Multi-attribute decision making with Pythagorean fuzzy sets via conversions to intuitionistic fuzzy sets and ORESTE method

2020 ◽  
pp. 1-22
Author(s):  
Zhifu Tao ◽  
Jiaming Zhu ◽  
Ligang Zhou ◽  
Jinpei Liu ◽  
Huayou Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Pythagorean Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making

scholarly journals The n-Pythagorean Fuzzy Sets

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1772
Author(s):  
Anna Bryniarska
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Quadratic Function ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Functions ◽  
Power Functions ◽  
Pythagorean Fuzzy Sets ◽  
Conceptual Apparatus ◽  
Intuitionistic Fuzzy ◽  
Classic Theory

The following paper presents deductive theories of n-Pythagorean fuzzy sets (n-PFS). N-PFS objects are a generalization of the intuitionistic fuzzy sets (IFSs) and the Yager Pythagorean fuzzy sets (PFSs). Until now, the values of membership and non-membership functions have been described on a one-to-one scale and a quadratic function scale. There is a symmetry between the values of this membership and non-membership functions. The scales of any power functions are used here in order to increase the scope of the decision-making problems. The theory of n-PFS introduces a conceptual apparatus analogous to the classic theory of Zadeh fuzzy sets, consistently striving to correctly define the n-PFS algebra.

Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets

2021 ◽  
Vol 40 (1) ◽  
pp. 1147-1160
Author(s):  
Yali Cheng ◽  
Yonghong Li ◽  
Jie Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Linguistic Intuitionistic Fuzzy Sets ◽  
Linguistic Scale Function ◽  
Different Response

Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

On pythagorean fuzzy soft topological spaces

2021 ◽  
pp. 1-9
Author(s):  
Ibtesam Alshammari ◽  
Mani Parimala ◽  
Saeid Jafari
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Topological Spaces ◽  
Decision Making Process ◽  
Soft Sets ◽  
New Methods ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Fuzzy Soft Sets

Imprecision in the decision-making process is an essential consideration. In order to navigate the imprecise decision-making framework, measuring tools and methods have been developed. Pythagorean fuzzy soft sets are one of the new methods for dealing with imprecision. Pythagorean fuzzy soft topological spaces is an extension of intuitionistic fuzzy soft topological spaces. These sets generalizes intuitionistic fuzzy sets for a broader variety of implementations. This work is a gateway to study such a problem. The concept of Pythagorean fuzzy soft topological spaces(PyFSTS), interior, closure, boundary, neighborhood of Pythagorean fuzzy soft spaces PyFSS, base and subspace of PyFSTSs are presented and its properties are figured out. We established an algorithm under uncertainty based on PyFSTS for multi-attribute decision-making (MADM) and to validate this algorithm, a numerical example is solved for suitable brand selection. Finally, the benefits, validity, versatility and comparison of our proposed algorithms with current techniques are discussed.The advantage of the proposed work is to detect vagueness with more sizably voluminous valuation space than intuitionistic fuzzy sets.

New generalized intuitionistic fuzzy divergence measure with applications to multi-attribute decision making and pattern recognition

2020 ◽  
Vol 13 ◽  
Author(s):  
Adeeba Umar ◽  
Ram Naresh Saraswat
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
The Other ◽  
Divergence Measure ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Prime Objective ◽  
Fuzzy Divergence

Background: The notion of fuzzy set was introduced by Zadeh. After that, many researchers extended the concept of fuzzy sets in different ways. Atanassov introduced the concept of intuitionistic fuzzy sets as an extension of fuzzy sets. This concept is applied in many fields such as bio-informatics, image processing, decision making, feature selection, pattern recognition etc. Objectives: The prime objective of this paper is to introduce a new generalized intuitionistic fuzzy divergence measure with proof of its validity and discussions on its elegant properties. Applications of the proposed divergence measure in multi-attribute decision making and pattern recognition are also discussed with some numerical illustrations. Further, the proposed divergence measure is compared with other methods for solving MADM and pattern recognition problems which exist in the literature. Methods: Divergence measure method is used to measure the divergence between two given sets. Also, the results of the other existing measures are also given to compare with the proposed measure. Results: We see that our proposed divergence measure found much better results in comparison with the other existing methods. Conclusion: A new divergence measure for intuitionistic fuzzy sets is introduced with some of its properties. Applications of the proposed divergence measure to pattern recognition and MADM are illustrated through examples. The comparison of the proposed method with the existing methods shows the legacy of the results of the proposed method. It is concluded that the proposed divergence measure is effective for solving real world problems related to MADM and pattern recognition.

scholarly journals Covering-Based Spherical Fuzzy Rough Set Model Hybrid with TOPSIS for Multi-Attribute Decision-Making

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 547 ◽  
Author(s):  
Shouzhen Zeng ◽  
Azmat Hussain ◽  
Tahir Mahmood ◽  
Muhammad Irfan Ali ◽  
Shahzaib Ashraf ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Rough Set ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Rough Set ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Topsis Technique ◽  
Picture Fuzzy Sets

In real life, human opinion cannot be limited to yes or no situations as shown in an ordinary fuzzy sets and intuitionistic fuzzy sets but it may be yes, abstain, no, and refusal as treated in Picture fuzzy sets or in Spherical fuzzy (SF) sets. In this article, we developed a comprehensive model to tackle decision-making problems, where strong points of view are in the favour; neutral; and against some projects, entities, or plans. Therefore, a new approach of covering-based spherical fuzzy rough set (CSFRS) models by means of spherical fuzzy β -neighborhoods (SF β -neighborhoods) is adopted to hybrid spherical fuzzy sets with notions of covering the rough set. Then, by using the principle of TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) to present the spherical fuzzy, the TOPSIS approach is presented through CSFRS models by means of SF β -neighborhoods. Via the SF-TOPSIS methodology, a multi-attribute decision-making problem is developed in an SF environment. This model has stronger capabilities than intuitionistic fuzzy sets and picture fuzzy sets to manage the vague and uncertainty. Finally, the proposed method is demonstrated through an example of how the proposed method helps us in decision-making problems.

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