scholarly journals Reduction of an intuitionistic fuzzy matrix to fuzzy matrix with some algebraic properties

2017 ◽  
Vol 13 (4) ◽  
pp. 475-483 ◽  
Author(s):  
T. Muthuraji ◽  
S. Sriram
Keyword(s):  
Fuzzy Matrix ◽  
Intuitionistic Fuzzy ◽  
Algebraic Properties

scholarly journals Generalized orthopair fuzzy matrices

2021 ◽  
Vol 5 (1) ◽  
pp. 288-299
Author(s):  
I. Silambarasan ◽  
Keyword(s):  
Real World ◽  
Scalar Multiplication ◽  
Fuzzy Matrix ◽  
Intuitionistic Fuzzy ◽  
Algebraic Properties ◽  
Algebraic Operations

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.

Intuitionistic Fuzzy X-Subalgebra of Near-Subtraction Semigroups

2021 ◽  
Vol 7 (3) ◽  
Author(s):  
J. Siva Ranjini ◽  
V. Mahalakshmi
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Algebraic Properties

The theory of Intuitionistic fuzzy set is the extension of the fuzzy set that deals with truth and false membership data. We will discuss along with some fundamentals and their algebraic Properties. The results obtained are entirely more beneficial to the researchers. We also expand the Complement of the Set and Homomorphism. The motivation of the present manuscript is to extend the concept of Intuitionistic fuzzy X-subalgebra in near-subtraction semigroups.

Interval-Valued Intuitionistic Fuzzy Partition Matrices

2017 ◽  
pp. 64-81
Author(s):  
Amal Kumar Adak
Keyword(s):  
Kronecker Product ◽  
Kronecker Sum ◽  
Fuzzy Partition ◽  
Fuzzy Matrix ◽  
Direct Sum ◽  
Intuitionistic Fuzzy ◽  
Different Types ◽  
Interval Valued

If in an interval-valued intuitionistic fuzzy matrix each element is again a smaller interval-valued intuitionistic fuzzy matrix then the interval-valued intuitionistic fuzzy matrix is called interval-valued intuitionistic fuzzy partion matrix (IVIFPMs). In this paper, the concept of interval-valued intuitionistic fuzzy partion matrices (IVIFPMs) are introduced and defined different types of interval-valued intuitionistic fuzzy partion matrices (IVIFPMs). The operations like direct sum, Kronecker sum, Kronecker product of interval-valued intuitionistic fuzzy matrices are presented and shown that their resultant matrices are also interval-valued intuitionistic fuzzy partion matrices (IVIFPMs).

Ordered Intuitionistic Fuzzy Soft Sets and Its Application in Decision Making Problem

2018 ◽  
Vol 7 (3) ◽  
pp. 76-98
Author(s):  
Pachaiyappan Muthukumar ◽  
Sai Sundara Krishnan Gangadharan
Keyword(s):  
Decision Making ◽  
Soft Sets ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Algebraic Properties ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

In this article, some new basic operations and results of Ordered Intuitionistic Fuzzy Soft (OIFS) sets, such as equality, complement, subset, union, intersection, OR, and AND operators along with several examples are investigated. Further, based on the analysis of several operations on OIFS sets, numerous algebraic properties and famous De Morgans inclusions and De Morgans laws are established. Finally, using the notions of OIFS sets, an algorithm is developed and implemented in a numerical example.

Eigenvalue of Intuitionistic Fuzzy Matrices Over Distributive Lattice

2019 ◽  
Vol 8 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Ali Ebrahimnejad ◽  
Amal Kumar Adak ◽  
Ezzatallah Baloui Jamkhaneh
Keyword(s):  
Distributive Lattice ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Matrix ◽  
Intuitionistic Fuzzy ◽  
Eigenvalue And Eigenvector

In this article, the concepts of intuitionistic fuzzy complete and complete distributive lattice are introduced and the relative pseudocomplement relation of intuitionistic fuzzy sets is defined. The concepts of intuitionistic fuzzy eigenvalue and eigenvector of an intuitionistic fuzzy matrixes are presented and proved that the set of intuitionistic fuzzy eigenvectors of a given intuitionistic fuzzy eigenvalue form an intuitionistic fuzzy subspace. Also, the authors obtain an intuitionistic fuzzy maximum matrix of a given intuitionistic fuzzy eigenvalue and eigenvector and give some properties of an intuitionistic fuzzy maximum matrix. Finally, the invariant of an intuitionistic fuzzy matrix over a distributive lattice is given with some properties.

Analysis of triangular intuitionistic fuzzy matrix games using robust ranking

2017 ◽  
Vol 33 (1) ◽  
pp. 327-336 ◽  
Author(s):  
Ankan Bhaumik ◽  
Sankar Kumar Roy ◽  
Deng-Feng Li
Keyword(s):  
Matrix Games ◽  
Fuzzy Matrix ◽  
Intuitionistic Fuzzy
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