Interval-valued Fuzzy Numbers Research Articles

Complex Pythagorean Normal Interval-Valued Fuzzy Aggregation Operators for Solving Medical Diagnosis Problem

This paper presents a new methodology for solving multiple-attribute decision-making problems (MADMs) using a complex Pythagorean normal interval-valued fuzzy set (CPNIVFS), which is an extended concept of a complex Pythagorean fuzzy set. Four types of different aggregating operations (AOs), including CPNIVF weighted averaging (CPNIVFWA), CPNIVF weighted geometric (CPNIVFWG), generalized CPNIVFWA (CGPNIVFWA), and generalized CPNIVFWG (CGPNIVFWG), are discussed. The scoring function, accuracy function, and operational laws of the CPNIVFS are defined. Algebraic structures, such as associative, distributive, idempotent, bounded, commutativity, and monotonicity properties, are also shown to be satisfied by complex Pythagorean normal interval-valued fuzzy numbers. Furthermore, an algorithm is proposed to solve the MADM problems based on the defined AOs. The proposed approach is then used for a medical diagnosis problem about brain tumors because computer science and machine tool technology are among the most important components of brain tumor research. The five types of brain tumors diagnosed in these patients are gliomas, meningiomas, metastases, embryonal tumors, and ependymomas. Several types of treatments are available, which are often combined as part of an overall treatment plan. Brain tumors can be treated in various ways, including surgery, radiation therapy, chemotherapy, immunotherapy, and clinical trials. Based on the comparisons and options gathered, the most suitable treatment can be chosen. In this regard, it is evident that the value of the integer ⅁\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Game $$\\end{document} plays a significant role in determining the model. The candidate models under consideration can be validated by comparing them with the previously proposed ones. The proposed technique is compared with the existing method to demonstrate its superiority and validity, and the results conclude that the former is more reliable and effective than the latter. Finally, the criteria are evaluated by expert assessments to determine the most appropriate options.

A multi-objective model for selecting response strategies of primary and secondary project risks under interval-valued fuzzy uncertainty

Risks are uncertain events that can affect criteria such as project cost, quality, and completion time and ultimately lead to project failure. That is why the project risk management process, which is one of the most fundamental parts of project management, must be done properly. In this paper, a new multi-objective fuzzy model is proposed to respond appropriately to the primary and secondary project risks. The contributions, such as risk interdependency, considering the project with multi-mode activities, resource considerations, as well as attention to interval-valued fuzzy uncertainties are regarded simultaneously for the first time. The purpose of the proposed multi-objective mathematical model is to minimize cost, quality reduction, and project completion time. Then, a new two-stage uncertain solution approach is introduced in this paper. In this solution approach, using the equivalent method in the first step and then using the extended multi-choice goal programming method in the second step, for both the lower and upper limits of the membership functions for interval-valued fuzzy numbers, the computational processes are performed. To show the application and effectiveness of the proposed model, a case study adapted from the literature is given. Finally, sensitivity analysis is conducted to analyze the behavior of the developed mixed-integer programming model. The analysis of obtained results indicates that the utilization of the proposed model leads to better and more appropriate solutions.

Ride-Hailing Matching with Uncertain Travel Time: A Novel Interval-Valued Fuzzy Multi-Objective Linear Programming Approach

This study introduces an innovative approach to tackle multi-objective linear programming (MOLP) problems amidst uncertainty, employing interval-valued fuzzy numbers. The method is tailored to resolve ride-hailing matching challenges encompassing uncertain travel times. Findings reveal that managing uncertainty parameters within interval-valued fuzzy MOLP is achieved through strategic reformulations, focusing on constraint coefficients, resulting in streamlined linear programming formulations conducive to solution simplicity. The efficacy of the proposed model in efficiently handling ride-hailing matching quandaries is demonstrated. Moreover, this study delves into the prospective applications of the developed method, including its potential for generalization to address non-linear programming (NLP) issues pertinent to the ride-hailing domain. This research advances decision-making processes under uncertainty and paves the way for broader applications beyond ride-hailing.

