Interval Data Aggregation Technology for Large Scale Decision Making

In this paper, an improved multiple attribute decision making (MADM) method based on the proposed novel score function and accuracy function of interval-valued intuitionistic fuzzy numbers (IVIFNs) is proposed to aggregate large-scale data. The attribute values in the decision matrices provided by each decision-maker (DM), which are characterized by interval numbers. First, a transformation matrix is introduced to define the concepts of satisfactory set, un- satisfactory set and uncertainty set of alternatives. An approach is then developed for aggregating attribute values into IVIFNs, and we will obtain the collective evaluation of each alternative. Next, using the interval-valued intuitionistic fuzzy weighted averaging operator, the collective attribute values characterized by IVIFNs are aggregated to get the overall evaluation of alternatives. The score function and accuracy function are applied to calculate the score degree and the rank of each alternative. Finally, a large-scale example is given to verify the validity of the reported method.

N-Fuzzy Sets and Their Applications

The purpose of this paper is to define n-Fuzzy sets and study their relationship with intuitionistic fuzzy sets, Pythagorean fuzzy sets and Fermatean fuzzy sets. The n-Fuzzy sets can deal with more uncertain situations than intuitionistic fuzzy sets, Pythagorean fuzzy sets and Fermatean fuzzy sets because of its larger range of describing the membership grades. The set operations, score function, accuracy function and Euclidean distance of n-Fuzzy sets will study. Finally, we study the Sanchez$^{,}$s approach for medical diagnosis and extend this concept with the notion of n-Fuzzy set.

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

About the confusion-matrix-based assessment of the results of imbalanced data classification

When applying classifiers in real applications, the data imbalance often occurs when the number of elements of one class is greater than another. The article examines the estimates of the classification results for this type of data. The paper provides answers to three questions: which term is a more accurate translation of the phrase "confusion matrix", how preferable to represent data in this matrix, and what functions to be better used to evaluate the results of classification by such a matrix. The paper demonstrates on real data that the popular accuracy function cannot correctly estimate the classification errors for imbalanced data. It is also impossible to compare the values of this function, calculated by matrices with absolute quantitative results of classification and normalized by classes. If the data is imbalanced, the accuracy calculated from the confusion matrix with normalized values will usually have lower values, since it is calculated by a different formula. The same conclusion is made for most of the classification accuracy functions used in the literature for estimation of classification results. It is shown that to represent confusion matrices it is better to use absolute values of object distribution by classes instead of relative ones, since they give an idea of the amount of data tested for each class and their imbalance. When constructing classifiers, it is recommended to evaluate errors by functions that do not depend on the data imbalance, that allows to hope for more correct classification results for real data.

Nucleolus of Vague Payoff Cooperative Game

This paper focuses on the problem of cooperative game with payoff of vague value and its nucleolus. Firstly, the paper defines the score function and accuracy function of vague sets and the method for ranking of vague sets and proposes the concept of core and nucleolus of vague payoff cooperative game. Based on this, the model of vague payoff cooperative game is built. Then, the relationship between the core and the nucleolus of vague payoff cooperative game is further discussed, and the existence and unique characteristics of the nucleolus are proved. We use the ranking method defined in the paper to transform the problem of finding the nucleolus solution into a nonlinear programming problem. Finally, the paper verifies the feasibility and effectiveness of the method for finding the nucleolus with an experimental analysis.

Multi-objective fully intuitionistic fuzzy fixed-charge solid transportation problem

During past few decades, fuzzy decision is an important attention in the areas of science, engineering, economic system, business, etc. To solve day-to-day problem, researchers use fuzzy data in transportation problem for presenting the uncontrollable factors; and most of multi-objective transportation problems are solved using goal programming. However, when the problem contains interval-valued data, then the obtained solution was provided by goal programming may not satisfy by all decision-makers. In such condition, we consider a fixed-charge solid transportation problem in multi-objective environment where all the data are intuitionistic fuzzy numbers with membership and non-membership function. The intuitionistic fuzzy transportation problem transforms into interval-valued problem using $$(\alpha ,\beta )$$ ( α , β ) -cut, and thereafter, it reduces into a deterministic problem using accuracy function. Also the optimum value of alternative corresponds to the optimum value of accuracy function. A numerical example is included to illustrate the usefulness of our proposed model. Finally, conclusions and future works with the study are described.

Double Integral-Based Method for Ranking Intuitionistic Multiplicative Sets and Its Application in Selecting Logistics Transfer Station

Intuitionistic multiplicative sets can be applied in many practical situations, most of which are based on ranking of intuitionistic multiplicative numbers. This study develops an integral method for ranking intuitionistic multiplicative numbers based on the new definitions of multiplicative score function and accuracy function. The ranking method considers both the risk preference and infinitely many possible values in feasible region. Some reasonable properties of multiplicative score function and accuracy function are studied, respectively. We construct a total order relation on the set of intuitionistic multiplicative numbers. The multiplicative score function and accuracy function are utilized to select the optimal logistics transfer station. A comparison example is developed to highlight the advantage of the risk preference-based ranking method.

Best Selection of Generative Adversarial Networks Hyper-Parameters using Genetic Algorithm

Generative Adversarial Networks (GANs) are most popular generative frameworks that have achieved compelling performance. They follow an adversarial approach where two deep models generator and discriminator compete with each other In this paper, we propose a Generative Adversarial Network with best hyper-parameters selection to generate fake images for digits number 1 to 9 with generator and train discriminator to decide whereas the generated images are fake or true. Using Genetic Algorithm technique to adapt GAN hyper-parameters, the final method is named GANGA:Generative Adversarial Network with Genetic Algorithm. Anaconda environment with tensorflow library facilitates was used, python as programming language also used with needed libraries. The implementation was done using MNIST dataset to validate our work. The proposed method is to let Genetic algorithm to choose best values of hyper-parameters depending on minimizing a cost function such as a loss function or maximizing accuracy function. GA was used to select values of Learning rate, Batch normalization, Number of neurons and a parameter of Dropout layer.

Concept of Yager operators with the picture fuzzy set environment and its application to emergency program selection

PurposeThe aim of this study as to find out an approach for emergency program selection.Design/methodology/approachThe authors have generated six aggregation operators (AOs), namely picture fuzzy Yager weighted average (PFYWA), picture fuzzy Yager ordered weighted average, picture fuzzy Yager hybrid weighted average, picture fuzzy Yager weighted geometric (PFYWG), picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators.FindingsFirst of all, the authors defined the score and accuracy function for picture fuzzy set (FS), and some fundamental operational laws for picture FS using the Yager aggregation operation. After that, using the developed operational laws, developed some AOs, namely PFYWA, picture fuzzy Yager ordered weighted average, picture fuzzy Yager hybrid weighted average, PFYWG, picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators, have been proposed along with their desirable properties. A decision-making (DM) approach based on these operators has also been presented. An illustrative example has been given for demonstrating the approach. Finally, discussed the comparison of the proposed method with the other existing methods and write the conclusion of the article.Originality/valueTo find the best alternative for emergency program selection.