Some novel features of Pythagorean m-polar fuzzy sets with applications

On the similarity measures of N-cubic Pythagorean fuzzy sets using the overlapping ratio

The similarity measures are essential concepts to discuss the closeness between sets. Fuzzy similarity measures and intuitionistic fuzzy similarity measures dealt with the incomplete and inconsistent data more efficiently. With time in decision-making theory, a complex frame of the environment that occurs cannot be specified entirely by these sets. A generalization like the Pythagorean fuzzy set can handle such a situation more efficiently. The applicability of this set attracted the researchers to generalize it into N-Pythagorean, interval-valued N-Pythagorean, and N-cubic Pythagorean sets. For this purpose, first, we define the overlapping ratios of N-interval valued Pythagorean and N-Pythagorean fuzzy sets. In addition, we define similarity measures in these sets. We applied this proposed measure for comparison analysis of plagiarism software.

Linear Diophantine Fuzzy Rough Sets: A New Rough Set Approach with Decision Making

In this article, a new hybrid model named linear Diophantine fuzzy rough set (LDFRS) is proposed to magnify the notion of rough set (RS) and linear Diophantine fuzzy set (LDFS). Concerning the proposed model of LDFRS, it is more efficient to discuss the fuzziness and roughness in terms of linear Diophantine fuzzy approximation spaces (LDFA spaces); it plays a vital role in information analysis, data analysis, and computational intelligence. The concept of (<p,p′>,<q,q′>)-indiscernibility of a linear Diophantine fuzzy relation (LDF relation) is used for the construction of an LDFRS. Certain properties of LDFA spaces are explored and related results are developed. Moreover, a decision-making technique is developed for modeling uncertainties in decision-making (DM) problems and a practical application of fuzziness and roughness of the proposed model is established for medical diagnosis.

A new distance measure for pythagorean fuzzy sets based on earth mover’s distance and its applications

In uncertain information processing, new knowledge can be discovered by measuring the proximity between discovered and undiscovered knowledge. Pythagorean Fuzzy Sets (PFSs) is one of the important tools to describe the natural attributes of uncertain information. Therefore, how to appropriately measure the distance between PFSs is an important topic. The earth mover’s distance (EMD) is a real distance metric that can be used to describe the difference between two distribution laws. In this paper, a new distance measure for PFSs based on EMD is proposed. It is a new perspective to measure the distance between PFSs from the perspective of distribution law. First, a new distance measure namely DEMD is presented and proven to satisfy the distance measurement axiom. Second, an example is given to illustrate the advantages of DEMD compared with other distance measures. Third, the problem statements and solving algorithms of pattern recognition, medical diagnosis and multi-criteria decision making (MCDM) problems are given. Finally, by comparing the application of different methods in pattern recognition, medical diagnosis and MCDM, the effectiveness and practicability of DEMD and algorithms presented in this paper are demonstrated.

Power Muirhead Mean Operators for Interval-Valued Linear Diophantine Fuzzy Sets and Their Application in Decision-Making Strategies

It is quite beneficial for every company to have a strong decision-making technique at their disposal. Experts and managers involved in decision-making strategies would particularly benefit from such a technique in order to have a crucial impact on the strategy of their company. This paper considers the interval-valued linear Diophantine fuzzy (IV-LDF) sets and uses their algebraic laws. Furthermore, by using the Muirhead mean (MM) operator and IV-LDF data, the IV-LDF power MM (IV-LDFPMM) and the IV-LDF weighted power MM (IV-LDFWPMM) operators are developed, and some special properties and results demonstrated. The decision-making technique relies on objective data that can be observed. Based on the multi-attribute decision-making (MADM) technique, which is the beneficial part of the decision-making strategy, examples are given to illustrate the development. To demonstrate the advantages of the developed tools, a comparative analysis and geometrical interpretations are also provided.

Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets

 Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.

