Advances in Fuzzy Systems

Coloring of fuzzy graphs has many real-life applications in combinatorial optimization problems like traffic light system, exam scheduling, and register allocation. The coloring of total fuzzy graphs and its applications are well studied. This manuscript discusses the description of 2-quasitotal graph for fuzzy graphs. The proposed concept of 2-quasitotal fuzzy graph is explicated by several numerical examples. Moreover, some theorems related to the properties of 2-quasitotal fuzzy graphs are stated and proved. The results of these theorems are compared with the results obtained from total fuzzy graphs and 1-quasitotal fuzzy graphs. Furthermore, it defines 2-quasitotal coloring of fuzzy total graphs and which is justified.

In todayʼs world where technology is rapidly evolving, hotels need to be the best in all conditions to be one step ahead of other competitors. Digital marketing and hotel website solutions play a lead role in this competition. Therefore, hotel websites need to be innovative, user-friendly, and descriptive. The main purpose of the study is to evaluate and rank potential hotel websites and digital solutions provider firms. Since there are various potentially competing quantitative and qualitative criteria to take into consideration in the decision-making process, a multicriteria decision-making (MCDM) method is needed. As the MCDM method, fuzzy best-worst method (FBWM) is integrated with the Fuzzy Technique for Order Preference by Similarity to Ideal Solution (F-TOPSIS). In this integration, FBWM is applied to determine fuzzy evaluation criteria weights and then F-TOPSIS is implemented to rank alternatives utilizing the obtained fuzzy weights. A case study is presented, where 4 alternative hotel websites and digital solutions provider firms for Paloma Hotels in Turkey are evaluated based on 9 criteria by 3 hotel managers.

This research work aims to study a capacitated transportation problem (CTP) with penalty cost, supplies, and demands represented by hexagonal fuzzy numbers. Based on ranking function, the supplies and demands are converted to the crisp form. Through the use of the level, the problem is converted into interval linear programming. To optimize the interval objective function, we define the order relations represented by policy maker’s choice between intervals. The maximization (minimization) problem considering the interval objective function is transformed to multiobjective optimization problem based on order relations introduced by the preference of policy makers between interval profits (costs). A numerical example is given for illustration and to check the validity of the suggested approach.

In recent months, the world has experienced the outbreak and spread of a new infectious disease, COVID-19. The spread of this disease has been so severe, and even many developed countries have struggled to manage this situation. However, some countries, such as China and Australia, have shown success in taking effective steps towards tackling the crisis. So far, some preventive measures to contain the spread of infection have emerged. Numerous studies have been undertaken worldwide in parallel in order to develop strategies to contain the virus, as well as to determine climatic or atmospheric conditions favoring COVID-19 spread. In this research, an artificial intelligence (AI) system has been adopted to assess the effective role of various environmental conditions in the spread of COVID-19. Temperature, relative humidity (RH), and UV index (UVI) of some affected countries were considered as input parameters while the total number of infected people is taken as the output variable. After plotting all available data as linguistic variables, a relationship is established between temperature, RH, UVI, and the number of infected people. From the surface graph, it can be stated that in addition to UVI, temperature and RH have a significant impact on the number of affected people. The maximum and minimum temperatures as well as other parameters are considered on the basis of mean values.

The paper aims to propose a distributed method for machine learning models and its application for medical data analysis. The great challenge in the medicine field is to provide a scalable image processing model, which integrates the computing processing requirements and computing-aided medical decision making. The proposed Fuzzy logic method is based on a distributed approach of type-2 Fuzzy logic algorithm and merges the HPC (High Performance Computing) and cognitive aspect on one model. Accordingly, the method is assigned to be implemented on big data analysis and data science prediction models for healthcare applications. The paper focuses on the proposed distributed Type-2 Fuzzy Logic (DT2FL) method and its application for MRI data analysis under a massively parallel and distributed virtual mobile agent architecture. Indeed, the paper presents some experimental results which highlight the accuracy and efficiency of the proposed method.

The main purpose of this paper is to consider the strong law of large numbers for random sets in fuzzy metric space. Since many years ago, limited theorems have been expressed and proved for fuzzy random variables, but despite the uncertainty in fuzzy discussions, the nonfuzzy metric space has been used. Given that the fuzzy random variable is defined on the basis of random sets, in this paper, we generalize the strong law of large numbers for random sets in the fuzzy metric space. The embedded theorem for compact convex sets in the fuzzy normed space is the most important tool to prove this generalization. Also, as a result and by application, we use the strong law of large numbers for random sets in the fuzzy metric space for the bootstrap mean.