Interval-valued Fuzzy Environment Research Articles

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.

Programming models-based method for deriving profits allocation scheme with interval-valued cooperative games

Owing to the fact that the payoff of grand coalition is limited to players’ allocation, what is more, other players will not satisfy with the allocation scheme if one of the possible coalitions allocate too much. Based on this fact, it is better to pursuit the allocation scheme of all players in coalition are as close to the coalition’s payoff as possible. In contrast, if the allocation scheme of all players in coalition is far from the coalition’s payoff, this will lead to the instability of the coalition. To address this issue, several linear programming models are constructed for taking into account the players in the coalition with compromise limit constraints. First, the profits allocation model with undominated nonnegative excess vector is extended to interval-valued fuzzy environments. Second, several linear programming models are constructed respectively considering without and with coalitions’ compromise limit constraints. Third, an illustrative example in conjunction with comparative analyses is employed to demonstrate the validity and applicability of the proposed models. Finally, the relationship of the models is discussed between without and with coalitions’ compromise limit constraints.

Weight computation of criteria in a decision-making problem by entropy measure under interval-valued fuzzy environment

Weight computation of criteria in a decision-making problem by entropy measure under interval-valued fuzzy environment

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.

Interval-Valued Fuzzy Multi-Criteria Decision-Making with Dependent Evaluation Criteria for Evaluating Service Performance of International Container Ports

Due to COVID-19 barriers, the needs of international container ports have become more important than in the past. Therefore, it is very critical and essential for the scientific developments of port-logistics. To gain the scientific developments of port logistics, effective and efficient evaluation methods for decision-making are indispensable, especially for assessing service performance of international container ports based on dependent evaluation criteria (DEC). Among numerous decision-making methods, technique for order preference by similarity to ideal solution (TOPSIS) was often expanded under fuzzy environments into fuzzy multi-criteria decision-making (FMCDM) to preserve imprecise messages. The FMCDM was able to be associated with quality function deployment (QFD) into a hybrid method to solve problems with DEC. To gain more messages, QFD and TOPSIS are combined and then expanded under interval-valued fuzzy environment (IVFE) to solve a FMCDM problem with DEC. Practically, evaluating service performance of international container ports in Taiwan and the surrounding sea areas is considered a problem with DEC because the related evaluation criteria are partially connected. By the hybrid method of combining QFD with TOPSIS under IVFE, international container ports with DEC are effectively and efficiently evaluated for service performance, and more insights are gained than the past for establishing essential fundamentals in recent scientific developments of port logistics on account of breaking down COVID-19 barriers.

Interval-Valued Fuzzy Multi-Criteria Decision-Making by Combining Analytic Hierarchy Process with Utility Representation Function

To encompass uncertainty and vagueness of information, the analytic hierarchy process (AHP) was often extended into fuzzy multi-criteria decision-making (FMCDM) under an uncertain environment. However, the extension of AHP was rarely constructed on interval-valued fuzzy numbers. Recently, interval-valued fuzzy numbers were utilized for decision-making to obtain more messages than others. For AHP extended under a fuzzy environment into fuzzy AHP, fuzzy computations are critical to derive priorities of pairwise comparison matrices. Although AHP’s approximate computations including the normalization of row arithmetic averages may be adopted to the fuzzy environment, the fuzzy extension of AHP is still complicated for division and multiplication of fuzzy numbers, especially interval-valued fuzzy numbers. To resolve complicated ties, a utility representation function of interval-valued fuzzy numbers in fuzzy AHP is used for yielding vectors consisting of priority representations of fuzzy pairwise comparison matrices on evaluation criteria based on objective, alternatives based on evaluation criteria, and more hierarchies. Then, sum product of multiplying the priority representation vectors is derived to form the utility representations of alternative performance indices, and alternative performance indices are represented by their corresponding utility representations. Therefore, FMCDM problems are easily solved by fuzzy AHP, i.e., combining AHP with the utility representation function under an interval-valued fuzzy environment.