A Multi-MOORA decision making method based on Muirhead mean operators and complex spherical fuzzy uncertain linguistic setting

The Muirhead mean (MM) operators offer a flexible arrangement with its modifiable factors because of Muirhead’s general structure. On the other hand, MM aggregation operators perform a significant role in conveying the magnitude level of options and characteristics. In this manuscript, the complex spherical fuzzy uncertain linguistic set (CSFULS), covering the grade of truth, abstinence, falsity, and their uncertain linguistic terms is proposed to accomplish with awkward and intricate data in actual life dilemmas. Furthermore, by using the MM aggregation operators with the CSFULS, the complex spherical fuzzy uncertain linguistic MM (CSFULMM), complex spherical fuzzy uncertain linguistic weighted MM (CSFULWMM), complex spherical fuzzy uncertain linguistic dual MM (CSFULDMM), complex spherical fuzzy uncertain linguistic dual weighted MM (CSFULDWMM) operators, and their important results are also elaborated with the help of some remarkable cases. Additionally, multi-attribute decision-making (MADM) based on the Multi-MOORA (Multi-Objective Optimization Based on a Ratio Analysis plus full multiplicative form), and proposed operators are developed. To determine the rationality and reliability of the elaborated approach, some numerical examples are illustrated. Finally, the supremacy and comparative analysis of the elaborated approaches with the help of graphical expressions are also developed.

Novel Pythagorean fuzzy entropy and Pythagorean fuzzy cross-entropy measures and their applications1

 Entropy and cross-entropy are very vital for information discrimination under complicated Pythagorean fuzzy environment. Firstly, the novel score factors and indeterminacy factors of intuitionistic fuzzy sets (IFSs) are proposed, which are linear transformations of membership functions and non-membership functions. Based on them, the novel entropy measures and cross-entropy measures of an IFS are introduced using Jensen Shannon-divergence (J-divergence). They are more in line with actual fuzzy situations. Then the cases of Pythagorean fuzzy sets (PFSs) are extended. Pythagorean fuzzy entropy, parameterized Pythagorean fuzzy entropy, Pythagorean fuzzy cross-entropy, and weighted Pythagorean fuzzy cross-entropy measures are introduced consecutively based on the novel score factors, indeterminacy factors and J-divergence. Then some comparative experiments prove the rationality and effectiveness of the novel entropy measures and cross-entropy measures. Additionally, the Pythagorean fuzzy entropy and cross-entropy measures are designed to solve pattern recognition and multiple criteria decision making (MCDM) problems. The numerical examples, by comparing with the existing ones, demonstrate the applicability and efficiency of the newly proposed models.

A q-rung orthopair fuzzy non-cooperative game method for competitive strategy group decision-making problems based on a hybrid dynamic experts’ weight determining model

How to select the optimal strategy to compete with rivals is one of the hottest issues in the multi-attribute decision-making (MADM) field. However, most of MADM methods not only neglect the characteristics of competitors’ behaviors but also just obtain a simple strategy ranking result cannot reflect the feasibility of each strategy. To overcome these drawbacks, a two-person non-cooperative matrix game method based on a hybrid dynamic expert weight determination model is proposed for coping with intricate competitive strategy group decision-making problems within q-rung orthopair fuzzy environment. At the beginning, a novel dynamic expert weight calculation model, considering objective individual and subjective evaluation information simultaneously, is devised by integrating the superiorities of a credibility analysis scale and a Hausdorff distance measure for q-rung orthopair fuzzy sets (q-ROFSs). The expert weights obtained by the above model can vary with subjective evaluation information provided by experts, which are closer to the actual practices. Subsequently, a two-person non-cooperative fuzzy matrix game is formulated to determine the optimal mixed strategies for competitors, which can present the specific feasibility and divergence degree of each competitive strategy and be less impacted by the number of strategies. Finally, an illustrative example, several comparative analyses and sensitivity analyses are conducted to validate the reasonability and effectiveness of the proposed approach. The experimental results demonstrate that the proposed approach as a CSGDM method with high efficiency, low computation complexity and little calculation burden.

Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making

In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their uncertain linguistic terms to handle problematic and challenging data in factual life impasses. By using the elaborated CLDULSs, some operational laws are also settled. Furthermore, by using the power Einstein (PE) aggregation operators based on CLDULS: the complex linear Diophantine uncertain linguistic PE averaging (CLDULPEA), complex linear Diophantine uncertain linguistic PE weighted averaging (CLDULPEWA), complex linear Diophantine uncertain linguistic PE Geometric (CLDULPEG), and complex linear Diophantine uncertain linguistic PE weighted geometric (CLDULPEWG) operators, and their useful results are elaborated with the help of some remarkable cases. Additionally, by utilizing the expounded works dependent on CLDULS, I propose a multi-attribute decision-making (MADM) issue. To decide the quality of the expounded works, some mathematical models are outlined. Finally, the incomparability and relative examination of the expounded approaches with the assistance of graphical articulations are evolved.

