This research contributes to the advancement of traffic state estimation and prediction methodologies by leveraging the benefits of the nonlocal LWR model within a physics-informed deep learning (PIDL) framework. The classical LWR model, while useful, falls short of accurately representing real-world traffic flows due to the assumption that traffic speed is solely dependent upon local traffic density. The nonlocal LWR model addresses this limitation by considering the speed as a weighted mean of the downstream traffic densities. In this paper, we propose a novel PIDL framework that incorporates the nonlocal LWR model paired with Greenshields and Underwood fundamental diagrams. We introduce both fixed-length and variable-length look-ahead kernels for nonlocal speed-density relationships and develop the required mathematics. The proposed PIDL framework undergoes a comprehensive evaluation, assessing various convolutional kernels and look-ahead windows using NGSIM and CitySim datasets. The results demonstrate improvements over the baseline PIDL approach using the local LWR model. The findings highlight the potential of the proposed approach to enhance the accuracy and reliability of traffic state estimation, enabling more effective traffic management strategies.

Abstract Dual hesitant q‐rung orthopair fuzzy (DHq‐ROF) set appears as a powerful tool in compare to other variants of fuzzy sets to deal with uncertainties associated with available information in various real‐life decision‐making cases. In order to make DHq‐ROF aggregation information process flexible, at first some operations viz., addition, multiplication, scalar multiplication, exponential laws based on Schweizer‐Sklar class of t‐conorms and t‐norms are defined. Subsequently, using these operations, weighted average and geometric operators and ordered weighted average and geometric operators are introduced. But weighted average or geometric operators and ordered weighted average or geometric operators consider only the weight of the opinions and the weight of the ordered position of each given opinion respectively. To resolve weights of the arguments, hybrid aggregation operators viz., DHq‐ROF Schweizer‐Sklar hybrid averaging, DHq‐ROF Schweizer‐Sklar hybrid geometric operators are developed and their properties are discussed. Afterwards, a new method to deal with multicriteria group decision making problems under DHq‐ROF environment is framed. To illustrate the proposed method a decision making problem related to investment company selection is considered and solved. To show the advantages of the proposed study, a comparative analysis among the developed and existing studies is discussed.

Abstract The objective of this paper is to develop Pythagorean fuzzy (PF) multi‐objective optimization by ratio analysis (PF‐MOORA) plus full MULTIplicative form (PF‐MULTIMOORA) method for solving multicriteria decision making (MCDM) problems with completely unknown information of criteria weights. In the model formulation process, a new distance measure is defined to quantify the difference between PF sets by combining Hamming distance and Hausdorff metric. This distance measure is, subsequently, implemented in entropy weight model for determining unknown weights of criteria, and also in reference point approach for obtaining preference indices of alternatives. To overcome the deficiencies occurred in existing MULTIMOORA method, like multiple comparisons, circular reasoning, and so on, an aggregation‐based approach is recommended in the proposed PF‐MULTIMOORA. To demonstrate the feasibility and practicality of the proposed method, an example concerning strategy prioritization of a tiles manufacturing company is presented. In the strategy evaluation process, at first, the judgement values provided by the decision maker are expressed in linguistic terms, and then those are converted into PF numbers through a PF weighting scale. The sensitivity of the proposed model is validated by changing of weights of criteria which impact on the ranks of the strategies. To show robustness of the developed method, the result attained by applying PF‐MULTIMOORA is compared with existing techniques, not only in crisp and fuzzy quantitative strategic planning matrix context, but also using four other MCDM methods, namely, modified PF‐MOORA, as a particular case of the proposed PF‐MULTIMOORA technique, PF weighted sum, PF‐TOPSIS and PF‐VIKOR.

This article presents a new family of linguistic Pythagorean fuzzy aggregation operations based on Einstein t-norms and t-conorms. Some of their necessary properties are also discussed. In the proposed method, a generalized weighted distance measure is developed using a linguistic-scale function to evaluate differences among linguistic Pythagorean fuzzy sets (LPFSs). An entropy measure is also introduced for LPFS to measure fuzziness associated with linguistic decision information. Moreover, a technique for ordering preference by similarity to ideal solution (TOPSIS)-based methodology is constructed through the newly defined concepts to address linguistic Pythagorean fuzzy multicriteria group decision-making problems, where the information about weight is either completely known or unknown. Subsequently, weights of decision makers are computed through a TOPSIS-based algorithm, and weights of criteria are evaluated by introducing a linguistic Pythagorean fuzzy entropy weight model. To minimize information loss throughout the decision-making procedure, aggregation is done at the final stage for obtaining the final ranking of alternatives. Finally, several practical examples are considered, solved, and compared with existing methods to exhibit the robustness of the proposed methodology. Also, a sensitivity analysis is performed to establish the dynamic nature of the proposed model.