Group Decision-Making Problems Based on Mixed Aggregation Operations of Interval-Valued Fuzzy and Entropy Elements in Single- and Interval-Valued Fuzzy Environments

Fuzzy sets and interval-valued fuzzy sets are two kinds of fuzzy information expression forms in real uncertain and vague environments. Their mixed multivalued information expression and operational problems are very challenging and indispensable issues in group decision-making (GDM) problems. To solve single- and interval-valued fuzzy multivalued hybrid information expression, operations, and GDM issues, this study first presents the notion of a single- and interval-valued fuzzy multivalued set/element (SIVFMS/SIVFME) with identical and/or different fuzzy values. To effectively solve operational problems for various SIVFME lengths, SIVFMS/SIVFME is converted into the interval-valued fuzzy and entropy set/element (IVFES/IVFEE) based on the mean and information entropy of SIVFME. Then, the operational relationships of IVFEEs and the expected value function and sorting rules of IVFEEs are defined. Next, the IVFEE weighted averaging and geometric operators and their mixed-weighted-averaging operation are proposed. In terms of the mixed-weighted-averaging operation and expected value function of IVFEEs, a GDM method is developed to solve multicriteria GDM problems in the environment of SIVFMSs. Finally, the proposed GDM method was utilized for a supplier selection problem in a supply chain as an actual sample to show the rationality and efficiency of SIVFMSs. Through the comparative analysis of relative decision-making methods, we found the superiority of this study in that the developed GDM method not only compensates for the defects of existing GDM methods, but also makes the GDM process more reasonable and flexible.

An extended TDM method under probabilistic interval-valued hesitant fuzzy environment for stock selection.

Generally, in real decision-making, all the pieces of information are used to find the optimal alternatives. However, in many cases, the decision-makers (DMs) only want “how good/bad a thing can become.” One possibility is to classify the alternatives based on minimum (tail) information instead of using all the data to select the optimal options. By considering the opportunity, we first introduce the value at risk (VaR), which is used in the financial field, and the probabilistic interval-valued hesitant fuzzy set (PIVHFS), which is the generalization of the probabilistic hesitant fuzzy set (PHFS). Second, deemed value at risk (DVaR) and reckoned value at risk (RVaR) are proposed to measure the tail information under the probabilistic interval-valued hesitant fuzzy (PIVHF) environment. We proved that RVaR is more suitable than DVaR to differentiate the PIVHFEs with example. After that, a novel complete group decision-making model with PIVHFS is put forward. This study aims to determine the most appropriate alternative using only tail information under the PIVHF environment. Finally, the proposed methods’ practicality and effectiveness are tested using a stock selection example by selecting the ideal stock for four recently enrolled stocks in China. By using the novel group decision-making model under the environment of PIVHFS, we see that the best stock is E4 when the distributors focus on the criteria against 10% certainty degree and E1 is the best against the degree of 20%, 30%, 40% and 50% using the DVaR method. On the other hand when RVaR method is used then the best alternative is E4 and the worst is E2 against the different certainty degrees. Furthermore, a comparative analysis with the existing process is presented under the PHF environment to illustrate the effectiveness of the presented approaches.

A new fuzzy-stochastic compromise ratio approach for green supplier selection problem with interval-valued possibilistic statistical information

Organizations must regard environmental and green concepts in their decision-makings and all of the significant tasks in supplier selection process for the supply chain. For this purpose, the evaluation of conflicting criteria with environmental and conventional approaches can be simultaneously considered in the green supplier selection problem (GSSP). This paper introduces a novel group decision-making process with Monte Carlo simulation under interval-valued fuzzy and stochastic environments for solving the GSSPs. The proposed compromise ratio model includes some main phases: (1) weighting and rating phase, (2) aggregating phase, (3) simulating phase, and (4) ranking phase. New separation measure matrixes are developed with an interval-valued fuzzy possibilistic statistical approach. Then, new distinguish indexes and new final score index are presented to indicate the last inclination arrangement of green supplier candidates. An application example in the GSSP is provided from the recent literature to show the applicability of proposed interval-valued fuzzy-stochastic group decision model. Finally, a comparative analysis is conducted to highlight the advantages of the model in comparison with similar decision methods.

