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 ...
Read More
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.
Intuitionistic fuzzy sets and their variants
Nour Abed Alhaleem; Abd Ghafur Ahmad
Abstract
In this paper, the (α,β)-level sets where α and β are elements in the interval [0,1] is introduced. Several related properties for (α,β)-cut of intuitionistic fuzzy normed ideals in a normed ring (NR) will be studied and proven. Further, for any two normed rings NR,NR^' ...
Read More
In this paper, the (α,β)-level sets where α and β are elements in the interval [0,1] is introduced. Several related properties for (α,β)-cut of intuitionistic fuzzy normed ideals in a normed ring (NR) will be studied and proven. Further, for any two normed rings NR,NR^' with a mapping f:NR → NR^', a relation between the intuitionistic fuzzy normed ideal I of NR and the intuitionistic fuzzy normed ideal f(I) (the image of I) of NR^' will been obtained with the support of their (α,β)-level subsets.
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 ...
Read More
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.
Intuitionistic fuzzy sets and their variants
Rasul Rasuli
Abstract
In our work in this paper, we define intuitionistic fuzzy complex subgroups with respect to t-norm T and s-norm S and investigate some properties of them in detail. Next, we obtain some results about them and give some relationships between them. Later, we introduce the inverse, composition, intersection ...
Read More
In our work in this paper, we define intuitionistic fuzzy complex subgroups with respect to t-norm T and s-norm S and investigate some properties of them in detail. Next, we obtain some results about them and give some relationships between them. Later, we introduce the inverse, composition, intersection and normality of them and we prove some basic new results and present some properties of them such that the inverse and composition of two intuitionistic fuzzy complex subgroups with respect to t-norm T and s-norm S will be intuitionistic complex fuzzy subgroups with respect to t-norm T and s-norm S. Also we consider and give some characterizations of them. Finally, we discuss them under group homomorphisms and investigate some related properties such that the image and preimage of two intuitionistic fuzzy complex subgroups with respect to t-norm T and s-norm S will be intuitionistic complex fuzzy subgroups with respect to t-norm T and s-norm S.
Intuitionistic fuzzy sets and their variants
Imo Jeremiah Eyo; Olufemi Sunday Adeoye; Udoinyang Godwin Inyang; Ini John Umoeka
Abstract
A novel hybrid intelligent approach for tuning the parameters of Interval Type-2 Intuitionistic Fuzzy Logic System (IT2IFLS) is introduced for the modeling and prediction of coronavirus disease 2019 (COVID-19) time series. COVID-19 is known to be a virus caused by Severe Acute Respiratory Syndrome Coronavirus ...
Read More
A novel hybrid intelligent approach for tuning the parameters of Interval Type-2 Intuitionistic Fuzzy Logic System (IT2IFLS) is introduced for the modeling and prediction of coronavirus disease 2019 (COVID-19) time series. COVID-19 is known to be a virus caused by Severe Acute Respiratory Syndrome Coronavirus 2 (SARSCoV-2) with a huge negative impact on human, work and world economy. Globally, more than 100 million people have been infected with over two million deaths and it is not certain when the pandemic will end. Predicting the trend of the COVID-19 therefore becomes an important and challenging task. Many approaches ranging from statistical approaches to machine learning methods have been formulated and applied for the prediction of the disease. In this work, the sliding mode control learning algorithm is used to adjust the parameters of the antecedent parts of IT2IFLS system while the gradient descent backpropagation is adopted to tune the consequent parameters in a hybrid manner. The results of the hybrid intelligent learning model are compared with results of single learning models using sliding mode control and gradient descent algorithms and found to provide good performance in terms of Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) especially in noisy environments. The type-2 hybrid model also outperforms its type-1 counterparts in the different problem instances.
Intuitionistic fuzzy sets and their variants
Jaydip Bhattacharya
Abstract
An operator is a special symbol for performing a specific function. Several operators like modal operators, topological operators, level operators, etc. have been defined over intuitionistic fuzzy sets. At the same time, so many operations were introduced and studied. The key objective of this paper ...
Read More
An operator is a special symbol for performing a specific function. Several operators like modal operators, topological operators, level operators, etc. have been defined over intuitionistic fuzzy sets. At the same time, so many operations were introduced and studied. The key objective of this paper is to study those operations over intuitionistic fuzzy sets and to investigate their properties. Some new results are obtained and proved.
Intuitionistic fuzzy sets and their variants
Ivanosca Andrade Da Silva; Berta Bedregal; Benjamin Bedregal; Regivan Hugo Nunes Santiago
Abstract
In this paper we extend the notion of interval representation for interval-valued Atanassov’s intuitionistic representations, in short Lx-representations, and use this notion to obtain the best possible one, of the Weighted Average (WA) and Ordered Weighted Average (OWA) operators. A main characteristic ...
Read More
In this paper we extend the notion of interval representation for interval-valued Atanassov’s intuitionistic representations, in short Lx-representations, and use this notion to obtain the best possible one, of the Weighted Average (WA) and Ordered Weighted Average (OWA) operators. A main characteristic of this extension is that when applied to diagonal elements, i.e. fuzzy degrees, they provide the same results as the WA and OWA operators, respectively. Moreover, they preserve the main algebraic properties of the WA and OWA operators. A new total order for interval-valued Atanassov’s intuitionistic fuzzy degrees is also introduced in this paper which is used jointly with the best Lx-representation of the WA and OWA, in a method for multi-attribute group decision making where the assesses of the experts, in order to take in consideration uncertainty and hesitation, are interval-valued Atanassov’s intuitionistic fuzzy degrees. A characteristic of this method is that it works with interval-valued Atanassov’s intuitionistic fuzzy values in every moments, and therefore considers the uncertainty on the membership and non-membership in all steps of the decision making. We apply this method in two illustrative examples and compare our result with other methods.
