fuzzy matrix
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Author(s):  
Fatemeh Babakordi ◽  
Nemat Allah Taghi-Nezhad

Calculating the matrix inverse is a key point in solving linear equation system, which involves complex calculations, particularly  when the matrix elements are  (Left and Right) fuzzy numbers. In this paper, first, the method of Kaur and Kumar for calculating the matrix inverse is reviewed, and its disadvantages are discussed. Then, a new method is proposed to determine the inverse of  fuzzy matrix based on linear programming problem. It is demonstrated that the proposed method is capable of overcoming the shortcomings of the previous matrix inverse. Numerical examples are utilized to verify the performance and applicability of the proposed method.


2021 ◽  
Author(s):  
Soumen Ghosh ◽  
Jayanta Pal ◽  
Bansibadan Maji ◽  
Dilip Kumar Bhattacharya

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yirong Sun ◽  
Junyang An ◽  
Xiaobin Guo

In this paper, a kind of complex fuzzy linear matrix equation A X ˜ B = C ˜ , in which C ˜ is a complex fuzzy matrix and A and B are crisp matrices, is investigated by using a matrix method. The complex fuzzy matrix equation is extended into a crisp system of matrix equations by means of arithmetic operations of fuzzy numbers. Two brand new and simplified procedures for solving the original fuzzy equation are proposed and the correspondingly sufficient condition for strong fuzzy solution are analysed. Some examples are calculated in detail to illustrate our proposed method.


Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 254
Author(s):  
Jun-Lin Lin ◽  
Laksamee Khomnotai ◽  
Hsin-Chieh Liu
Keyword(s):  

In the literature, the powers of a square fuzzy matrix with respect to the max-weighted power mean composition have been shown to always converge. This study considers the max-weighted power mean composition for a sequence of fuzzy matrices. It reveals that the repeated compositions of a sequence of n fuzzy matrices oscillate among n fuzzy matrices once the number of compositions exceeds a certain threshold. The previous finding can be considered as a special case of this study with n = 1.


2021 ◽  
Vol 5 (1) ◽  
pp. 288-299
Author(s):  
I. Silambarasan ◽  

A q-rung orthopair fuzzy matrix (q-ROFM), an extension of the Pythagorean fuzzy matrix (PFM) and intuitionistic fuzzy matrix (IFM), is very helpful in representing vague information that occurs in real-world circumstances. In this paper we define some algebraic operations, such as max-min, min-max, complement, algebraic sum, algebraic product, scalar multiplication \((nA)\), and exponentiation \((A^n)\). We also investigate the algebraic properties of these operations. Furthermore, we define two operators, namely the necessity and possibility to convert q-ROFMs into an ordinary fuzzy matrix, and discuss some of their basic algebraic properties. Finally, we define a new operation(@) on q-ROFMs and discuss distributive laws in the case where the operations of \(\oplus_{q}, \otimes_{q}, \wedge_{q}\) and \(\vee_{q}\) are combined each other.


2021 ◽  
Vol 1979 (1) ◽  
pp. 012022
Author(s):  
T. Subhramaniyan ◽  
S. Suruthi ◽  
M.S. Paulraj ◽  
M. G. Ragunathan ◽  
J. Jayanthi

2021 ◽  
pp. 1-10
Author(s):  
Namarta Singla ◽  
Parmpreet Kaur ◽  
Umesh Chandra Gupta

In the word of uncertain competitive situations everything is in the state of flux. Under such situations knowing the exact outcomes of mixed strategies adopted by a player is nearly impossible. It is highly rational to assume that no two experts will project the similar fuzzy payoffs for mix of strategies used. Aggregation of expert’s judgement becomes utmost important before solving such competitive situations. Considering this the present paper proposes a method to solve intuitionistic fuzzy game problems by using aggregation operators on payoff judgments of more than one expert. The proposed method significantly adds to the existing literature by overcoming the limitation of Li’s existing method that considers only one expert’s opinion for solving intuitionistic fuzzy game problems. Illustrative example has been given for showing the superiority of the proposed method.


2021 ◽  
Author(s):  
Ahmed Elsayed ◽  
Nazihah Ahmad ◽  
Ghassan Malkawi

Abstract There are many applications where couple of Sylvester matrix equations (CSME) are required to be solved simultaneously, especially in analyzing the stability of control systems. However, there are some situations in which the crisp CSME are not well equipped to deal with the uncertainty problem during the process of stability analysis in control system engineering. Thus, in this paper a new method for solving a coupled trapezoidal fully fuzzy Sylvester matrix equation (CTrFFSME) with arbitrary coefficients is proposed. The arithmetic fuzzy multiplication operation is applied to convert the CTrFFSME into a system of non-linear equations. Then the obtained non-linear system is reduced and converted to a system of absolute equations where the fuzzy solution is obtained by solving that system. The proposed method can solve many unrestricted fuzzy systems such as Sylvester and Lyapunov fully fuzzy matrix equations with triangular and trapezoidal fuzzy numbers. We illustrate the proposed methods by solving numerical example.


Author(s):  
Shishir Kumar ◽  
Chhaya Gangwal

Objective: Medical diagnosis process extends within the degree to which they plan to affect different complicating aspects of diagnosis. In this research work, the concept of fuzzy relation with medical diagnosis is studied and the application of fuzzy relations to such problems by extending the Sanchez’s approach is introduced. Method: An application of fuzzy relation with Sanchez's approach for medical diagnosis is presented. Based on the composition of the fuzzy relations, an algorithm for medical diagnosis as follows- first input the number of objects and attributes to obtain patient symptom matrix, symptom-disease matrix and the composition of fuzzy relations to get the patient-diagnosis matrix. Then find the maximum value to evaluate which patient is suffering from what disease. Result: Using the algorithm for medical diagnosis, the disease for which the membership value is maximum gives the final decision. If almost equal values for different diagnosis in composition are obtained, the case for which non-membership is minimum and hesitation is least is considered. The output matched well with the doctor’s diagnosis. Conclusion: In the process of medical diagnosis, state of patient are given by the patient through linguistic terminology like as temperature, cough, stomach pain etc., consideration of fuzzy sets as grades for association instead of membership grades in [0,1] is more advantageous to model the state of the patient. Similarly fuzzy relation has been introduced representing the association between symptoms and diseases. Sanchez’s approach has been extended for medical diagnosis in this reference. The approach used to form fuzzy matrix showing the association of symptoms and diseases is based on the sanchez’s approach.


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