Hamy Mean Operators Based on Complex q-Rung Orthopair Fuzzy Setting and Their Application in Multi-Attribute Decision Making

To determine the connection among any amounts of attributes, the Hamy mean (HM) operator is one of the more broad, flexible, and dominant principles used to operate problematic and inconsistent information in actual life dilemmas. Furthermore, for the option to viably portray more complicated fuzzy vulnerability data, the idea of complex q-rung orthopair fuzzy sets can powerfully change the scope of sign of choice data by changing a boundary q, dependent on the distinctive wavering degree from the leaders, where ζ≥1, so they outperform the conventional complex intuitionistic and complex Pythagorean fuzzy sets. In genuine dynamic issues, there is frequently a communication problem between credits. The goal of this study is to initiate the HM operators based on the flexible complex q-rung orthopair fuzzy (Cq-ROF) setting, called the Cq-ROF Hamy mean (Cq-ROFHM) operator and the Cq-ROF weighted Hamy mean (Cq-ROFWHM) operator, and some of their desirable properties are investigated in detail. A multi-attribute decision-making (MADM) dilemma for investigating decision-making problems under the Cq-ROF setting is explored with certain examples. Finally, a down-to-earth model for big business asset-arranging framework determination is provided to check the created approach and to exhibit its reasonableness and adequacy. The exploratory outcomes show that the clever MADM strategy is better than the current MADM techniques for managing MADM issues.

A mathematical approach to medical diagnosis via Pythagorean fuzzy soft TOPSIS, VIKOR and generalized aggregation operators

Hepatitis is a therapeutic disorder caused by the inflammation/infection of liver and regarded as the existence of cells causing inflammation in the tissues of body parts. Hepatitis is deliberated as a lethal disease worldwide, especially in developing countries mainly due to contaminated drinking water, unhygienic sanitary conditions and careless blood transfusion. This infection is basically considered as viral infection even though this sort of liver infection can also take place due to autoimmune, toxin, medications, unprotected physical relations, drugs and alcohol. Many approaches of identifying viral hepatitis have been sought so for, which include physical inspection, liver function tests (LFTs), liver surgery (biopsy), imaging studies such as sonogram or CT scan, ultrasound, blood tests, viral serology panel, DNA test, and viral antibody testing. In this article, we propose mathematical analysis of viral hepatitis types using Pythagorean fuzzy soft sets (PFSSs) via TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution), VIKOR (Vise Kriterijumska Optimizacija Kompromisno Resenje) and generalized aggregation operators models and show that all the three techniques render the same optimal choice. We also present a commentary yielding comparison between the three techniques considering their structure of evaluation.

Linear Diophantine Fuzzy Relations and Their Algebraic Properties with Decision Making

Binary relations are most important in various fields of pure and applied sciences. The concept of linear Diophantine fuzzy sets (LDFSs) proposed by Riaz and Hashmi is a novel mathematical approach to model vagueness and uncertainty in decision-making problems. In LDFS theory, the use of reference or control parameters corresponding to membership and non-membership grades makes it most accommodating towards modeling uncertainties in real-life problems. The main purpose of this paper is to establish a robust fusion of binary relations and LDFSs, and to introduce the concept of linear Diophantine fuzzy relation (LDF-relation) by making the use of reference parameters corresponding to the membership and non-membership fuzzy relations. The novel concept of LDF-relation is more flexible to discuss the symmetry between two or more objects that is superior to the prevailing notion of intuitionistic fuzzy relation (IF-relation). Certain basic operations are defined to investigate some significant results which are very useful in solving real-life problems. Based on these operations and their related results, it is analyzed that the collection of all LDF-relations gives rise to some algebraic structures such as semi-group, semi-ring and hemi-ring. Furthermore, the notion of score function of LDF-relations is introduced to analyze the symmetry of the optimal decision and ranking of feasible alternatives. Additionally, a new algorithm for modeling uncertainty in decision-making problems is proposed based on LDFSs and LDF-relations. A practical application of proposed decision-making approach is illustrated by a numerical example. Proposed LDF-relations, their operations, and related results may serve as a foundation for computational intelligence and modeling uncertainties in decision-making problems.