scholarly journals Selection of Vendor Based on Intuitionistic Fuzzy Analytical Hierarchy Process

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Prabjot Kaur
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Analytical Hierarchy Process ◽  
Intuitionistic Fuzzy Set ◽  
Pairwise Comparison ◽  
Business Environment ◽  
Global Market ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Hierarchy Process

Business environment is characterized by greater domestic and international competitive position in the global market. Vendors play a key role in achieving the so-called corporate competition. It is not easy however to identify good vendors because evaluation is based on multiple criteria. In practice, for VSP most of the input information about the criteria is not known precisely. Intuitionistic fuzzy set is an extension of the classical fuzzy set theory (FST), which is a suitable way to deal with impreciseness. In other words, the application of intuitionistic fuzzy sets instead of fuzzy sets means the introduction of another degree of freedom called nonmembership function into the set description. In this paper, we proposed a triangular intuitionistic fuzzy number based approach for the vendor selection problem using analytical hierarchy process. The crisp data of the vendors is represented in the form of triangular intuitionistic fuzzy numbers. By applying AHP which involves decomposition, pairwise comparison, and deriving priorities for the various levels of the hierarchy, an overall crisp priority is obtained for ranking the best vendor. A numerical example illustrates our method. Lastly a sensitivity analysis is performed to find the most critical criterion on the basis of which vendor is selected.

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.

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 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.

Some Measures of Picture Fuzzy Sets and Their Application

2017 ◽  
Vol 3 (2) ◽  
pp. 35
Author(s):  
Nguyen Van Dinh ◽  
Nguyen Xuan Thao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Dissimilarity Measure ◽  
Intuitionistic Fuzzy ◽  
Picture Fuzzy Set ◽  
The Difference ◽  
Picture Fuzzy Sets

To measure the difference of two fuzzy sets (FSs) / intuitionistic sets (IFSs), we can use the distance measure and dissimilarity measure between fuzzy sets/intuitionistic fuzzy set. Characterization of distance/dissimilarity measure between fuzzy sets/intuitionistic fuzzy set is important as it has application in different areas: pattern recognition, image segmentation, and decision making. Picture fuzzy set (PFS) is a generalization of fuzzy set and intuitionistic set, so that it have many application. In this paper, we introduce concepts: difference between PFS-sets, distance measure and dissimilarity measure between picture fuzzy sets, and also provide  the formulas for determining these values. We also present an application of dissimilarity measures in the sample recognition problems, can also be considered a decision-making problem.

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

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