Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables

High computation complexity restricts the application prospects of the interval type-2 fuzzy variable (IT2-FV), despite its high degree of freedom in representing uncertainty. Thus, this paper studies the fuzzy operations for the regular symmetric triangular IT2-FVs (RSTIT2-FVs)—the simplest IT2-FVs having the greatest membership degrees of 1. Firstly, by defining the medium of an RSTIT2-FV, its membership function, credibility distribution, and inverse distribution are analytically and explicitly expressed. Secondly, an operational law for fuzzy arithmetic operations regarding mutually independent RSTIT2-FVs is proposed, which can simplify the calculations and directly output the inverse credibility of the functions. Afterwards, the operational law is applied to define the expected value operator of the IT2-FV and prove the linearity of the operator. Finally, some comparative examples are provided to verify the efficiency of the proposed operational law.

Assessing the quality of international trade and economic relations in the agricultural sector

Purpose of the research. The main purpose of the article is to improve the methodical support for assessing the quality of international trade and economic relations in the agricultural sector. Methodology. In the course of the research, the following methods were applied: fuzzy logic inference, generalization, comparison, graphical, expert assessments, etc. Results. The role of international trade and economic relations in the development of the domestic economy has been substantiated. The expediency of using forecasting as a tool for assessing the prospects for expanding cooperation in the field of agriculture with other countries has been proved. The main indicators have been determined that are used in the process of measuring the relationships quality. The necessity of developing tools for assessing the quality of international trade and economic relations has been substantiated. It has been proposed to carry out an assessment using the fuzzy sets theory based on the formed thesaurus, which includes a fuzzy set, membership function, fuzzy variable, linguistic variable, fuzzy knowledge base, fuzzy logic inference. The scheme of the procedure for assessing the quality of international trade and economic relations using the method of fuzzy logic inference and description of the fuzzy system for assessing the quality of international trade and economic relations of the agricultural sector of Ukraine have been developed. An analysis has been carried out within the research framework of bilateral agreements between Ukraine and partners in the field of agriculture and it has been determined that an example of high-quality international trade and economic relations is cooperation with China, India, Germany, the United Arab Emirates; moderate – with Georgia, Poland, France, Korea; low – with Japan, Iran, Kazakhstan, etc. Practical meaning. Based on the results of the assessment, in accordance with the quality level of international trade and economic relations, priority areas of cooperation for Ukraine with partner countries to promote the development of its economy have been identified. Prospects for further research by the author are to develop a mechanism for increasing the quality of international trade and economic relations between Ukraine and partner countries.

Some q-rung orthopair trapezoidal fuzzy linguistic hamacher aggregation operators and their applications

A Hamacher operator in a q-rung orthopair trapezoidal fuzzy linguistic environment is studied based on the definition of the q-rung orthopair fuzzy set and the Hamacher aggregation operator. First, we define a new fuzzy variable called q-rung orthopair trapezoidal fuzzy linguistic sets, and the operational laws, score function, accuracy function, comparison rules, and distance measures of the IVPFLVS are defined. Second, based on the Hamacher operator and the q-rung orthopair trapezoidal fuzzy linguistic sets, we propose several q-rung trapezoidal fuzzy linguistic Hamacher operator information aggregation operators, such as the generalized q-rung orthopair trapezoidal fuzzy linguistic Hamacher weighted averaging (q-GROTrFLHWA) operator, and the generalized q-rung orthopair trapezoidal fuzzy linguistic Hamacher weighted geometric (q-GROTrFLHWG) operator. Third, some desirable properties of the correlation operators, such as idempotency, boundedness, and monotonicity are discussed. Finally, there are two group decision schemes based on q-rung orthopair trapezoidal fuzzy information with known attribute weights. The decision-making scheme is applied to the evaluation of school teaching quality, and the practicability and effectiveness of the scheme are demonstrated by different methods.

Positive solutions and stability of fuzzy Atangana–Baleanu variable fractional differential equation model for a novel coronavirus (COVID-19)

This work provides a new fuzzy variable fractional COVID-19 model and uses a variable fractional operator, namely, the fuzzy variable Atangana–Baleanu fractional derivatives in the Caputo sense. Next, we explore the proposed fuzzy variable fractional COVID-19 model using the fixed point theory approach and determine the solution’s existence and uniqueness conditions. We choose an appropriate mapping and with the help of the upper/lower solutions method. We prove the existence of a positive solution for the proposed fuzzy variable fractional COVID-19 model and also obtain the result on the existence of a unique positive solution. Moreover, we discuss the generalized Hyers–Ulam stability and generalized Hyers–Ulam–Rassias stability. Further, we investigate the results on maximum and minimum solutions for the fuzzy variable fractional COVID-19 model.

The Scalar Mean Chance and Expected Value of Regular Bifuzzy Variables

As a natural extension of the fuzzy variable, a bifuzzy variable is defined as a mapping from a credibility space to the collection of fuzzy variables, which is an appropriate tool to model the two-fold fuzzy phenomena. In order to enrich its theoretical foundation, this paper explores some important measures for regular bifuzzy variables, the most commonly used type of bifuzzy variables. Firstly, we introduce the regular bifuzzy variables’ mean chance measure and some properties, including self-duality and its calculation formulas. Furthermore, we also investigate the mean chance distribution for strictly monotone functions of regular bifuzzy variables based on the proposed operational law. Finally, we present the expected value operator as well as equivalent analytical formulas of the expected value of regular bifuzzy variables and their strictly monotone functions.