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
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; Simon Collart Dutilleul
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 sensor ...
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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
Complex Fuzzy Sets and their variants
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.
Research Paper
Fuzzy sets and their variants
Sapan Kumar Das; Indrani Maiti; RAJEEV PRASAD; Surapati Pramanik; Tarni Mandal
Abstract
The prediction of a real-life problem like in industrial sector or health sector the outcome is impossible or sometimes it is difficult. Due to high information uncertainty and complicated influencing factors of industrial sector, the traditional data-driven prediction approaches can hardly reflect the ...
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The prediction of a real-life problem like in industrial sector or health sector the outcome is impossible or sometimes it is difficult. Due to high information uncertainty and complicated influencing factors of industrial sector, the traditional data-driven prediction approaches can hardly reflect the real changes in practical situation. Fuzzy programming is a powerful prediction reasoning and risk assessment model for uncertain environment. This article mainly explores and applies a modified form of fuzzy programming; namely Fuzzy Linear Fractional Programming Problem (FLFPP) having the coefficients of the objectives and constraints as triangular fuzzy numbers (TFNs). The FLFPP is converted into an equivalent crisp multi-objective linear fractional programming problem (MOLFPP) and solved individually to associate an aspiration level to it. Then by applying fuzzy goal programming (FGP) technique the maximum degree of each membership goal is obtained by minimizing the negative deviational variables. We carry out two industrial application simulations in a hypothetical industrial scenario. Our study shows that the proposed model is practical and applicable to the uncertain practical environment to realize the prediction and the obtained results are compared with that of the existing methods.
Research Paper
Hesitant fuzzy sets and their variants
Lubna Shafi; Shilpi Jain; Praveen Agarwal; Pervaiz Iqbal; Aadil Rashid Sheergojri
Abstract
Fuzzy time series forecasting is an approach for dealing with uncertainty in time series data that uses fuzzy logic. The hesitant fuzzy set theory emphasizes the chances of capturing fuzziness and uncertainty due to randomness better than the classic fuzzy set theory. This study aims to improve the previously ...
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Fuzzy time series forecasting is an approach for dealing with uncertainty in time series data that uses fuzzy logic. The hesitant fuzzy set theory emphasizes the chances of capturing fuzziness and uncertainty due to randomness better than the classic fuzzy set theory. This study aims to improve the previously identified hesitant fuzzy time series forecasting models by including various degrees of hesitation to improve forecasting performance. The goal is to deal with the issue of identifying a common membership grade when several fuzzification methods are available to fuzzify time series data.The proposed method utilizes trapezoidal and bell-shaped fuzzy membership functions for constructing hesitant fuzzy sets.Ahesitant fuzzy weighted averaging operator is then applied to the hesitant fuzzy elements to create fuzzy logical relations.The suggested technique is employed to forecast enrollment in the University of Alabama and cancer incidence rates in India. The efficiency of the proposed forecasting approach is determined by rigorously comparing it to various computational fuzzy time series forecasting methods in terms of error measurements like root mean square error, average forecasting error, and mean absolute deviation. The validity of the proposed forecasting model is verified by using correlation coefficients, coefficients of determination, tracking signals, and performance parameters. The significance of improved accuracy in forecasted results is confirmed as well using the two-tailed t-test. The results of the study revealed that the enhanced hesitant fuzzy time series model is more effective and accurate in forecasting the university enrolment of Alabama and the cancer incidence rates of India.
Research Paper
Intuitionistic fuzzy sets and their variants
Poonam Kumar Sharma
Abstract
The investigation of mathematics underlines accuracy, precision, and flawlessness, yet in numerous genuine circumstances, individuals face equivocalness, ambiguity, imprecision, and so forth. Intuitionistic fuzzy set theory, rough set theory, and soft set theory are three noble techniques in mathematics ...
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The investigation of mathematics underlines accuracy, precision, and flawlessness, yet in numerous genuine circumstances, individuals face equivocalness, ambiguity, imprecision, and so forth. Intuitionistic fuzzy set theory, rough set theory, and soft set theory are three noble techniques in mathematics that are utilized for decision-making in vague and uncertain information systems. Intuitionistic fuzzy algebra-based math plays a huge part in the current era of mathematical research, and it deals with the algebraic concepts and models of intuitionistic fuzzy sets. The investigation of different ordered algebraic structures, like lattice-ordered groups, Riesz spaces, etc., is of great importance in algebra. The theory of lattice-ordered G-modules is very useful in the study of lattice-ordered groups and similar algebraic structures. In this article, the theories of intuitionistic fuzzy sets and lattice-ordered G-modules are synchronised in a reasonable way to develop a novel concept in mathematics, i.e., intuitionistic fuzzy lattice-ordered G-modules, which would pave the way for new researchers in intuitionistic fuzzy mathematics to explore much more in this field.