Ride-Hailing Assignment Problem under Waiting Time Uncertainty using Interval-Valued Fuzzy Quadratic

Ride-hailing is a creative idea created by transportation supported by science and technology. Ride-hailing services can help daily community activities. The issue with ride-hailing is that traffic conditions are unpredictable, implying that waiting times are uncertain. The time passengers spend waiting from when they book a ride service until the driver arrives at the pick-up location is called waiting time. This study suggests a quadratic programming technique for minimizing waiting time while accounting for the unpredictability of pick-up travel time. The interval-valued fuzzy quadratic programming method handles the uncertainty and imprecision of the anticipated journey time. When allocating drivers to pick up passengers, interval-valued fuzzy numbers can provide a more realistic representation of waiting time uncertainty. As a result, the interval-valued fuzzy quadratic programming model can handle the uncertainty in waiting time for ride-hailing assignment problems. The model's performance is evaluated using waiting time and the number of people served. The model's performance is demonstrated numerically using the simulation-based case study. This study shows how to utilize a mathematical method to solve real-world problems with uncertainty and improve user welfare.

On n-polygonal interval-valued fuzzy numbers and application in e-commerce risk assessment

The polygonal interval-valued fuzzy number is constructed based on the polygonal fuzzy number and the interval-valued fuzzy number. Its main feature is that the linear operation of finite ordered points reduces the complexity of traditional interval-valued fuzzy number operations. This research presents a generalized distance formula between two polygonal interval-valued fuzzy numbers and explores topological properties under the distance of polygonal interval-valued fuzzy numbers. In addition, we adopt the TOPSIS (technique for order preference by similarity to an ideal solution) and prospect theory approach for the multi-attribute decision-making problem. The information of attributes describes with polygonal interval-valued fuzzy numbers, and we then implement optimized ranking on the alternatives according to the profit and loss ratio. Finally, we verify the effectiveness and practicability of the decision-making method and fuzzy numbers at polygonal interval-valued fuzzy numbers in e-commerce risk assessment.

Enhancing Contractor Selection Process by a New Interval-Valued Fuzzy Decision-Making Model Based on SWARA and CoCoSo Methods

Contractor selection is a crucial aspect of construction projects, with a significant impact on project success. However, traditional methods may not effectively handle the complexities and uncertainties involved in decision-making. To address this, advanced techniques like Multi-Criteria Decision-Making (MCDM) have been developed. In this study, we propose a new approach based on two uncertain methods, Interval-Valued Fuzzy Step-Wise Weight Assessment Ratio Analysis (IVF-SWARA) and Interval-Valued Fuzzy Combined Compromise Solution (IVF-CoCoSo), for contractor selection in construction projects. These methods use interval-valued fuzzy numbers (IVFNs) to handle decision-making under uncertainty and imprecision. By leveraging the benefits of IVFNs, the proposed methods enhance accuracy and flexibility, enabling more informed and reliable decisions. An application example illustrates the effectiveness of the methods, and sensitivity analysis examines how varying criteria weights affect contractor rankings. The study concludes that the IVF-SWARA and IVF-CoCoSo methods assist decision-makers in selecting suitable contractors and achieving project success. These methods provide a robust framework to navigate complexities and uncertainties, leading to improved decision-making in contractor selection for construction projects.

Various defuzzification and ranking techniques for the heptagonal fuzzy number to prioritize the vulnerable countries of stroke disease

The idea of fuzzy numbers is determined according to their uncertainty points, which include interval values, triangular, trapezoidal, and heptagonal fuzzy numbers, etc. This article contains two types of fuzzy numbers: the heptagonal fuzzy number (HpFN) and heptagonal interval-valued fuzzy numbers (HpIVFN). For both the HpFN and HpIVFNs, the new distinct rational perspective and viewpoints are presented. First, the membership function (MF) is generalized to the linear and non-linear for observing the symmetric and asymmetric HpFN and HpIVFN. In light of this, α-cut is constructed for both linear and non-linear MF of HpFN and HpIVFN. The various types of HpIVFNs are classified along with the graphical representation. Then, new defuzzification under HpFN is determined using three methods, namely the centroid method, mean of α-cut method, and removal of area methods, and a comparison is demonstrated. A ranking method is also performed for HpFN. Using the proposed defuzzification approach in the weighted aggregates sum product assessment (WASPAS) method, an analysis is conducted to identify the countries with the highest vulnerability to stroke disease. The results indicated that world Bank upper-middle-income countries is significantly affected by stroke disease. The obtained outcome is validated through comparative and sensitivity analyses.

