scholarly journals IMAGE DAN PRE-IMAGE TRANSLASI PADA GRUP FUZZY INTUITIONISTIK

2016 ◽  
Vol 8 (2) ◽  
pp. 41
Author(s):  
Dian Pratama
Keyword(s):  
Membership Function ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Translation Operator ◽  
Membership Functions ◽  
Fuzzy Subset ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Group ◽  
Fuzzy Subgroup

A intuitionistic fuzzy set in is set gives a membership function and a non-membership function (the complement of membership function) for each with the sum worth one. When it’s applied in group’s theory, it will called intuitionistic fuzzy group with conditions membership function is fuzzy subgroup and non-membership function is anti-fuzzy subgroup. In this research, the operator will be given a fuzzy set is called fuzzy translation operator. This operator is a mapping imposed on membership functions (fuzzy subset) to interval [ 0,1]. This research will discuss the properties homomorphism of translation on intuitionistic fuzzy groups. These properties is the structure of the image and pre-image homomorphism of translation on intuitionistic fuzzy group. We obtain that image and pre-image of translation on intuitionistic fuzzy (normal) groups is also intuitionistic fuzzy (normal) groups.

scholarly journals MBJ-neutrosophic subalgebras and filters in $ BE $-algebras

2022 ◽  
Vol 7 (4) ◽  
pp. 6016-6033
Author(s):  
Rajab Ali Borzooei ◽  
◽  
Hee Sik Kim ◽  
Young Bae Jun ◽  
Sun Shin Ahn ◽  
...  
Keyword(s):  
Membership Function ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
The Relationship ◽  
Interval Valued

<abstract><p>The concept of a neutrosophic set, which is a generalization of an intuitionistic fuzzy set and a para consistent set etc., was introduced by F. Smarandache. Since then, it has been studied in various applications. In considering a generalization of the neutrosophic set, Mohseni Takallo et al. used the interval valued fuzzy set as the indeterminate membership function because interval valued fuzzy set is a generalization of a fuzzy set, and introduced the notion of MBJ-neutrosophic sets, and then they applied it to BCK/BCI-algebras. The aim of this paper is to apply the concept of MBJ-neutrosophic sets to a $ BE $-algebra, which is a generalization of a BCK-algebra. The notions of MBJ-neutrosophic subalgebras and MBJ-neutrosophic filters of $ BE $-algebras are introduced and related properties are investigated. The conditions under which the MBJ-neutrosophic set can be a MBJ-neutrosophic subalgebra/filter are searched. Characterizations of MBJ-neutrosophic subalgebras and MBJ-neutrosophic filters are considered. The relationship between an MBJ-neutrosophic subalgebra and an MBJ-neutrosophic filter is established.</p></abstract>

scholarly journals Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 1

2021 ◽  
Vol 27 (1) ◽  
pp. 53-59
Author(s):  
Mladen V. Vassilev-Missana
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Sets Theory ◽  
Membership Functions ◽  
Real Numbers ◽  
Intuitionistic Fuzzy ◽  
Sets Theory

The inequality \mu^{\frac{1}{\nu}} + \nu^{\frac{1}{\mu}} \leq 1 is introduced and proved, where \mu and \nu are real numbers, for which \mu, \nu \in [0, 1] and \mu + \nu \leq 1. The same inequality is valid for \mu = \mu_A(x), \nu = \nu_A(x), where \mu_A and \nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x \in E. Also, a generalization of the above inequality for arbitrary n \geq 2 is proposed and proved.

MODELS FOR MULTIPLE ATTRIBUTE DECISION MAKING WITH INTUITIONISTIC FUZZY INFORMATION

2007 ◽  
Vol 15 (03) ◽  
pp. 285-297 ◽  
Author(s):  
Z. S. XU
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Information ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by Atanassov [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems 20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy Sets", Information and Control 8 (1965) 338–353] to deal with fuzziness and uncertainty. In this paper, we investigate the multiple attribute decision making (MADM) problems, in which the information about attribute weights is incomplete, and the attribute values are expressed in intuitionistic fuzzy numbers (IFNs). We first define the concept of intuitionistic fuzzy ideal solution (IFIS), and then, based on the IFIS and the distance measure, we establish some optimization models to derive the attribute weights. Furthermore, based on the developed models, we develop some procedures for the rankings of alternatives under different situations, and extend the developed models and procedures to handle the MADM problems with interval-valued intuitionistic fuzzy information. Finally, we give some illustrative examples to verify the effectiveness and practicability of the developed models and procedures.

scholarly journals A New Multiple Criteria Decision Making Method and its Application in Cloud Computing for Education

2015 ◽  
Vol 10 (8) ◽  
pp. 21
Author(s):  
Heng Sun
Keyword(s):  
Decision Making ◽  
Cloud Computing ◽  
Membership Function ◽  
Fuzzy Set ◽  
Choquet Integral ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Score Function ◽  
Multiple Criteria ◽  
Intuitionistic Fuzzy