Weight Computation of Criteria in a Decision Making Problem by Entropy Measure Under Interval-Valued Fuzzy Environment

Weight Computation of Criteria in a Decision Making Problem by Entropy Measure Under Interval-Valued Fuzzy Environment

Infectious Waste Management Strategy during COVID-19 Pandemic in Africa: an Integrated Decision-Making Framework for Selecting Sustainable Technologies.

The emerging and underdeveloped countries in Africa face numerous difficulties managing infectious waste during the SARS-CoV-2 disease, known as the COVID-19 pandemic. Hence, the main aim of this paper is to help decision-makers in African countries to select the best available waste management strategy during the COVID-19 pandemic. The present research undertakes seamless assessment and prioritization of infectious solid waste (SW) and wastewater (WW) treatment technologies based on a criteria system involving four dimensions, i.e., environment-safety, technology, economics, and sociopolitics. A combined approach that integrates the results of life-cycle assessments and life-cycle costs (LCA–LCC), analytic hierarchy process (AHP), and VIKOR method in an interval-valued fuzzy (IVF) environment is proposed. The results reveal that combined incineration and chemical disinfection approach, and combined chlorination and ultraviolet irradiation are the most sustainable technologies for managing infectious SW and WW treatment in the present context. The proposed approach, alongside the findings of the study, constitutes a reference to devise urgent planning for contagious waste management in African countries as well as developing countries worldwide.

A New Version of Earned Value Analysis for Mega Projects Under Interval-valued Fuzzy Environment

The earned value technique is a crucial and important technique in analysis and control the performance and progress of mega projects by integrating three elements of them, i.e., time, cost and scope. This paper proposes a new version of earned value analysis (EVA) to handle uncertainty in mega projects under interval-valued fuzzy (IVF)-environment. Considering that uncertainty is very common in mega projects’ activities, the proposed IVF-EVA model is very useful and applicable in evaluating the progress of projects. In this paper, analyzing earned value indices and calculating them with linguistic terms have been discussed. They are then converted into interval-valued fuzzy numbers (IVFNs) for the evaluations. Finally, an application example from the recent literature is presented and steps of the proposed IVF-EVA are elaborated.

Combining technique for order preference by similarity to ideal solution with relative preference relation for interval-valued fuzzy multi-criteria decision-making

In the past, technique for order preference by similarity to ideal solution (TOPSIS) was one of multi-criteria decision-making (MCDM) methods and often extended into a fuzzy multi-criteria decision-making (FMCDM) one for encompassing uncertainty and vagueness messages. Obviously, TOPSIS extended under fuzzy environment is useful to solve FMCDM problems, but the extension only constructed on general fuzzy numbers (i.e., triangular or trapezoidal fuzzy ones), not interval-valued fuzzy ones. In real world, the recent decision-making process is getting complicated and thus more information now must be grasped than ever. For presenting varied and added data, general fuzzy numbers may not be adequate, whereas interval-valued fuzzy numbers are suitable. Based on above, TOPSIS should be extended under interval-valued fuzzy environment. In this paper, we associate TOPSIS with a relative preference relation under interval-valued fuzzy environment into interval-valued FMCDM for dealing with complicated decision-making problems to obtain more information. The proposed relative preference relation as similar as Wang’s relative preference relation is also improved from Lee’s fuzzy preference relation on general fuzzy numbers. An important difference is the proposed relative preference relation used on interval-valued fuzzy numbers, but Wang’s relative preference relation is utilized on triangular fuzzy numbers. Through the combination of TOPSIS and relative preference relation under interval-valued fuzzy environment, interval-valued FMCDM can be feasibly and rationally finished.

