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Considering the double uncertainty caused by the ambiguity of statistical data and the ambiguity produced by the subjective assessment of decision makers, the crisp values of criteria may be insufficient to model the multi-criteria decision-making (MCDM) problem in the real world. This paper proposes a fuzzy best-worst method (FBWM) based on a dual-interval solution algorithm to extend the best-worst method (the most recent MCDM method) to fuzzy environments. The reference comparisons for the best criteria and for the worst criteria are represented by fuzzy numbers. Then, according to the BWM method, a nonlinear constrained optimization problem with fuzzy parameters is formulated. We decompose the membership function in fuzzy numbers into several interval numbers of special form and solve the aforementioned fuzzy BWM problem by compound interval algorithm to obtain fuzzy weights of different criteria. Meanwhile, an integral type-reduced method is proposed for determining the fuzzy consistency ratio in order to assess the reliability of the FBWM results. The viability of the new algorithm to expand the BWM method into fuzzy environments has been validated through three numerical examples. In contrast to the existing FBWM method, the proposed method avoids the arithmetic operation between fuzzy numbers during the solution process, directly transfers the uncertain information in the membership function corresponding to the fuzzy comparison vector to the result, and generates fuzzy weight value, which indicates that the proposed algorithm is able to obtain accurate BWM results in fuzzy environments. The results of the study provide new solution ideas for multi-criteria optimization problems under uncertainty. [ABSTRACT FROM AUTHOR]

One of the special cases of type-2 fuzzy sets are the interval type-2 fuzzy sets, which are less complicated and easier to understand than T2FSs. In this study, we explore the interval type-2 fuzzy linear programming problem with the resources vector that have imprecision of the vagueness type. These types of vagueness are expressed via membership functions. First, we review the three available methods, including the Figueroa and Sarani methods. Then, using the three ideas of Verdegay, Werners, and Guu and Wu for solving fuzzy linear programming problems with vagueness in the resources vector, we propose three new methods for solving interval type-2 fuzzy linear programming problems with vagueness in the resources vector. Finally, we demonstrate the effectiveness of our proposed methods by solving an example and comparing the results obtained with each other and with those of previous methods.

In this study, Interval number and Fuzzy number Linear Programming problems are addressed. We deal with some convenient methods to solve the addressed problems. We focus on preparing an improving approach based on Tang Shaocheng method to solve linear programming problems with interval or fuzzy numbers. Also, some applications of our proposed approach in fractional programming are presented. Particularly, we propose an algorithm using our improved approach to solve a fuzzy multi-objective linear fractional programming problem. Finally, we illustrate the proposed approach using numerical and some real life examples. [ABSTRACT FROM AUTHOR]

This research addresses the Inventory-Routing Problem (IRP) with priority customers under conditions of uncertainty. The problem involves devising a plan to supply a set of customers from a facility, establishing precedence rules, and making transportation and inventory management decisions while considering uncertainty in customer demand. Priority in deliveries is assigned to customers in the health sector in accordance with government regulations. Companies must uphold product quality for health sector customers while simultaneously aiming to minimize total costs. We propose a fuzzy mixed-integer linear programming model to solve the IRP with priority customers and uncertainty in demand rates, modeled using triangular fuzzy numbers. To convert the fuzzy linear programming model into a deterministic one, an ordering method for fuzzy numbers is applied. The model is implemented using CPLEX, and a set of benchmark instances is solved. The primary results indicate that prioritizing customers leads to an increase in total costs due to visiting these customers first on each route created. Additionally, routes without priority customers exhibit higher average vehicle capacity utilization. In most cases, the solutions obtained maintain quality within the specified time limits. [ABSTRACT FROM AUTHOR]