Green multiple-criteria decision-making method of selection of diamond cutting tool for promoting cleaner production in the natural stone industry

Selection of a reasonable diamond cutting tool (DCT) is a crucial Multiple Criteria Decision-Making (MCDM) problem for promoting cleaner production for a natural stone company. It has severe uncertainties in the decision information, complex interdependences among the DM criteria and needs to balance stakeholders' opinions and adopt the non-complete compensation idea in the DM process. This paper establishes a specialized index system with changing the evaluation object from ontology of DCT to the ‘stone machining system’ within the boundary demarcated by LCA. Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is applied to analyze the interdependence relationships existing in the index system and then the indicators' weights can be obtained by Analytic Network Process (ANP) method. In order to avoid complete compensation among indicators, Preference Ranking Organization Method for Enrichment Evaluations II (PROMETHEE II) method is used to prioritize the alternatives and identify the most reasonable DCT. The new developed MCDM algorithm is expressed based on interval-valued fuzzy set (IVFS) theory to handle the uncertain information in DM process. Integration of IVFS theory with MCDM method allows the decision-maker to use linguistic variables which correspond to interval-valued fuzzy numbers to describe their judgments and ensures all the stakeholders' preferences can be trade-off in the DM process. In the case application, the proposed method has been applied to select a suitable DCT to cut the Lotus red granite (G3768) for a stone processing company in China. As a result, the iron-based DCT (TJ-15) obtained the highest priority net flow (0.373) among five DCT alternatives and it was identified as the most reasonable DCT for the case company. The application study demonstrates the effectiveness and robustness of the developed method and indicates that pursuit of matching DCT with the characteristics of natural stone is more rational than blindly adopting more advanced and expensive DCT.

Sustainability performance analysis of micro-mobility solutions in urban transportation with a novel IVFNN-Delphi-LOPCOW-CoCoSo framework

Almost all megacities worldwide are under pressure from environmental pollution and excessive resource usage due to rapid urbanization and increasing urban population. Within this scope, micro-mobility solutions (MMSs), an extension to the primary urban transportation network, have become even more critical recently. However, when we executed a preliminary investigation concerning MMSs' sustainability, we noted some critical theoretical and managerial gaps: (1) the number of studies assessing MMSs using decision-making approaches is excessively scarce, (2) no paper in the literature deals with the MMSs' sustainability performance, and (3) there are no commonly accepted criteria set to assess the sustainability of the MMSs in the literature. The current study aims to present a practical and robust decision-making framework that can overcome excessively complicated uncertainties to evaluate the sustainability performance of MMSs. Further, it suggests a novel methodological framework, i.e., Delphi, LogarithmicPercentageChange-DrivenObjectiveWeighting (LOPCOW), and Combined Compromise Solution (CoCoSo) methods with interval-valued fuzzy neutrosophic number (IVFNN) information, which can be defined as a reconciliation tool to set the criteria affecting the assessment processes. Findings present that computing time, scenic adoption, and accidents are the foremost criteria, whereas mini-electric VH, powered standing scooter, and powered seated scooter are the most promising MMSs, respectively. Findings reveal that computing time, scenic adoption, and accidents are the critical factors for the sustainability assessment of MMSs, whereas mini-electric VH, powered standing scooter, and powered seated scooter are the most promising MMSs, respectively. The current paper's overall outcomes and findings can assist practitioners and policy-makers in the urban transportation industry in setting sustainability policies and investing in the more rational and sustainable MMSs.

Extending Quality Function Deployment and Analytic Hierarchy Process under Interval-Valued Fuzzy Environment for Evaluating Port Sustainability

To confront the related problems of environmental protection, energy saving, and carbon reduction, sustainability has been a prominent issue for enterprises seeking to meet the requirements of the Earth Summit’ sustainable development goals (SDGs). Basically, sustainability evaluation of enterprises must be considered from environmental, social, and economic perspectives, recognized as quality requirements. Numerous enterprises, especially for international ports, must pay attention to these requirements in expressing their corporate social responsibility (CSR) for decreasing marine pollution. Practically, the three requirements may be dependent under uncertain environments, and rationally evaluated by fuzzy multi-criteria decision-making (FMCDM) with dependent evaluation criteria (DEC). In other words, evaluating port sustainability, containing location expanding, should belong to FMCDM with DEC. For DEC under uncertain environments, fuzzy extension of the analytic network process (ANP) is a feasible solution to solve the above problems. However, fuzzy computations of ANP are heavily complicated; thus, we desire to combine quality function deployment (QFD) with the analytic hierarchy process (AHP) under the interval-valued fuzzy environment (IVFE) into a hybrid method for evaluating port sustainability. In numerous multi-criteria decision-making (MCDM) efforts, AHP was often extended into FMCDM to encompass the imprecision and vagueness of data, but the extension was properly used for FMCDM with independent evaluation criteria (IDEC). Herein, QFD is utilized to express the dependent relationships between criteria, and thus transforms IDEC into DEC for the evaluation of port sustainability. Through the hybrid method, QFD is combined with AHP to replace ANP under IVFE, the complicated ties of ANP-corresponding interval-valued fuzzy numbers (IVFNs) are overcome, and the problem of evaluating port sustainability is rationally solved.

