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
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.
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
Complex 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
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.