Cloud computing can extend the traditional education framework. In education, cloud can provide students and teachers with tools to deploy computing resources on-demand for lectures and labs according to their learning needs. But how to select a perfect cloud server is a key point, which is considered as a multiple criteria decision making problem. So, in this paper, intuitionistic fuzzy set is first introduced to express the decision maker’s views. Intuitionistic fuzzy set (IFS) includes a membership function and a non-membership function. More importantly, a new operator with choquet integral is developed to deal with assessment of education using cloud computing. Meanwhile, score function and accuracy function are demonstrated to obtain the final result. Finally, we develop this method to apply in a case study to show its applicability.

scholarly journals Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 2

2021 ◽  
Vol 27 (4) ◽  
pp. 78-81
Author(s):  
Mladen Vassilev-Missana
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Sets Theory ◽  
Membership Functions ◽  
Intuitionistic Fuzzy ◽  
Sets Theory

In the paper, the inequality \frac{\mu^{\frac{1}{\nu}}}{\nu} + \frac{\nu^{\frac{1}{\mu}}}{\mu} \leq \frac{1}{2\mu\nu} - 1 is introduced and proved. The same inequality is valid for \mu = \mu_A(x), \nu = \nu_A(x), where \mu_A and \nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x \in E.

scholarly journals Representation of flat EEG images via fuzzy limit

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
S. Zenian ◽  
Tahir Ahmad ◽  
A. Idris
Keyword(s):  
Membership Function ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Membership Value ◽  
Definition Of ◽  
The Relationship ◽  
The Way

Sugeno type intuitionistic fuzzy generator is one of the way to compute the non-membership value in the theory of intuitionistic fuzzy set (IFS).  It can be extended to the concept of fuzzy limit in order to determine the hesitation value.  The value of parameter, namely , in the non-membership function will influence the hesitation value and the results will be demonstrated in the form of images.  Hence, by implementing the definition of fuzzy limit, different value of  will be tested in obtaining the values of parameter  that will determine the value of .  Moreover, the relationship between hesitation and membership value will be demonstrated graphically.

The prediction of online time series with concept drift based on dynamic intuitionistic fuzzy cognitive map

2021 ◽  
Vol 25 (4) ◽  
pp. 949-972
Author(s):  
Nannan Zhang ◽  
Xixi Yao ◽  
Chao Luo
Keyword(s):  
Fuzzy Set ◽  
Sequence Data ◽  
Concept Drift ◽  
Intuitionistic Fuzzy Set ◽  
Cognitive Map ◽  
Fuzzy Cognitive Maps ◽  
Fuzzy Cognitive Map ◽  
Online Data ◽  
Intuitionistic Fuzzy ◽  
Public Data

Fuzzy cognitive maps (FCMs) have widely been applied for knowledge representation and reasoning. However, in real life, reasoning is always accompanied with hesitation, which is deriving from the uncertainty and fuzziness. Especially, when processing the online data, since the internal and external interference, the distribution and characteristics of sequence data would be considerably changed along with the passage of time, which further increase the difficulty of modeling. In this article, based on intuitionistic fuzzy set theory, a new dynamic intuitionistic fuzzy cognitive map (DIFCM) scheme is proposed for online data prediction. Combined with a novel detection algorithm of concept drift, the structure of DIFCM can be adaptively updated with the online learning scheme, which can effectively improve the representation of online information by capturing the real-time changes of sequence data. Moreover, in order to tackle with the possible hesitancy in the process of modeling, intuitionistic fuzzy set is applied in the construction of dynamic FCM, where hesitation degree as a quantitative index explicitly expresses the hesitancy. Finally, a series of experiments using public data sets verify the effectiveness of the proposed method.

Complex intuitionistic fuzzy Maclaurin symmetric mean operators and its application to emergency program selection

2021 ◽  
pp. 1-22
Author(s):  
Riaz Ali ◽  
Saleem Abdullah ◽  
Shakoor Muhammad ◽  
Muhammad Naeem ◽  
Ronnason Chinram
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Functions ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Program Selection ◽  
Maclaurin Symmetric Mean ◽  
Complex Intuitionistic Fuzzy Set

Due to the indeterminacy and uncertainty of the decision-makers (DM) in the complex decision making problems of daily life, evaluation and aggregation of the information usually becomes a complicated task. In literature many theories and fuzzy sets (FS) are presented for the evaluation of these decision tasks, but most of these theories and fuzzy sets have failed to explain the uncertainty and vagueness in the decision making issues. Therefore, we use complex intuitionistic fuzzy set (CIFS) instead of fuzzy set and intuitionistic fuzzy set (IFS). A new type of aggregation operation is also developed by the use of complex intuitionistic fuzzy numbers (CIFNs), their accuracy and the score functions are also discussed in detail. Moreover, we utilized the Maclaurin symmetric mean (MSM) operator, which have the ability to capture the relationship among multi-input arguments, as a result, CIF Maclarurin symmetric mean (CIFMSM) operator and CIF dual Maclaurin symmetric mean (CIFDMSM) operator are presented and their characteristics are discussed in detail. On the basis of these operators, a MAGDM method is presented for the solution of group decision making problems. Finally, the validation of the propounded approach is proved by evaluating a numerical example, and by the comparison with the previously researched results.

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