Research on robust recruitment optimization in interval-valued fuzzy evaluation environments

Research on robust recruitment optimization in interval-valued fuzzy evaluation environments

Combining quality function deployment with simple additive weighting for interval-valued fuzzy multi-criteria decision-making with dependent evaluation criteria

In the past, lots of multi-criteria decision-making (MCDM) methods included simple additive weighting (SAW) extended under fuzzy environment into multi-criteria decision-making (FMCDM) methods to encompass uncertainty and vagueness of data. The extensions were first used in FMCDM with independent evaluation criteria, and then, FMCDM could be associated with quality function deployment (QFD) to break the tie of dependent evaluation criteria. Commonly, alternative ratings and criteria weights in FMCDM were expressed by general fuzzy numbers (i.e., triangular or trapezoidal fuzzy numbers). Recently, some approaches proposed FMCDM with independent evaluation criteria under interval-valued fuzzy environment. For interval-valued fuzzy numbers, FMCDM with dependent evaluation criteria was scarcely elaborated due to computation complexity. Besides, QFD was also generalized under some fuzzy environments consisting of triangular fuzzy numbers or trapezoidal fuzzy numbers, but not interval-valued fuzzy environment. Practically, interval-valued fuzzy numbers are deemed as a kind of fuzzy number that can grasp more information than other fuzzy numbers, but the kind of fuzzy number is more complex on computation than others. Based on above, we desire to extend QFD and SAW under interval-valued fuzzy environment for FMCDM with dependent evaluation criteria. By a rational technique of combining QFD with SAW under fuzzy environment, the computation tie of interval-valued fuzzy numbers corresponding to dependent evaluation criteria is resolved, and more messages are grasped than using other fuzzy numbers in FMCDM.

Interval-valued fuzzy multi-criteria decision-making based on simple additive weighting and relative preference relation

To encompass imprecise messages, traditional multi-criteria decision-making (MCDM) was generalized into fuzzy multi-criteria decision-making(FMCDM) in solving decision-making problems. In numerous MCDM methods, simple additive weighting(SAW) is the simplest one, but fuzzy multiplication for generalizing SAW under fuzzy environment is still complicated, especially interval-valued fuzzy numbers. In the past, Wang proposed a model based on SAW and relative preference relation to resolve fuzzy multiplication tie. Practically, Wang's model is useful to fuzzy generalization of SAW. However, the model is only used in triangular fuzzy numbers. Recently, more and varied messages are obtained and processed for decision-making problems. Triangular fuzzy numbers are insufficient to express the variance, whereas interval-valued fuzzy numbers are suitable. Therefore, SAW had to be generalized under interval-valued fuzzy environment. In this paper, we combine SAW with a relative preference relation into interval-valued FMCDM to avoid fuzzy multiplication and grasp more messages. Our proposed relative preference relation improved from Lee's fuzzy preference relation is similar to Wang's relative preference relation. The main difference is that the proposed relation is utilized in interval-valued fuzzy numbers, whereas Wang's is used in triangular fuzzy numbers. To sum up, we provide the FMCDM to solve decision-making problems with interval-valued fuzzy numbers easily and quickly.

An extended multi-attribute group decision approach for selection of outsourcing services activities for information technology under risks

In recent years, selection of outsourcing services activities for information technology (IT) which are defined under some outsourcing projects is a challenge for companies under competitive and uncertain environments. To address the issue, assessment techniques via group decision-making could be provided to appropriately appraise the candidates regarding the incomplete information and existing complexity. This study proposes a new integrated group assessment approach based on interval-valued hesitant fuzzy (IVHF) environment to select the best outsourcing projects regarding risks and incomplete information. The proposed approach is established via some procedures to determine experts' weights, criteria weights and candidates' rankings. The interval-valued hesitant fuzzy-collective wisdom weighting (IVHF-CWW) method is presented to compute the weight of each expert/decision maker (DM). Moreover, the interval-valued hesitant fuzzy-preference weighting (IVHF-PW) technique is presented to determine weights of evaluation criteria. Furthermore, the IVHF-utility index approach is elaborated to rank the candidate outsourcing projects. Finally, a practical study is provided to check the feasibility and validity of the proposed interval-valued hesitant fuzzy-integrated group decision-making (IVHF-IGDM) approach.

