Fuzzy Optimzation and Modeling
Volume:4 Issue: 1, Winter 2023

When a correlation between datasets is presented, it is clear from this statement that it quantifies how strongly these datasets are connected. Meanwhile, this coefficient is a well-known metric for assessing the link between two sets. The Fermatean fuzzy set is a significant extension of the extant intuitionistic and Pythagorean fuzzy sets, with the benefit of more comprehensively characterizing ambiguous data. In other words, Fermatean fuzzy sets are powerful and useful tools for representing imprecise information. The purpose of this work is to generate novel correlation coefficients using Fermatean fuzzy sets. These coefficients specify the degree and kind of correlation (positive or negative) between two Fermatean fuzzy sets. The new coefficient values will similarly be in the [-1,1] range. During formulation, pairs of membership and non-membership degrees were viewed as a vector representation containing the two elements. Furthermore, the novel approach was compared to existing methods. A medical diagnosis application and pattern recognition as a data mining application were used to exemplify the effectiveness of the proposed method.

The application of fuzzy linear programming and optimization techniques has a rich history in various domains. In recent years, the rise in employee terminations within large companies has underscored the significance of employee performance and its impact on organizational progress. To address this issue, it becomes crucial to determine the appropriate number of employees required to effectively execute company projects, considering employee performance and organizational needs. Additionally, it is essential to identify an optimal employee count as a benchmark prior to hiring. This optimal value can be achieved through the utilization of optimization methodologies, such as fuzzy linear programming. This research paper presents a solution to the employee hiring problem in a factory by utilizing the fuzzy linear programming method. The findings reveal that increasing the number of hires does not necessarily correlate with enhanced performance. The findings of this paper enable organizations to make informed decisions regarding employee recruitment and enhance overall operational efficiency.

Identifying and presenting a high-risk investment model for insurance institutions in line with the establishment of an insurance risk-taking investment fund. This research is considered to be applied in terms of purpose and field descriptive in terms of nature, and because it tries to present a model using the process of fuzzy network analysis, it is also considered as a type of modelling. In this paper, it has been tried to identify and introduce the most important factors and effective factors of venture capital (VC) using the fuzzy network analysis process technique in the insurance industry. The population of this study was insurance companies and the statistical sample includes 54 experts in the field of insurance. The required information was collected in 2023 using a standard questionnaire. Due to the lack of independence and dependence between the effective factors, the fuzzy network analysis process method was used to identify the possible dependencies between the factors and measure them for the development of the VC model, and the results were prioritized by the non-fuzzy network analysis process method. The findings of the research show that operating cycle indicators, total asset turnover ratio, total investment return, loss ratio, asset-to-debt ratio are ranked first to fifth among VC indicators. Venture capital helps the insurance industry to establish internal accounting rules and standardize their financial statements. In other words, venture capital support modifies the "hard" and "soft" information required for insurance.

Systems of simulations linear equations play major role in various areas such as mathematics, statistics, and social sciences. Since in many applications, at least some of the system’s parameters and measurements are represented by fuzzy rather than crisp numbers, therefore, it is important to develop mathematical models and numerical procedures that would appropriately treat general fuzzy linear systems and solve them. In this paper, a new method based on fuzzy operations approach for solving Fuzzy Linear System (FLS) is introduced. The related theorems are proved in details. Finally, the proposed method is illustrated by solving two numerical examples.

This paper seeks to address the multi-commodity flow problem in uncertainty conditions, in which the objective function of the problem is of fractional type. The cost coefficients and capacities of the problem are uncertain. The purpose of using uncertainty theory is to deal with unknown factors in the uncertain network. After stating the optimality conditions, the problem is transformed into a certain fractional multi-commodity flow problem by applying the uncertain chance-constrained programming approach. Then, the variable transformation approach is used to transform the nonlinear objective function to its linear form. Finally, two numerical examples are evaluated to verify the efficiency of the proposed formulation.

The issue of integration in different industries is very important and brings many benefits at different economic and social levels. Given the size of the telecommunications industry, this industry is no exception to this rule and the integration of telecommunications infrastructure creates a lot of added value. But the interactions between tangible and intangible indicators have emerged by doing so, which policymakers must consider. Our goal is to study the integration of telecommunications infrastructure and study its interactions on factors identified by experts and then verified. To achieve the correct result, after collecting the opinions of industry experts, using the fuzzy Delphi method and after the steps of this method, the effective factors were examined and the basic indicators that should be considered were identified and ranked. Classified. Then, in order to determine the effect of each of the indicators on the integration of telecommunication technology infrastructure, by combining fuzzy logic and the formation of a neural network through the mathematical method of Enfis, the extent and how the effect of all factors was examined. These results are a new approach in the telecommunications industry and design an innovative model for this industry.