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.

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.

scholarly journals Intuitionistic Fuzzy Planar Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Noura Alshehri ◽  
Muhammad Akram
Keyword(s):  
Graph Theory ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Planar Graphs ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Dual Graphs ◽  
Intuitionistic Fuzzy

Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. We introduce the notions of intuitionistic fuzzy multigraphs, intuitionistic fuzzy planar graphs, and intuitionistic fuzzy dual graphs and investigate some of their interesting properties. We also study isomorphism between intuitionistic fuzzy planar graphs.

scholarly journals A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yafei Song ◽  
Xiaodan Wang ◽  
Lei Lei ◽  
Aijun Xue
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Axiomatic Definition

As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns.

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.

scholarly journals New Distance Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application in Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 429 ◽  
Author(s):  
Di Ke ◽  
Yafei Song ◽  
Wen Quan
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Research Area ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
The Difference ◽  
Atanassov’S Intuitionistic Fuzzy Sets

The intuitionistic fuzzy set introduced by Atanassov has greater ability in depicting and handling uncertainty. Intuitionistic fuzzy measure is an important research area of intuitionistic fuzzy set theory. Distance measure and similarity measure are two complementary concepts quantifying the difference and closeness of intuitionistic fuzzy sets. This paper addresses the definition of an effective distance measure with concise form and specific meaning for Atanassov’s intuitionistic fuzzy sets (AIFSs). A new distance measure for AIFSs is defined based on a distance measure of interval values and the transformation from AIFSs to interval valued fuzzy sets. The axiomatic properties of the new distance measure are mathematically investigated. Comparative analysis based in numerical examples indicates that the new distance measure is competent to quantify the difference between AIFSs. The application of the new distance measure is also discussed. A new method for multi-attribute decision making (MADM) is developed based on the technique for order preference by similarity to an ideal solution method and the new distance measure. Numerical applications indicate that the developed MADM method can obtain reasonable preference orders. This shows that the new distance measure is effective and rational from both mathematical and practical points of view.

scholarly journals A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2115
Author(s):  
Pavle Milošević ◽  
Bratislav Petrović ◽  
Ivana Dragović
Keyword(s):  
Boolean Algebra ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Novel Approach ◽  
Problematic Situations ◽  
Special Case

One of the main issues in IFS theory are generalizations of intuitionistic fuzzy set (IFS) definition as well as IFS operations. In this paper, we present the LBIFS-IBA approach by applying operations based on interpolative Boolean algebra (IBA) on generalized IFS. Namely, LBIFS are defined as a special case of Liu’s generalized IFS with the maximal interpretational surface. By extending the interpretational surface, the descriptive power of the approach is enhanced, and therefore the problematic situations when μA+νA>1 can be modeled. In addition, IBA-based algebra secures Boolean properties of the proposed approach. Considerable attention is given to comprehension of uncertainty within LBIFS-IBA, i.e., we propose a novel manner of uncertainty interpretation by treating values from [−1,1] interval. In order to prove its importance, we compare LBIFS-IBA with several well-known IFS generalizations, showing that only our approach offers meaningful uncertainty interpretation is all selected cases. Additionally, we illustrate the practical benefits of LBIFS-IBA by applying it to an example of modeling Japanese candlesticks for price charting and paying special attention to uncertainty interpretation.

scholarly journals Intuitionistic Fuzzy Sets Based Inpainting for Reconstruction of Heritage Images

2021 ◽  
Vol 12 (3) ◽  
pp. 5556-5565
Author(s):  
Shweta Dhondse Et. al.
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Image Inpainting ◽  
Assessment Method ◽  
Intuitionistic Fuzzy Sets ◽  
Characteristic Functions ◽  
Intuitionistic Fuzzy ◽  
Full Structure ◽  
Quality Assessment Method

Image inpainting is a process of reconstructing damaged or missing part of an image. Initially the work of restoration was performed by skilled artists and was limited to paintings and other artwork of eminence but this process was very tedious and strenuous and therefore digital image inpainting was introduced. The application of inpainting in reconstruction of heritage images is garnering a lot of attention from researchers. The reconstruction of heritage images using inpainting poses a challenging task because of its very high resolution and high meaning full structure content. In traditional exemplar based algorithms the patch with the minimum distance or high similarity may not always be the best match patch.   One of the characteristic functions of the Intuitionistic fuzzy set is its definition of degree of hesitancy. In the proposed paper this concept is used to find best exemplars. The mathematical model of intuitionistic fuzzy set is studied and a modified exemplar algorithm based on Intuitionistic fuzzy sets is proposed to solve image inpainting problem. The proposed intuitionistic based inpainting algorithm is applied to heritage images. The results are compared with existing and earlier proposed algorithms on the basis of subjective inpainting quality assessment method

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.

Circular intuitionistic fuzzy sets

2020 ◽  
Vol 39 (5) ◽  
pp. 5981-5986
Author(s):  
Krassimir T. Atanassov
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy

In this paper an extension of the Intuitionistic Fuzzy Set called Circular Intuitionistic Fuzzy Set is introduced and studied. Some of the relations and operations over C-IFS are established.

PARTIAL CORRELATION COEFFICIENTS OF INTUITIONISTIC FUZZY SETS

2002 ◽  
Vol 10 (01) ◽  
pp. 105-112 ◽  
Author(s):  
WEN-LIANG HUNG
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Partial Correlation ◽  
Intuitionistic Fuzzy Set ◽  
Correlation Coefficients ◽  
Intuitionistic Fuzzy Sets ◽  
Correlation Model ◽  
Intuitionistic Fuzzy ◽  
Multivariate Correlation ◽  
Degree Of Membership

In many applications, partial correlation for three or more intuitionistic fuzzy sets are very important, but Hung [12] do not discuss this problem. In this paper, we propose a method to calculate the partial correlation of intuitionistic fuzzy sets by means of multivariate correlation model. In order to fit into normal framework, we use empirical logit transform (see Agresti [1] and Johnson and Wichern [13]) for the degree of membership of intuitionistic fuzzy set to achive this.

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