In this paper, Bonferroni mean (BM) and Dombi t-conorms and t-norms (D t-CN& t-Ns) are combined under dual hesitant q-rung orthopair fuzzy (DH q-ROF) environment to produce DH q-ROF-Dombi BM, weighted Dombi BM, Dombi geometric BM, and Dombi weighted geometric BM aggregation operators (AOs). Using these operators, the decision making processes would become more flexible and also would possess the capabilities of capturing interrelationships among input arguments under imprecise decision making environments. Apart from those, a large number of AOs either already developed or not yet developed may also be derived from the proposed AOs. In the process of developing the AOs, some operational laws of DH q-ROF numbers based on D t-CN& t-Ns are defined first. Several important properties of the developed operators are discussed. The proposed AOs are used to frame a new methodology to solve multicriteria group decision making problems under DH q-ROF contexts. Several illustrative examples are solved to demonstrate effectiveness and benefits of the developed method. Sensitivity analysis is performed to show the variations of ranking values with the change of different parameters in the decision making contexts. Finally, the introduced method is compared with several existing techniques to establish superiority and effectiveness of the proposed method.

In this study, a new technique for order preference by similarity to ideal solution (TOPSIS)-based methodology is proposed to solve multicriteria group decision-making problems within Pythagorean fuzzy environment, where the information about weights of both the decision makers (DMs) and criteria are completely unknown. Initially, generalized distance measure for Pythagorean fuzzy sets (PFSs) is defined and used to initiate a new Pythagorean fuzzy entropy measure for computing weights of the criteria. In the decision-making process, at first, weights of DMs are computed using TOPSIS through the geometric distance model. Then, weights of the criteria are determined using the entropy weight model through the newly defined entropy measure for PFSs. Based on the evaluated criteria weights, TOPSIS is further applied to obtain the score value of alternatives corresponding to each decision matrix. Finally, the score values of the alternatives are aggregated with the calculated DMs’ weights to obtain the final ranking of the alternatives to avoid the loss of information, unlike other existing methods. Several numerical examples are considered, solved, and compared with the existing methods.

In multicriteria decision-making (MCDM), the existing aggregation operators are mostly based on algebraic t-conorm and t-norm. But, Archimedean t-conorms and t-norms are the generalized forms of t-conorms and t-norms which include algebraic, Einstein, Hamacher, Frank, and other types of t-conorms and t-norms. From that view point, in this paper the concepts of Archimedean t-conorm and t-norm are introduced to aggregate Pythagorean hesitant fuzzy information. Some new operational laws for Pythagorean hesitant fuzzy numbers based on Archimedean t-conorm and t-norm have been proposed. Using those operational laws, Archimedean t-conorm and t-norm-based Pythagorean hesitant fuzzy weighted averaging operator and weighted geometric operator are developed. Some of their desirable properties have also been investigated. Afterwards, these operators are applied to solve MCDM problems in Pythagorean hesitant fuzzy environment. The developed Archimedean aggregation operators are also applicable in Pythagorean fuzzy contexts also. To demonstrate the validity, practicality, and effectiveness of the proposed method, a practical problem is considered, solved, and compared with other existing method.

In this paper, a series of similarity measures based on point operators for Pythagorean fuzzy sets are proposed. Using the proposed similarity measures, two new aggregation operators, viz., Pythagorean fuzzy-dependent averaging operator and Pythagorean fuzzy-dependent geometric operator, are developed. The advantage of using these operators is that the influence of unfair arguments of aggregated results could be eliminated, since the associated weights are taken from the aggregated Pythagorean fuzzy arguments. Also, the proposed operators have the capability to adjust the degree of aggregated arguments with the controlling parameters. To establish the application potentiality of those operators, a methodology for solving multicriteria group decision-making problems having Pythagorean fuzzy arguments is developed. A numerical example is provided to demonstrate the proficiency of the proposed method. The achieved results are compared with the results of other existing technique.

The purpose of this paper is to develop a fuzzy goal programming methodology for solving quadratic multiobjective multilevel programming problems in a hierarchical decision making environment. In the proposed procedure, the tolerance membership functions in fuzzy set theory are defined first for measuring the degree of satisfactions of the objectives of each decision maker at each level. Then a nonlinear fuzzy goal programming model is formulated to achieve highest degree of each of the defined membership goals at each level to the extent possible on the basis of priorities of importance of optimizing the objectives. Afterwards the nonlinear fuzzy goals are converted into linear forms by applying a linear approximation technique. The model is then solved for measuring the degree of satisfaction of the objectives of decision makers at each level by arriving at a compromise decision regarding the optimality of the sets of decision variables controlled individually by each of them. To illustrate the proposed methodology a numerical example is solved and compared the solution with existing approaches.

This paper deals with a fuzzy goal programming methodology for solving multiobjective linear fractional chance constrained programming problems containing fuzzy numbers and exponentially distributed fuzzy random variables associated with the system constraints. In model formulation process, the problem is converted into an equivalent fuzzy programming model by applying chance constrained programming technique in a fuzzily defined probabilistic decision making situation. Then using the concept of α-cut for fuzzy numbers and by considering the tolerance level of fuzzy numbers the problem reduces to an equivalent sub problem with interval coefficients. In this method the convex combination of each interval is used and the problem is reduced to a nonlinear programming problem. Finally the model is solved by converting nonlinear model into its equivalent multiobjective linear programming model by using Taylor series; and a priority based fuzzy goal programming method is used for achievement of the highest membership degree. To demonstrate the efficiency of the proposed technique an illustrative example, studied previously, is solved and the solution is compared with the existing methodology.