Intuitionistic fuzzy sets and their variants
Imo Eyo; Jeremiah Eyoh; Uduak Umoh
Abstract
This paper presents a time series analysis of a novel coronavirus, COVID-19, discovered in China in December 2019 using intuitionistic fuzzy logic system with neural network learning capability. Fuzzy logic systems are known to be universal approximation tools that can estimate a nonlinear function as ...
Read More
This paper presents a time series analysis of a novel coronavirus, COVID-19, discovered in China in December 2019 using intuitionistic fuzzy logic system with neural network learning capability. Fuzzy logic systems are known to be universal approximation tools that can estimate a nonlinear function as closely as possible to the actual values. The main idea in this study is to use intuitionistic fuzzy logic system that enables hesitation and has membership and non-membership functions that are optimized to predict COVID-19 outbreak cases. Intuitionistic fuzzy logic systems are known to provide good results with improved prediction accuracy and are excellent tools for uncertainty modelling. The hesitation-enabled fuzzy logic system is evaluated using COVID-19 pandemic cases for Nigeria, being part of the COVID-19 data for African countries obtained from Kaggle data repository. The hesitation-enabled fuzzy logic model is compared with the classical fuzzy logic system and artificial neural network and shown to offer improved performance in terms of root mean squared error, mean absolute error and mean absolute percentage error. Intuitionistic fuzzy logic system however incurs a setback in terms of the high computing time compared to the classical fuzzy logic system.
Intuitionistic fuzzy sets and their variants
Atiqe Ur Rahman; Muhammad Rayees Ahmad; Muhammad Saeed; Muhammad Ahsan; Muhammad Arshad; Muhammad Ihsan
Abstract
Zadeh conceptualized the theory of fuzzy set to provide a tool for the basis of the theory of possibility. Atanassov extended this theory with the introduction of intuitionistic fuzzy set. Smarandache introduced the concept of refined intuitionistic fuzzy set by further subdivision of membership and ...
Read More
Zadeh conceptualized the theory of fuzzy set to provide a tool for the basis of the theory of possibility. Atanassov extended this theory with the introduction of intuitionistic fuzzy set. Smarandache introduced the concept of refined intuitionistic fuzzy set by further subdivision of membership and non-membership value. The meagerness regarding the allocation of a single membership and non-membership value to any object under consideration is addressed with this novel refinement. In this study, this novel idea is utilized to characterize the essential elements e.g. subset, equal set, null set, and complement set, for refined intuitionistic fuzzy set. Moreover, their basic set theoretic operations like union, intersection, extended intersection, restricted union, restricted intersection, and restricted difference, are conceptualized. Furthermore, some basic laws are also discussed with the help of an illustrative example in each case for vivid understanding.
Intuitionistic fuzzy sets and their variants
Paul Augustine Ejegwa; Idoko Charles Onyeke
Abstract
The concept of correlation coefficient of intuitionistic fuzzy sets is a reliable tool in information theory with numerous applications in diverse areas. Correlation coefficients of intuitionistic fuzzy sets have been studied through two-way approach by many researchers. This approach inappropriately ...
Read More
The concept of correlation coefficient of intuitionistic fuzzy sets is a reliable tool in information theory with numerous applications in diverse areas. Correlation coefficients of intuitionistic fuzzy sets have been studied through two-way approach by many researchers. This approach inappropriately discarded the hesitation margins of the concerned intuitionistic fuzzy sets, which makes the results of such experiments unreliable. In this paper, we modified the correlation coefficient of intuitionistic fuzzy sets of Thao et al. [36] in a three-way approach by including the hesitation margins in the computational process to enhance reliable output through an algorithmic method. We show that the modified correlation coefficient of intuitionistic fuzzy sets is more reasonable with precise outputs than correlation coefficient method. In terms of application, we demonstrate an analysis of medical diagnosis on some selected patients via an algorithm of the novel approach coded with JAVA programming language.
Intuitionistic fuzzy sets and their variants
Suresh Mohan; Arun Prakash Kannusamy; Vengataasalam Samiappan
Abstract
The concept of an intuitionistic fuzzy number (IFN) is of importance for representing an ill-known quantity. Ranking fuzzy numbers plays a very important role in the decision process, data analysis and applications. The concept of an IFN is of importance for quantifying an ill-known quantity. Ranking ...
Read More
The concept of an intuitionistic fuzzy number (IFN) is of importance for representing an ill-known quantity. Ranking fuzzy numbers plays a very important role in the decision process, data analysis and applications. The concept of an IFN is of importance for quantifying an ill-known quantity. Ranking of intuitionistic fuzzy numbers plays a vital role in decision making and linear programming problems. Also, ranking of intuitionistic fuzzy numbers is a very difficult problem. In this paper, a new method for ranking intuitionistic fuzzy number is developed by means of magnitude for different forms of intuitionistic fuzzy numbers. In Particular ranking is done for trapezoidal intuitionistic fuzzy numbers, triangular intuitionistic fuzzy numbers, symmetric trapezoidal intuitionistic fuzzy numbers, and symmetric triangular intuitionistic fuzzy numbers. Numerical examples are illustrated for all the defined different forms of intuitionistic fuzzy numbers. Finally some comparative numerical examples are illustrated to express the advantage of the proposed method.