One of the special cases of type-2 fuzzy sets is the interval type-2 fuzzy sets, which are less complicated and easier to understand than T2FSs. In this study, we explore the interval type-2 fuzzy linear programming problem with the resources vector that has imprecision of the vagueness type. These types of vagueness are expressed via membership functions. First, we review the three available methods, including the Figueroa and Sarani methods. Then, using the three ideas of Verdegay, Werners, and Guu and Wu for solving fuzzy linear programming problems with vagueness in the resources vector, we propose three new methods for solving interval type-2 fuzzy linear programming problems with vagueness in the resources vector. Finally, we demonstrate the effectiveness of our proposed methods by solving an example and comparing the results obtained with each other and with those of previous methods. [ABSTRACT FROM AUTHOR]

In contemporary decision-making, reliance on information is paramount, yet much of it is fraught with uncertainty, making logical decision-making challenging. To tackle this uncertainty, various methods, including the use of fuzzy numbers, have been employed. This paper specifically delves into addressing linear programming (LP) problems characterized by fuzzy coefficients in the objective function, fuzzy values in the right-hand side, and fuzzy coefficients of constraints. The proposed approach involves employing linear ranking functions such as Maleki, Campos, Yager’s F1 and Yager linear ranking functions to solve these fuzzy linear programming (FLP) problems and attain optimal solutions. Furthermore, the paper elucidates the resolution steps through the presentation of numerical examples, in this study, a comprehensive methodology is presented for effectively addressing a wide range of linear programming problems.

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International law is mainly the law between countries, which is the code of conduct for countries to conduct international interactions, and this paper researches the role of international law in international relations interactions. First of all, this paper combines the fuzzy set on the basis of the classical linear regression model algorithm, establishes the fuzzy linear programming model, and explores the fuzzy correlation analysis. Then, taking EU law as an example, the role of EU law in EU relations is analyzed through the theory of EU law, EU and the role of EU law in the EU embodied. Finally, based on the role of EU law, the importance of international law in international relations is studied through a fuzzy linear programming model, and the role of strengthening international law is considered. The results show that the countries consider the legitimacy of EU law to be above 0.9, and the countries’ participation in EU law also ranges from 0.9 to 1.0, and the countries’ self-identification increases by about 0.1 to 0.2 after the enactment of EU law. The correlation coefficients of international law on the construction of the identities of the 10 countries are all greater than 0.75, and the interests of the countries have increased by about 2.3, and international law promotes the order of international relations.

To achieve carbon neutrality, the power structure is bound to usher in fundamental transformations. In this study, an energy–carbon–water nexus (F-ECWN) system model is developed to assess trade-offs among different decision-making objectives within a power system under varying policy orientations. The model incorporates forecast data derived from various global climate models, leverages neural network prediction, draws upon multi-criteria decision-making theory, and incorporates fuzzy theory. Moreover, to effectively handle a multitude of fuzzy parameters within the model, a novel dual-interval algorithm for solving fuzzy linear programming is proposed. The F-ECWN model has the capability to derive the fuzzy membership function for each variable within the model ensuring that errors remain below 1 %, reflecting the uncertainty stemming from diverse policy orientations and technology choices. Various scenarios were formulated to gauge the impact of policy orientation on the allocation decisions of regional energy systems. Additionally, sensitivity analysis has been conducted to assess the effects of uncertain parameters on modeling outputs. The results of the applied research in Fujian Province have revealed that the presence of uncertainties in the energy system's parameters can significantly influence model outputs and decision-making processes. Furthermore, the modeling results demonstrate the region's substantial potential for reducing carbon emissions. Under optimal policy guidance and climate conditions, the total carbon emissions can be reduced by 65 %, with a 36.14 % increase in the total system cost. These findings are anticipated to provide valuable support for formulating optimal decisions regarding regional energy-carbon-water nexus system and related environmental policies. [Display omitted] • A new algorithm for solving fuzzy multi-objective programming problems is proposed. • A robust fuzzy number reduction algorithm based on probabilistic integration is proposed. • E -C-W nexus in Fujian Province under different policy orientations is quantified. • Incorporation of CMIP6 forecast data into renewable energy parameters construction. • Carbon and water synergy effects in regional power system optimization are observed. [ABSTRACT FROM AUTHOR]