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Abstract In the current era, IoT-based healthcare solutions play a pivotal role in transforming the healthcare landscape by addressing key challenges and significantly enhancing the quality, accessibility, and efficiency of medical services, particularly for individuals in remote areas. This paper introduces innovative operations on fractional fuzzy sets (FFS), specifically the Hamacher sum and product, and establishes corresponding operational laws. Building upon these foundations, we propose novel aggregation operators (AoPs) leveraging Hamacher norms and rigorously analyze their properties within the FFS framework. Furthermore, we integrate these advancements into decision-making methodologies, including Extended TOPSIS, TODIM, and Extended GRA, tailored for applications in FFS. To illustrate the practicality and effectiveness of our approach, we present a detailed case study on healthcare system selection. Finally, a comparative analysis of the proposed methods with existing aggregation operators highlights the robustness and suitability of our solution in real-world scenarios. more...

The normal wiggly probabilistic hesitant fuzzy set (NWPHFS) enhances the conventional probabilistic hesitant fuzzy set (PHFS) by capturing not only explicit probabilistic information but also critical underlying details that may be hidden in the original inputs provided by decision-makers (DMs). This paper introduces a novel extension of the Tomada de Decisão Interativa Multicritério (TODIM) method, called the normal wiggly probabilistic hesitant fuzzy TODIM (NWPHFT) method based on the proposed distance measures of NWPHFSs. Initially, two novel basic operations over NWPHFSs—the subtraction and division operations—are defined. Additionally, several distance measures specific to normal wiggly probabilistic hesitant fuzzy sets are developed, and their properties are thoroughly examined. Furthermore, for scenarios where the weights of criteria are partially or completely unknown, two optimization models are established to determine these weights using the maximizing deviation approach and the Lagrange function technique, respectively. Next, the traditional TODIM approach is extended to develop the NWPHFT for addressing MCDM problems by utilizing the proposed distance measures and criteria weight determination models. The proposed method is then applied to a problem related to selecting solid waste disposal methods to demonstrate its practical applicability. Finally, comprehensive sensitivity analyses and comparisons are conducted to illustrate the stability and effectiveness of the proposed approach. more...

Aiming at the defects of the existing probabilistic hesitation fuzzy distance measures, which require the number of membership degree to be consistent and the order to be rearranged, a probabilistic hesitation fuzzy multi-attribute decision making method based on the comprehensive characteristic distance measure is proposed. First, a new law of probability hesitant fuzzy number comparison is defined. Then four characteristics of aggregation, discreteness, fuzziness and consistency are defined, and a new comprehensive distance measure is defined based on definitions above. Finally, on the basis of traditional TODIM method and prospect theory, the validity and rationality of the distance measure and new probability hesitant fuzzy recognition method in this paper are verified by examples and comparative analysis. more...

Abstract The primary objective of this research is to examine how the Russia–Ukraine war impacted the global economy. To achieve this goal, we propose operational laws, a score and accuracy function, and a divergence measure for complex dual hesitant fuzzy sets. Furthermore, we investigate the challenges associated with multi-criteria decision-making (MCR) using aggregation operators and the TODIM method with complex dual hesitant fuzzy (CDHF) information. Drawing inspiration from arithmetic aggregation operations, we introduce several aggregation operators for complex dual hesitant fuzzy information, including the complex dual hesitant fuzzy weighted average (CDHFWA) operator, complex dual hesitant fuzzy ordered weighted average (CDHFOWA) operator, and complex dual hesitant fuzzy hybrid average (CDHFHA) operator. We thoroughly analyze the unique characteristics of these proposed operators and use them in conjunction with the TODIM method to develop practical approaches for solving complex dual hesitant fuzzy multi-criteria decision-making problems. To validate our approach and demonstrate its applicability, we provide a practical example of how the Russia–Ukraine war affected the global economy. Our study confirms the effectiveness of our approach and highlights how it can be used to solve real-world problems. more...

