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.

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.

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.

ERP software selection using intuitionistic fuzzy and interval grey number-based MACBETH method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mustafa Said Yurtyapan ◽  
Erdal Aydemir
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Selection Process ◽  
Intuitionistic Fuzzy Set ◽  
Decision Makers ◽  
Software Selection ◽  
Content Type ◽  
Intuitionistic Fuzzy ◽  
Expert Opinions ◽  
Erp Software

PurposeEnterprise Resource Planning (ERP) software which is a knowledge-based design on the interconnective communication of business units and information share, ensures that business processes such as finance, production, purchasing, sales, logistics and human resources, are integrated and gathered under one roof. This integrated system allows the company to make fast and accurate decisions and increases its competitiveness. Therefore, for an enterprise, choosing the suitable ERP software is extremely important. The aim of this study is to present new research on the ERP software selection process by clarifying the uncertainties and find suitable software in a computational way.Design/methodology/approachERP selection problem design includes uncertainties on the expert opinions and the criteria values using intuitionistic fuzzy set theory and interval grey-numbers to MACBETH multi criteria decision making method. In this paper, a new interval grey MACBETH method approach is proposed, and the degree of greyness approach is used for clarifying the uncertainties. Using this new approach in which grey numbers are used, it is aimed to observe the changes in the importance of the alternatives. Moreover, the intuitionistic fuzzy set method is applied by considering the importance of expert opinions separately.FindingsThe proposed method is based on quantitative decision making derived from qualitative judgments. The results given under uncertain conditions are compared with the results obtained under crisp conditions of the same methods. With the qualitative levels of experts reflected in the decision process, it is clearly seen that ERP software selection problem area has more effective alternative decision solutions to the uncertain environment, and decision makers should not undervalue the unsteadiness of criteria during ERP software selection process.Originality/valueThis study contributes to the relevant literature by (1) utilizing the MACBETH method in the selection of the ERP software by optimization, and (2) validating the importance of expert opinions with uncertainties on a proper ERP software selection procedure. So, the findings of this study can help the decision-makers to evaluate the ERP selection in uncertain conditions.

A Hesitant Intuitionistic Fuzzy Set Approach to Study Ideals of Semirings

2021 ◽  
Vol 10 (3) ◽  
pp. 1-17
Author(s):  
Debabrata Mandal
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Set ◽  
Ideal Theory ◽  
Hesitant Fuzzy Set ◽  
Neutrosophic Set ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
The Ideal

The classical set theory was extended by the theory of fuzzy set and its several generalizations, for example, intuitionistic fuzzy set, interval valued fuzzy set, cubic set, hesitant fuzzy set, soft set, neutrosophic set, etc. In this paper, the author has combined the concepts of intuitionistic fuzzy set and hesitant fuzzy set to study the ideal theory of semirings. After the introduction and the priliminary of the paper, in Section 3, the author has defined hesitant intuitionistic fuzzy ideals and studied several properities of it using the basic operations intersection, homomorphism and cartesian product. In Section 4, the author has also defined hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals of a semiring and used these to find some characterizations of regular semiring. In that section, the author also has discussed some inter-relations between hesitant intuitionistic fuzzy ideals, hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals, and obtained some of their related properties.

scholarly journals A Tychonoff theorem in intuitionistic fuzzy topological spaces

2004 ◽  
Vol 2004 (70) ◽  
pp. 3829-3837
Author(s):  
Doğan Çoker ◽  
A. Haydar Eş ◽  
Necla Turanli
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Tychonoff Theorem

The purpose of this paper is to prove a Tychonoff theorem in the so-called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some characterizations concerning fuzzy compactness. Lastly we give a Tychonoff-like theorem.

scholarly journals Some results on χ-single valued neutrosophic subgroups

2021 ◽  
Vol 23 (3) ◽  
pp. 1583
Author(s):  
M. Shazib Hameed ◽  
Zaheer Ahmad ◽  
Salman Mukhtar ◽  
Asad Ullah
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Vital Role ◽  
Neutrosophic Set ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Novel Structure ◽  
Fuzzy Subgroups

<p>In this study, we develop a novel structure χ-single valued neutrosophic set, which is a generalization of the intuitionistic set, inconsistent intuitionistic fuzzy set, Pythagorean fuzzy set, spherical fuzzy set, paraconsistent set, etc. Fuzzy subgroups play a vital role in vagueness structure, it differ from regular subgroups in that it is impossible to determine which group elements belong and which do not. In this paper, we investigate the concept of a χ-single valued neutrosophic set and χ-single valued neutrosophic subgroups. We explore the idea of χ-single valued neutrosophic set on fuzzy subgroups and several characterizations related to χ-single valued neutrosophic subgroups are suggested.</p>

Sign in / Sign up

Export Citation Format

Share Document