Research Paper
Artificial Intelligence with uncertainty
Lincy Jacquline M; Sudha N
Abstract
Problem Statement: Chronic nephritic sickness is another name for chronic kidney disease (CKD). Numerous complications, such as elevated blood levels, anemia, weak bones, and nerve damage, constitute a problem. It is usually possible to prevent chronic uropathy from getting worse by early identification ...
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Problem Statement: Chronic nephritic sickness is another name for chronic kidney disease (CKD). Numerous complications, such as elevated blood levels, anemia, weak bones, and nerve damage, constitute a problem. It is usually possible to prevent chronic uropathy from getting worse by early identification and treatment. Methodology: To circumvent these problems, current research has presented the fruit fly optimization algorithm (FFOA) and effective multi-kernel support vector machine (MKSVM) for illness classification. Finding best features from a collection is usually done using FFOA. Main findings/Contributions: MKSVM categorizes medical data using chosen dataset criteria. The accuracy of classifier will be impacted by any range variations in data obtained for this study. MKSVM continues to yield more incorrectly classified findings. To resolve those problems introduces a pre-processing step based on min max normalization to normalize scale of input CKD data values. Then significant features will be selected utilizing Improved FFOA (IFFOA). The selected features will be clustered using Weighted Fuzzy C means clustering (WFCM) to predict the class label of the data sample to reduce the misclassification results. Finally, CKD classification will be performed using the Enhanced Adaptive Neuro Fuzzy Inference System (EANFIS) as normal or abnormal. Conclusions: The suggested strategy efficacy is demonstrated by findings in fields of recall, accuracy, precision, and f-measure.
Research Paper
Artificial Intelligence with uncertainty
Yinghao Li; Jawis M N
Abstract
In an effort to fulfil the requirements of China's quality education policy, several Chinese institutions and colleges have recently included badminton as an optional sport. Examining current issues in the field, the paper argues that badminton instruction in Chinese higher education needs improvement. ...
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In an effort to fulfil the requirements of China's quality education policy, several Chinese institutions and colleges have recently included badminton as an optional sport. Examining current issues in the field, the paper argues that badminton instruction in Chinese higher education needs improvement. It then proposes new approaches to teaching the sport in the classroom, including ideas for lesson plans, instructional strategies, and pedagogical techniques. Concerning badminton education in higher education, it outlines a strategy to address the issues. In order to overcome the obstacles of fuzzy assisted virtual reality badminton instruction, teachers should think about their own lesson planning and delivery processes, as well as their Badminton Students’ perceptions of physical education programmers. To teach badminton in universities, the article proposes VR-ITM, or fuzzy assisted virtual reality assisted interactive teaching techniques using neural network. This study aims to examine the advantages and disadvantages of utilizing fuzzy assisted virtual reality (VR) to teach badminton in PE classes, as well as the difficulties and solutions that teachers have found for these issues through the use of a neural network. This study investigates the potential benefits of incorporating virtual reality technology into the physical education curriculum and uses VR-ITM, which stands for virtual reality based interactive teaching methods, to teach badminton at college locations. Incorporating badminton into university curricula as a means of encouraging students to lead healthier lifestyles is the primary focus of this study. In addition to fostering Badminton Students’ professional skills, universities should emphasise the importance of Badminton Students’ physical well-being in comparison to the conventional approaches used by the control group to teach badminton, the neural network-based intelligent teaching system performs better.
Research Paper
Artificial Intelligence with uncertainty
Chunyan Xing
Abstract
Management models in education have recently emerged with plans to make school administration more effective and efficient. Higher education (HE), a postsecondary education, leads to academic degrees. An object class having membership grades that run along a continuum is called a fuzzy set. When tested ...
