian membership function, one that checks the validity of the verbal explanation suggested by the observer. The fuzzy estimation approach demonstrated here is based on a suitable framework for a natural behavior observed in nature. An application based on a group of MENA countries in 2015 is presented to estimate the Employment Poverty relationship.
Research Paper
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 ...
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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. We know that there are usually several goals for managers to achieve the desired performance. Therefore, in this study, firstly a description of the solution of the hesitant fuzzy linear programming problem (HFLP) 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, high flexibility of the model responses is evaluated by the proposed method. Under different circumstances with appropriate modifications, it is possible to extend the hesitant fuzzy model presented in this study to other supply chain management problems.
Short Communication
Fuzzy sets and their variants
Zanyar A. Ameen
Abstract
Thangaraj and Balasubramanian introduced the so-called somewhat fuzzy semicontinuous and somewhat fuzzy semiopen functions. Two years later, the same authors defined two other types of functions called somewhat fuzzy continuous and somewhat fuzzy open without indicating connections between them. At first ...
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Thangaraj and Balasubramanian introduced the so-called somewhat fuzzy semicontinuous and somewhat fuzzy semiopen functions. Two years later, the same authors defined two other types of functions called somewhat fuzzy continuous and somewhat fuzzy open without indicating connections between them. At first glance, we may easily conclude (from their definitions) that every somewhat fuzzy continuous (resp. open) function is somewhat fuzzy semicontinuous (resp. semiopen) but not conversely. In this note, we show that they are equivalent. We further prove that somewhat fuzzy continuous functions are weaker than fuzzy semicontinuous functions.
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Research Paper
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 by their intersection into a HyperSoft Set. Similarly, the IndetermSoft Product is extended be intersection to the IndetermHyperSoft Set. We also present several applications of the Soft Set Product to Fuzzy (and ...
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In this paper we define the Soft Set Product as a product of many soft sets and afterwards by their intersection into a HyperSoft Set. Similarly, the IndetermSoft Product is extended be intersection 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.
