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.

scholarly journals Generalized orthopair fuzzy sets based on Hamacher T-norm and T-conorm

2021 ◽  
Vol 5 (1) ◽  
pp. 44-64
Author(s):  
I. Silambarasan ◽  
Keyword(s):  
Fuzzy Sets ◽  
Uncertain Data ◽  
Intuitionistic Fuzzy Sets ◽  
Scalar Multiplication ◽  
Uncertain Information ◽  
Pythagorean Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Algebraic Properties

The concept of q-rung orthopair fuzzy sets generalizes the notions of intuitionistic fuzzy sets and Pythagorean fuzzy sets to describe complicated uncertain information more effectively. Their most dominant attribute is that the sum of the \(q^{th}\) power of the truth-membership and the \(q^{th}\) power of the falsity-membership must be equal to or less than one, so they can broaden the space of uncertain data. This set can adjust the range of indication of decision data by changing the parameter \(q, ~q\geq 1\). In this paper, we define the Hamacher operations of q-rung orthopair fuzzy sets and proved some desirable properties of these operations, such as commutativity, idempotency, and monotonicity. Further, we proved De Morgan's laws for these operations over complement. Furthermore, we defined the Hamacher scalar multiplication \(({n._{h}}A)\) and Hamacher exponentiation \((A^{\wedge_{h}n})\) operations on q-rung orthopair fuzzy sets and investigated their algebraic properties. Finally, we defined the necessity and possibility operators based on q-rung orthopair fuzzy sets and some properties of Hamacher operations that are considered.

An algebraic approach to N-soft sets with application in decision-making using TOPSIS

2021 ◽  
pp. 1-21
Author(s):  
Muhammad Shabir ◽  
Rimsha Mushtaq ◽  
Munazza Naz
Keyword(s):  
Decision Making ◽  
Mathematical Models ◽  
Real World ◽  
Algebraic Approach ◽  
Multi Criteria Decision Making ◽  
Commutative Monoids ◽  
Soft Sets ◽  
Algebraic Properties ◽  
Different Types ◽  
Selection Of

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.

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.

A New Approach Towards Intuitionistic Fuzzy Multisets

2022 ◽  
Vol 11 (1) ◽  
pp. 1-10
Author(s):  
Pinaki Majumdar
Keyword(s):  
Medical Diagnosis ◽  
New Approach ◽  
Intuitionistic Fuzzy ◽  
Algebraic Operations ◽  
Definition Of

In this paper a new definition of Intuitionistic fuzzy multisets (IFMS) has been introduced. Algebraic operations on these intuitionistic fuzzy multisets are defined and their properties under these algebraic operations are studied. The author has also introduced a new notion of complement for an IFMS in which the complement of the original set is also an IFMS. The notion of distance and similarity between two IFMS’s has been defined and their properties have also been studied here. An application of IFMS in solving a medical diagnosis problem has been provided at the end.

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.

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