The probabilistic hesitant fuzzy sets (P-HFSs) allow experts to express their preferences regarding different membership degrees with probabilistic information. Fuzzy entropy is an important concept to measure the uncertainty of probabilistic hesitant fuzzy information. In this paper, we propose a novel fuzzy entropy named as the exponential probabilistic hesitant fuzzy entropy for the P-HFEs. This novel fuzzy entropy not only observes the basic property of fuzzy entropy, but also has the same characteristics and change tends with the existing fuzzy entropy proposed and studied by other scholars. Then, based on the cardinal reconciliation method and TODIM(Tomada de decisao interativa multicriterio) method, we propose a multi-criteria decision-making (MCDM) problem, where the attribute weight is determined by the exponential probabilistic hesitant fuzzy entropy of the integration results. Finally, a application case in green building is given for the sake of illustrating the efficiency of the MCDM problem. Numerical and theoretical results show that a MCDM problem based on the proposed novel fuzzy entropy and the TODIM method have a wide range of application. more...

In modern business environments, a competitive Supply Chain Management is crucial to business continuity. In this context, Lean, Agile, Resilient and Green (LARG), are advocated as the fundamental paradigm for a competitive Supply Chain as a whole. Various paradigms have emerged in the supply chain from the beginning, from among which there are four paradigms lean, agile, resilient and green that are important in supply chain performance and competitiveness, which are referred to as the LARG supply chain. Each of these paradigms pursues a specific mission and purpose in the supply chain. The choice of best supplier in each supply chain is based on different decision-making criteria, but the weight of each criteria varies according to the supplier's priorities. The purpose of this research is to provide a hybrid model of multi-criteria decision for selecting suppliers in the LARG paradigms of tile and ceramic industry. In this research, in first, supplier selection indicators are identified and then weighted by the Best Worst Method. Subsequently, suppliers are ranked by piecewise linear value function and multi-criteria decision-making technique TODIM. This system can play an important role in improving supply chain performance in effective decision making by managers in the supplier selection process and provide results based to reality. more...

TODIM method (an acronym in Portuguese of Interactive and Multicriteria Decision Making) has attracted the attention of many scholars and achieved much success in multi-criteria decision making. Linguistic expression, as a qualitative information representation form, is much closer to human's cognition than specific numerical values. This paper combines the classical TODIM method with the continuous interval-valued linguistic term set to solve multi-criteria group decision-making problems. A distance measure of the continuous interval-valued linguistic term set is developed and then applied to develop a criteria-weighting method. In addition, the consensus level among experts are taken into account and an improved consensus reaching method is introduced to help experts reach an agreement. Subsequently, the framework of the continuous interval-valued linguistic TODIM method is introduced to show how to derive the optimal decision-making result with complicated and precise linguistic assessments in the qualitative situation. A case study concerning the green supplier selection for a food company is provided to verify the feasibility and practicality of the proposed method. Finally, the comparisons with other ranking methods are provided to demonstrate the advantages of the proposed method. more...

The paper focuses on the application of TODIM (TOmada de Decisao Interativa Multicriterio), which means in Portuguese ‘interactive and multi-criteria decision making’) method in identify-ing the most attractive and affordable under-construction housing project in the city of Kolkata in India. In this decision making problem, 14 under-construction housing projects spanning in and around Kolkata are evaluated with respect to ten important criteria. The deployment of TODIM method can well be validated with respect to its ability to deal with both qualitative and quantitative criteria in the presence of risk factors. This method is also acknowledged to be a robust tool being almost unaffected by the varying values of the attenuation factor of losses. Using TODIM method, an under-construction housing project at Rajarhat in the eastern fringes of Kolkata city is selected as the optimal choice while meeting the requirements of investors, inhabitants and other stakeholders. more...

Fuzzy information in venture capital can be well expressed by neutrosophic numbers, and TODIM method is an effective tool for multi-attribute decision-making. The distance measure is an essential step in TODIM method. The keystone of this paper is to define several new distance measures, in particular the improved interval neutrosophic Euclidean distance, and these measures are applied in the TODIM method for multi-attribute decision-making. Firstly, the normalized generalized interval neutrosophic Hausdorff distance is defined and proved to be valid in this paper. Secondly, we define a weighted parameter interval neutrosophic distance and discuss whether different weight parameters affect the decision result based on TODIM method. Thirdly, considering the preference perspective of decision-makers in behavioral economics, we define the improved interval neutrosophic Euclidean distance with the known parameter of risk preference. Finally, an application example is given to compare the effects of different parameters on the result and discuss the feasibility of these two distance measures in TODIM method. more...