Approximation results by fuzzy Bernstein type rational functions via interval-valued fuzzy number

Approximation results by fuzzy Bernstein type rational functions via interval-valued fuzzy number

On modeling regression in full interval-valued fuzzy environment

We apply the general extension-principle-based approach to make predictions based on a regression model in a full interval-valued fuzzy environment. We use triangular interval-valued fuzzy numbers that model the uncertainty of the observed inputs and outputs to derive the predicted outputs in full accordance with Zadeh's extension principle. On one side, we enhance the Monte Carlo based algorithm introduced in the literature for simulating the output predictions of a fuzzy regression model by reducing the universe of random selections still keeping the accuracy of the empirical results; and on the other side, we solve quadratic models to derive the left endpoints of the α-cut intervals of the exact results. We use one real-life problem from hydrology engineering with data recalled from the literature to carry out numerical experiments and illustrate our proposed methodology.

An option pricing model with adaptive interval-valued fuzzy numbers

An option pricing model with adaptive interval-valued fuzzy numbers

An option pricing model with adaptive interval-valued fuzzy numbers

An option pricing model with adaptive interval-valued fuzzy numbers

Economic-Environment-Energy (3E) objective-driven integrated municipal waste management under deep complexities – A novel multi-objective approach

• WtE technologies compatible with recycling are integrated into the MSW system; • Multi-objective-driven integrated MSW management is optimized to achieve sustainable goals; • An interval-valued fuzzy linear programming method is developed to address uncertainties; • The subsidy is still required to encourage anaerobic digestion from the environmental aspect. Waste-to-energy technologies compatible with recycling are promising solutions for sustainable municipal waste management from both economic and environmental perspectives. This study focuses on the economic-environment-energy (3E) objective-driven integrated waste management optimization problems under deep complexities. A novel multi-objective programming model is developed to assist the optimal decision-making with the consideration of system profit, greenhouse gas emission, and energy recovery simultaneously. Besides, it advances existing optimization methods by incorporating interval-valued fuzzy numbers to tackle the ambiguity and the essential fuzziness in experts’ judgment. It was verified by a case study from an urban district of Beijing, China. The optimum waste treatment facility planning and waste stream allocation strategies with multi-objective tradeoffs were obtained to support decision-making considering different preferences of importance ranking. In general, incineration and anaerobic digestion would be the main technologies for waste disposal in the study area. Recycling would be greatly encouraged when pursuing more economic profits and greenhouse gas emission reduction. With withdrawing the subsidy in the future, the investment in anaerobic digestion would become less attractive. Meanwhile, the landfill with gas recovery would even become economically infeasible if there is no further reduction in cost. In addition, waste source separation is also a crucial factor for successful integrated waste management. It is suggested that a proper government subsidy and public participation in waste source separation would guarantee the sustainable development of the integrated waste management system.

A multi-criteria framework for addressing digitalization solutions of medical system under interval-valued T-spherical fuzzy information

With the help of Internet technology, digital reform of the medical system has gradually sprung up and begun to reconstruct the medical and health industry chain and service model, which has brought great change to the medical industry. At present, there are many digitalization solutions of medical system on the market. However, there are many differences in the technical standards, functions, prices and service objects of these solutions, and the objective environment is uncertain. At the same time, decision-makers often have subjective uncertainty when making choices. Therefore, it is difficult for decision-makers to choose the most satisfactory one from many digitalization solutions. To solve these problems, this study proposes the IVT-SFS weighted Muirhead mean (IVTSFWMM) operator, and establishes the evaluation and decision-making method of digitalization solutions of medical system based on this operator. Then we apply this method to cases and select the best performing solution from the four existing digitalization solutions of medical system in the market to prove the effectiveness of the method. The advantage of the method proposed in this study is that it can express subjective uncertainty when the decision-maker gives the evaluation information in the form of interval-valued fuzzy numbers, and the interaction between any number of indicators can be considered when aggregating indicators. The results show that the method proposed in this paper can effectively express the fuzzy evaluation information in complex environments, and provide suggestions for system designers to provide decision support for the evaluation and selection of intelligent medical solutions.

