scholarly journals About the Images and Inverse Images of Intuitionistic or Vague Fuzzy Subsets

2012 ◽  
Vol 3 ◽  
pp. 1-4
Author(s):  
G. Vasanti
Keyword(s):  
Intuitionistic Fuzzy ◽  
Algebraic Properties ◽  
Standard Lattice ◽  
Fuzzy Subsets

In this paper an exclusive study of some standard (lattice) algebraic properties for Intuitionistic fuzzy (inverse) images of Intuitionistic fuzzy subsets is done. Further as in crisp setup, characterizations for injectivity and surjectivity of maps in terms of some (lattice) algebraic properties of Intuitionistic fuzzy images and Intuitionistic fuzzy inverse images are performed.

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.

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.

scholarly journals On the representation of L-M algebra by intuitionistic fuzzy subsets

2006 ◽  
Vol Volume 4, 2006 ◽  
Author(s):  
Zedam Lemnaouar ◽  
Amroune Abdelaziz
Keyword(s):  
Intuitionistic Fuzzy ◽  
Nous Montrons ◽  
International Audience ◽  
Fuzzy Subsets ◽  
Ensemble Flou

International audience In this paper we introduce the notions of intuitionistic weak alpha-cut and untuitionistic strong alpha-cut of intuitionistic fuzzy subsets of a universe X. These notions lead us to show that the set IF(X) of all intuitionistic fuzzy subsets on a universe X can be equipped with a structure of involutive theta-valued Lukasiewicz-Moisil algebra. Conversely, we show that every involutive theta-valued Lukasiewicz-Moisil algebra can be embedded into an algebra of intuitionistic fuzzy subsets. Dans ce travail nous introduisons les notions de alpha-coupes et de alpha-coupes strictes d'un ensemble flou intuitionsiste d'un référentiel X. A l'aide de ces notions, nous montrons que l'ensemble IF(X) des sous-ensembles flous intuitionistes d'un référentiel X admet une structure d'algèbre de Moisil-Lukasiewicz. theta-valente involutive. Réciproquement, nous montrons que toute algèbre de Moisil-Lukasiewicz theta-valente involutive se plonge dans une algèbre des sous-ensembles flous intuitionistes.

scholarly journals Intuitionistic fuzzy quasi-interior ideals of semigroups

2021 ◽  
Vol 27 (4) ◽  
pp. 36-43
Author(s):  
Sinem Tarsuslu (Yılmaz) ◽  
Keyword(s):  
Intuitionistic Fuzzy ◽  
Algebraic Properties ◽  
Quasi Interior

In this study, it is purposed to introduced the concept of quasi-interior ideal on intuitionistic fuzzy semigroups. The concept introduced is supported with examples and its basic algebraic properties are examined.

scholarly journals Multigranulation Roughness of Intuitionistic Fuzzy Sets by Soft Relations and Their Applications in Decision Making

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2587
Author(s):  
Muhammad Zishan Anwar ◽  
Shahida Bashir ◽  
Muhammad Shabir ◽  
Majed G. Alharbi
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Binary Relations ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Multigranulation Rough Set ◽  
Algebraic Properties ◽  
Two Universes

Multigranulation rough set (MGRS) based on soft relations is a very useful technique to describe the objectives of problem solving. This MGRS over two universes provides the combination of multiple granulation knowledge in a multigranulation space. This paper extends the concept of fuzzy set Shabir and Jamal in terms of an intuitionistic fuzzy set (IFS) based on multi-soft binary relations. This paper presents the multigranulation roughness of an IFS based on two soft relations over two universes with respect to the aftersets and foresets. As a result, two sets of IF soft sets with respect to the aftersets and foresets are obtained. These resulting sets are called lower approximations and upper approximations with respect to the aftersets and with respect to the foresets. Some properties of this model are studied. In a similar way, we approximate an IFS based on multi-soft relations and discuss their some algebraic properties. Finally, a decision-making algorithm has been presented with a suitable example.

scholarly journals Complex Intuitionistic Fuzzy Soft Lattice Ordered Group and Its Weighted Distance Measures

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 705 ◽  
Author(s):  
S. Rajareega ◽  
J. Vimala ◽  
D. Preethi
Keyword(s):  
Set Theory ◽  
Euclidean Distance ◽  
Distance Measures ◽  
Fuzzy Soft Set ◽  
Ordered Group ◽  
Weighted Distance ◽  
Intuitionistic Fuzzy ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Algebraic Properties

In recent years, the complex fuzzy set theory has intensified the attention of many researchers. This paper focuses on developing the algebraic structures pertaining to lattice ordered groups and lattice ordered subgroups for complex intuitionistic fuzzy soft set theory. Furthermore, some of their properties and operations are discussed. In addition, the weighted distance measures between two complex intuitionistic fuzzy soft lattice ordered groups such as weighted hamming, weighted normalized hamming, weighted euclidean and weighted normalized euclidean distance measures were introduced and also some of the algebraic properties of the weighted distance measures are verified. Moreover, the application of complex intuitionistic fuzzy soft lattice ordered groups by using the weighted distance measures is analysed.

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.

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