Nowadays robots have been commonly adopted in various manufacturing industries to improve product quality and productivity. The selection of the best robot to suit a specific production setting is a difficult decision making task for manufacturers because of the increase in complexity and number of robot systems. In this paper, we explore two key issues of robot evaluation and selection: the representation of decision makers’ diversified assessments and the determination of the ranking of available robots. Specifically, a decision support model which utilizes cloud model and TODIM (an acronym in Portuguese of interactive and multiple criteria decision making) method is developed for the purpose of handling robot selection problems with hesitant linguistic information. Besides, we use an entropy-based combination weighting technique to estimate the weights of evaluation criteria. Finally, we illustrate the proposed cloud TODIM approach with a robot selection example for an automobile manufacturer, and further validate its effectiveness and benefits via a comparative analysis. The results show that the proposed robot selection model has some unique advantages, which is more realistic and flexible for robot selection under a complex and uncertain environment. more...

Este artigo apresenta uma aplicação do método Utilité Additive - UTA e de sua variante Utilité Additive- CRiteria - UTA-CR à determinação das funções de utilidade para se abordar o problema da avaliação de imóveis residenciais. Ambos os métodos pertencem à Escola Americana de Apoio Multicritério à Decisão e visam determinar funções de utilidades dos critérios presentes na análise, baseando-se em informações a priori dos decisores. Pelo emprego dos modelos matemáticos referentes a cada uma das metodologias, verificam-se as vantagens do método UTA-CR. Observa-se ainda que o método UTA-CR faz uso das preferências dos decisores em relação ao conjunto de critérios, obtendo funções de utilidades o mais próximo possível das preferências dos decisores.This article presents an application of the UTA method and its variant UTA-CR to the determination of the utility functions for tackling the problem of evaluating residential real estate. Both methods belong to the American School of Multicriteria Decision Aiding. By using these methods, it is possible to determine the utility function of the CRiteria present in the evaluation analysis making use of previous information from the decision makers. The advantages of UTA-CR method over UTA are identified through the employment of the mathematical models embedded in each method. It can be observed that UTA-CR method makes use of decision-makers' preferences with respect to the CRiteria that lead to utility functions which are as close as possible to their preferences. more...

Hesitant fuzzy linguistic term sets (HFLTSs) are very useful for dealing with the situations in which the decision makers hesitate among several linguistic terms to assess an alternative. Some multi-criteria decision-making (MCDM) methods have been developed to deal with HFLTSs. These methods are derived under the assumption that the decision maker is completely rational and do not consider the decision maker's psychological behavior. But some studies about behavioral experiments have shown that the decision maker is bounded rational in decision processes and the behavior of the decision maker plays an important role in decision analysis. In this paper, we extend the classical TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method to solve MCDM problems dealing with HFLTSs and considering the decision maker's psychological behavior. A novel score function to compare HFLTSs more effectively is defined. This function is also used in the proposed TODIM method. Finally, a decision-making problem that concerns the evaluation and ranking of several telecommunications service providers is used to illustrate the validity and applicability of the proposed method. more...

Recently, the TODIM has been used to solve multiple attribute decision making (MADM) problems. The single-valued neutrosophic sets (SVNSs) are useful tools to depict the uncertainty of the MADM. In this paper, we will extend the TODIM method to the MADM with the single-valued neutrosophic numbers (SVNNs). Firstly, the definition, comparison, and distance of SVNNs are briefly presented, and the steps of the classical TODIM method for MADM problems are introduced. Then, the extended classical TODIM method is proposed to deal with MADM problems with the SVNNs, and its significant characteristic is that it can fully consider the decision makers’ bounded rationality which is a real action in decision making. Furthermore, we extend the proposed model to interval neutrosophic sets (INSs). Finally, a numerical example is proposed. more...