scholarly journals Multipolar Intuitionistic Fuzzy Hyper BCK-Ideals in Hyper BCK-Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1373
Author(s):  
Young Joo Seo ◽  
Hee Sik Kim ◽  
Young Bae Jun ◽  
Sun Shin Ahn
Keyword(s):  
Level Set ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Finite Degree ◽  
Intuitionistic Fuzzy ◽  
Upper Level

In 2020, Kang et al. introduced the concept of a multipolar intuitionistic fuzzy set of finite degree, which is a generalization of a k-polar fuzzy set, and applied it to a BCK/BCI-algebra. The specific purpose of this study was to apply the concept of a multipolar intuitionistic fuzzy set of finite degree to a hyper BCK-algebra. The notions of the k-polar intuitionistic fuzzy hyper BCK-ideal, the k-polar intuitionistic fuzzy weak hyper BCK-ideal, the k-polar intuitionistic fuzzy s-weak hyper BCK-ideal, the k-polar intuitionistic fuzzy strong hyper BCK-ideal and the k-polar intuitionistic fuzzy reflexive hyper BCK-ideal are introduced herein, and their relations and properties are investigated. These concepts are discussed in connection with the k-polar lower level set and the k-polar upper level set.

scholarly journals A p-Ideal in BCI-Algebras Based on Multipolar Intuitionistic Fuzzy Sets

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 993
Author(s):  
Jeong-Gon Lee ◽  
Mohammad Fozouni ◽  
Kul Hur ◽  
Young Bae Jun
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Finite Degree ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Ideal ◽  
The Relationship

In 2020, Kang, Song and Jun introduced the notion of multipolar intuitionistic fuzzy set with finite degree, which is a generalization of intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. In this paper, we used this notion to study p-ideals of BCI-algebras. The notion of k-polar intuitionistic fuzzy p-ideals in BCI-algebras is introduced, and several properties were investigated. An example to illustrate the k-polar intuitionistic fuzzy p-ideal is given. The relationship between k-polar intuitionistic fuzzy ideal and k-polar intuitionistic fuzzy p-ideal is displayed. A k-polar intuitionistic fuzzy p-ideal is found to be k-polar intuitionistic fuzzy ideal, and an example to show that the converse is not true is provided. The notions of p-ideals and k-polar ( ∈ , ∈ ) -fuzzy p-ideal in BCI-algebras are used to study the characterization of k-polar intuitionistic p-ideal. The concept of normal k-polar intuitionistic fuzzy p-ideal is introduced, and its characterization is discussed. The process of eliciting normal k-polar intuitionistic fuzzy p-ideal using k-polar intuitionistic fuzzy p-ideal is provided.

Interval-Valued Intuitionistic Fuzzy Subnear Rings

2020 ◽  
pp. 213-224
Author(s):  
Amal Kumar Adak
Keyword(s):  
Fuzzy Sets ◽  
Level Set ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
The Family ◽  
Interval Valued

The theory of interval-valued intuitionistic fuzzy sets is a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this chapter, the notion of interval-valued intuitionistic fuzzy subnear-ring is introduced, and some interesting properties are discussed. Some relations on the family of all interval-valued intuitionistic fuzzy subnear-ring are presented, and some related properties are investigated. Also, the authors represent upper and lower level set of interval-valued intuitionistic fuzzy set.

scholarly journals Multipolar Intuitionistic Fuzzy Set with Finite Degree and Its Application in BCK/BCI-Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 177 ◽  
Author(s):  
Kyung Tae Kang ◽  
Seok-Zun Song ◽  
Young Bae Jun
Keyword(s):  
Fuzzy Set ◽  
Coding Theory ◽  
Intuitionistic Fuzzy Set ◽  
Point Of View ◽  
Mathematical Tool ◽  
Finite Degree ◽  
Close Point ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Ideal

When events occur in everyday life, it is sometimes advantageous to approach them in two directions to find a solution for them. As a mathematical tool to handle these things, we can consider the intuitionistic fuzzy set. However, when events are complex and the key to a solution cannot be easily found, we feel the need to approach them for hours and from various directions. As mathematicians, we wish we had the mathematical tools that apply to these processes. If these mathematical tools were developed, we would be able to apply them to algebra, topology, graph theory, etc., from a close point of view, and we would be able to apply these research results to decision-making and/or coding theory, etc., from a distant point of view. In light of this view, the purpose of this study is to introduce the notion of a multipolar intuitionistic fuzzy set with finite degree (briefly, k-polar intuitionistic fuzzy set), and to apply it to algebraic structure, in particular, a BCK/BCI-algebra. The notions of a k-polar intuitionistic fuzzy subalgebra and a (closed) k-polar intuitionistic fuzzy ideal in a BCK/BCI-algebra are introduced, and related properties are investigated. Relations between a k-polar intuitionistic fuzzy subalgebra and a k-polar intuitionistic fuzzy ideal are discussed. Characterizations of a k-polar intuitionistic fuzzy subalgebra/ideal are provided, and conditions for a k-polar intuitionistic fuzzy subalgebra to be a k-polar intuitionistic fuzzy ideal are provided. In a BCI-algebra, relations between a k-polar intuitionistic fuzzy ideal and a closed k-polar intuitionistic fuzzy ideal are discussed. A characterization of a closed k-polar intuitionistic fuzzy ideal is considered, and conditions for a k-polar intuitionistic fuzzy ideal to be closed are provided.

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.

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.

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