Interval-valued intuitionistic fuzzy multi-attribute group decision-making method considering risk preference of decision-makers and its application

An improved interval-valued intuitionistic fuzzy multi-attribute group decision-making method considering the risk preference of decision-makers is proposed to solve the multi-attribute group decision-making problem with interval-valued intuitionistic fuzzy numbers and the condition that the attribute weight information is completely unknown. Firstly, the decision-maker weight of each attribute is determined by combining similarity and proximity. In order to consider the influence of the decision-maker's risk preference on the decision result and avoid the asymptotic behavior of interval-valued intuitionistic fuzzy matrix, the risk aversion coefficient of the decision-maker is introduced and combined with the determined decision-maker's weight aggregation to form a group decision matrix. Then, the information of group decision matrix is mined, and the interval-valued intuitionistic fuzzy entropy is used to determine the attribute weight and relative weight. Based on the interval-valued intuitionistic fuzzy distance measure formula and the TODIM method, the overall superiority of each scheme relative to other schemes is obtained by calculating the superiority between schemes, and the optimal scheme is determined by comparing and sequencing. Finally, the rationality and effectiveness of the proposed method are verified by an example of mechanical assembly supplier selection decision.

A two stage risk assessment model based on interval-valued fuzzy numbers and risk attitudes

Due to the lack of historical data, experts often score risks based on their experience and some linguistic terms in risk assessment, then the risk assessment is essentially a semi-quantitative problem. When experts score risks, the scores are possibly related to experts’ risk attitudes. On the other hand, the linguistic terms used are inevitably ambiguous, and interval-valued fuzzy numbers can deal with linguistic uncertainty better in complex situation. So a risk analysis model based on interval-valued fuzzy numbers and risk attitudes is novelly proposed in this paper. For safety risks in oil industry, the risk consequence often performs in several aspects, some of them are difficult to be measured by money and cannot be aggregated to a comprehensive index directly. A multi-expert and multi-criterion information fusion(MEMC-IF) model is needed. Firstly, linguistic terms and interval-valued fuzzy numbers are determined and a MEMC-IF model is constructed to derive the collective data and the comprehensive risk consequence. Secondly, a defuzzification model is presented to transform interval-valued fuzzy numbers to crisp values with considering risk attitudes novelly. Then, a risk matrix is constructed to assess which risks are serious and which risks can be ignored. In addition, a case study is demonstrated to show the efficiency of the proposed model and a discussion is completed.

Estimation of Construction Activity Duration Under Uncertainty Using Discrete Fuzzy Weighted Average Algorithm

This paper presents a qualitative risk assessment tool based on fuzzy set theory to estimate the amount of activity duration overrun under the combinatory effect of multiple risk factors. Applying proposed methodology, a set of duration modifiers to calculate the optimistic, most-likely and pessimistic duration values under uncertainty are calculated. To elaborate the methodology, a simulated bridge project with ten risk factors affecting activities duration is presented. Proposed model contributes to knowledge that could help minimize the schedule overrun and improve risk mitigation strategies through providing risk-based duration estimates instead of discrete values. Advantages of the developed approach compared to existing models include (1) considering the combinatory effect of multiple risk factors on activity duration, (2) accounting for uncertainty in experts’ evaluations by employing the interval-valued fuzzy numbers, and (3) utilizing a discrete fuzzy weighted average algorithm which avoids creation of incorrect fuzzy membership functions.

A Bi-Objective Model for Scheduling Construction Projects Using Critical Chain Method and Interval-Valued Fuzzy Sets

Numerous constraints affect construction projects, and lack of management may lead to schedule deviation. In the execution phase of the project, due to the lack of timely access to the required resources and the existence of uncertainty, the project activities do not progress following the schedule, and as a result, schedule deviation occurs. The scheduling addresses resource constraints by the critical chain method and deals with delays in activities by placing buffers that have emerged as a method for scheduling construction projects. This paper presents a new bi-objective mathematical model which aims to reduce delay and increase quality, based on the critical chain method and resource constraint for scheduling construction projects. In the proposed model, the activities have been considered multi-mode ones. Moreover, this paper has assumed each activity to be executed in a normal or crashing way. Due to the uncertainty in real-world problems, the duration of the activity is expressed using triangular interval-valued fuzzy numbers. A new interval-valued fuzzy solution process is presented in this paper using a two-step approach. First, the equivalent crisp model is given; then in the second step, a goal programming approach is applied for transforming the bi-objective model into the single-objective one. Finally, the mathematical model is implemented on a case study adapted from the literature, and sensitivity analysis of the results is conducted.