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Management models in education have recently emerged with plans to make school administration more effective and efficient. Higher education (HE), a postsecondary education, leads to academic degrees. An object class having membership grades that run along a continuum is called a fuzzy set. When tested in online classrooms with abnormal data, this method's effectiveness exceeded that of the intelligent education system. The challenging characteristics of such higher education using fuzzy sets are the students' low family income, a complicated network, and skill development due to the low quality of education. Block structure has been developed based on higher education in a fuzzy sets system for students in terms of low family income, complicated networks, and skill development due to the low quality of education. Hence, in this research, Double Deep Q-Learning network-enabled Multi-Criteria Decision-Making (D2QLN-MCDM) technologies have improved students' higher education with fuzzy sets. It has been used to design, develop, and verify students' higher education in fuzzy sets. The workforce tasked with integrating digital technology into HE have a profound effect on students' learning experiences. HE institutions will need experienced individuals with varied digital knowledge to manage and integrate these technologies effectively. The experimental analysis of D2QLN-MCDM outperforms fuzzy sets using the student's HE regarding precision (99.4), accuracy (90.4%), Recall ratio (97.5%), and specificity (93.9%).
Research Paper
Neutrosophic sets and their variants
Nirmal Sarkar; Ashoke Das; Towhid E Aman
Abstract
In this article, we introduce and discuss the concepts of neutrosophic $\mu$-dense, neutrosophic $\mu$-nowhere dense, and neutrosophic $\mu$-first category sets. We also define and characterize the concept of neutrosophic $\mu$-baire space. Moreover, we investigate neutrosophic $(\mu, \eta)$-continuity ...
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In this article, we introduce and discuss the concepts of neutrosophic $\mu$-dense, neutrosophic $\mu$-nowhere dense, and neutrosophic $\mu$-first category sets. We also define and characterize the concept of neutrosophic $\mu$-baire space. Moreover, we investigate neutrosophic $(\mu, \eta)$-continuity and neutrosophic $(\mu, \eta)$-open functions and establish some results on the preservation of neutrosophic $\mu$-baire space under such functions.
Research Paper
Fuzzy sets and their variants
Kamala Rafig Aliyeva
Abstract
Group decision making in capital investment involves a collaborative process where multiple stakeholders contribute their perspectives, insights, and expertise to evaluate investment opportunities and make informed decisions. The practical and methodological aims of this process can vary depending on ...
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Group decision making in capital investment involves a collaborative process where multiple stakeholders contribute their perspectives, insights, and expertise to evaluate investment opportunities and make informed decisions. The practical and methodological aims of this process can vary depending on the organization's goals, industry, and market conditions. Conducting research on capital investment group decision making is motivated by several factors such as optimizing investment decisions, enhancing performance, managing risk, adapting to changing conditions, building knowledge and expertise. The investment decision relates to the distribution of financial resources. Investors select the most appropriate investment opportunities based on risk profiles, investment aims and expected returns. Fuzzy multicriteria group decision making in capital investment extends the traditional decision-making process to accommodate multiple criteria that are often uncertain, vague, or subjective in nature. The goal of this paper is to suggest a technique known as the Fuzzy Technique for Order Preference by Similarity to Ideal Solution (fuzzy TOPSIS) for group decision making about investment in the respective vehicle. Fuzzy TOPSIS technique represents a decision for experts, which is multi-criteria and includes an aggregated decision-making process. This paper shows the application of this method when choosing the best alternative, considering the choice of vehicle.
Research Paper
Fuzzy multisets and their variants
Vakkas Ulucay; Nuh OKUMUŞ
Abstract
Sustainable tourism is one of today's rapidly growing economic areas. Promotional activities should be carried out to increase the income from sustainable tourism. In order to carry out these studies effectively, it is necessary to choose the best center. Multi-criteria decision-making approaches ...
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Sustainable tourism is one of today's rapidly growing economic areas. Promotional activities should be carried out to increase the income from sustainable tourism. In order to carry out these studies effectively, it is necessary to choose the best center. Multi-criteria decision-making approaches can be used in choosing the best tourism center. In this paper, a new generalized similarity measure on intuitionistic trapezoidal fuzzy multi-numbers is developed for decision information. The desirable properties of this proposed measure are presented in detail. Further, we develop an approach to multi-citeria decision-making (MCDM) problem on the basis of the proposed developed proposed measure. Finally, the effectiveness and applicability of our proposed MCDM model, as well as comparison analysis with other approaches are illustrated with a practical example.