Comment on “Least-squares approach to regression modeling in full interval-valued fuzzy environment”

To the best of our knowledge, only the existing approach (Rabiei et al. in Soft Comput 18(10), 2043–2059, 2014) has been proposed to construct a full interval-valued fuzzy linear regression model [a regression model when the observation of the response, independent variables as well as the regression coefficients are triangular interval-valued fuzzy numbers (TIVFNs)]. However, after a deep study, it is observed that a mathematical incorrect assumption has been considered in this approach. Furthermore, it is observed that to resolve this mathematical incorrect assumption, there is a need to propose the multiplication of an unrestricted TIVFN (regression coefficient) with a restricted TIVFN [observed values of independent variable(s)]. Keeping the same in mind, in this paper, the same type of multiplication is proposed, and with the help of proposed multiplication, a modified approach is proposed to construct a full interval-valued fuzzy regression model. Also, the modified results of some existing real-life problems are obtained with the help of the modified approach.

A fuzzy multi attribute decision framework with integration of QFD and grey relational analysis

ObjectiveThis paper proposes a multi attribute decision support model in a supply chain in order to solve complex decision problems. The paper provides a platform to ease decision process through the integration of quality function deployment (QFD) and grey relational analysis (GRA) in demonstrating main supply chain drivers under fuzzy environment. MethodologyThe proposed method is important because of several points: First of all, in a supply chain system, evaluation factors are not really independent and must be addressed in relation to the external factors such as customer requirements. Hence, we have applied QFD tool. Second, due to the constant uncertainty in the supply chain environment, fuzziness among the factors has to be considered. So, an interval valued fuzzy model was implemented. Third, to examine the proposed decision system in reality, it was applied in Risk and Uncertain Conditions for Agriculture Production Systems (RUC-APS) project. ContributionAn integrated version of QFD and GRA is presented. It is assumed that QFD can act to measure optimal solutions based on the distance to ideal solutions. In an interval-valued fuzzy environment the enormous volume of computation by Euclidean distance doesn't allow decision makers to obtain the results easily. This drawback is addressed using gray relational analysis. The gray relational coefficient is integrated to the fuzzy QFD to measure the distance of potential solutions from ideal solutions. This integration facilitates decision making process in further problems once big data are available. ResultsTo obtain the importance degrees of logistic indicators in the supply chain, expert team considered the environmental, social & cultural, and economic factors as external dimension of the QFD. The other dimension of QFD includes supply chain drivers such as quality, environmental management system, supply chain flexibility, corporate social responsibility, transportation service condition, and financial stability. The decision model is solved and the ranking of indicators is achieved. A sensitivity analysis helps to test and check the performance of the decision model.

An Assessment Method for Project Cash Flow under Interval-Valued Fuzzy Environment

Effective project management requires reliable knowledge of cash required in different stages of project life cycle. Getting this knowledge is highly dependent on sophisticated consideration of project environment. Nature of projects and their environments are associated with uncertain conditions. In this paper, a new project cash flow assessment method based on project scheduling is proposed to foresee projects' cash flow in their different stages. Interval-valued fuzzy sets (IVFSs) are applied to address the uncertainty of activity durations and costs. First, an IVF-project scheduling method is proposed to calculate early start time and early finish time of activities under IVF-environment and based on that, a new method of cash flow assessment is introduced under IVF-environment. For the purpose of illustration, the proposed method is implemented to generate cash flow of main activities of a large-scale project. The results show the flexibility of presented assessment method in expressing uncertainty, in addition to its capability in risk evaluation. Furthermore, using alpha-cuts to address different levels of uncertainty and risk provides a comprehensive insight of the cash required in different stages of project life cycle under different levels of risk and uncertainty. Finally, the results are discussed and the proposed method is believed to be useful in the project evaluation.