Multiple Attribute Decision Making Research Articles

Multiple attribute decision making with flexible linguistic expressions: A linguistic distribution-based approach with interval estimations

In linguistic multiple attribute decision making (MADM), flexible linguistic expressions can provide a general way to express complex preference data linguistically, which presents the challenge of handling such complex linguistic data. In this paper, we investigate the linguistic MADM with the concept of flexible linguistic expressions, and present a linguistic distribution-based approach with interval estimations to support the MADM with the data of flexible linguistic expressions. We first convert flexible linguistic expressions approximately to linguistic distributions through developing two models to estimate the lower and upper bounds of the approximated linguistic distributions’ expectations on the attribute level. Then, we generate the interval estimations of comprehensive values of approximated linguistic distributions on the alternative level, and propose the solution algorithm to support the linguistic MADM with flexible linguistic expressions. Finally, the numerical and comparative analysis is performed to illustrate and justify the flexible linguistic MADM methods.

Interval type-2 fuzzy development of FUCOM and activity relationship charts along with MARCOS for facilities layout evaluation

This paper presents a new interval type-2 fuzzy (IT2F) multiple attribute decision making (MADM) model for evaluating facility layout alternatives. To this end, The Full Consistency Method (FUCOM) is extended to IT2F sets, and the mathematical model of IT2F-FUCOM is proposed. IT2F-FUCOM method requires a manageable number of pairwise comparisons and can deal with imprecision and uncertainty. Furthermore, the Activity Relationship Charts (ARCs), which are powerful instruments to articulate preferences regarding closeness between departments in the facility design, are also modeled through IT2F sets. The proposed IT2F-ARCs are incorporated into the decision hierarchy as a cost-type criterion, a novel integration between ARCs and the MADM is provided. Finally, the state-of-the-art IT2F MADM method of Measurement Alternatives and Ranking according to the Compromise Solution (MARCOS) is utilized to rank the alternatives. A real-life case study is conducted in order to demonstrate the applicability of the proposed model.

2DLIF-PROMETHEE methods for multiple attribute decision making under 2-dimension linguistic intuitionistic fuzzy environments

<h2>Abstract</h2> In this paper, how to run 2DLIF-PROMETHEE methods are introduced to deal with the multiple attribute decision making (MADM) problems evaluated by 2-dimension linguistic intuitionistic fuzzy variables (2DLIFVs). Firstly, the Euclidean distance and the cosine similarity measures for 2DLIFSs are introduced respectively. Then a hybrid distance for 2DLIFSs is introduced by integrating these two measures. Based on the hybrid distances for 2DLIFSs, six improved preference functions are designed to form the kernel part of 2DLIF-PROMETHEE methods. Finally, the partial ranking order of alternatives or the total ranking order of alternatives may be obtained by 2DLIF-PROMETHEE methods.

Multiphase Procedure for Identifying District Metered Areas in Water Distribution Networks Using Community Detection, NSGA-III Optimization, and Multiple Attribute Decision Making

The formation of district metered areas (DMAs) is an efficient strategy for the operation and management of water distribution networks (WDNs). Identifying the most suitable DMA layout is a challenging task for water utilities as it may involve several aspects that need to be addressed simultaneously. This study presents a novel multiphase approach for optimal DMA design that involves: (1) a combination of a fast Newman algorithm (FNA) to identify initial clusters; (2) a nondominated sorting genetic algorithm (NSGA-III) to obtain a set of good DMA configurations while considering several objectives simultaneously; and (3) a multiple attribute decision-making method (MADM) to find the best suited DMA configuration from a set of feasible alternative solutions based on the preference given to each objective. The proposed methodology is applied to two networks including a large benchmark network and a real-life water network. Four problem objectives out of several possible objectives were considered. These are: (1) the total cost of implementation (economic criterion); (2) the pressure deviation (hydraulic criterion); (3) a resilience index (energy criterion); and (4) the total demand shortfall (customer satisfaction criterion). Finally, a multiple attribute decision-making tool [i.e., a simple additive weighing (SAW) method] was used to arrive at a unique solution out of a set of feasible solutions. Results show that the proposed methodology can effectively identify DMAs while considering multiple objectives.

Novel distance and entropy definitions for linear Diophantine fuzzy sets and an extension of TOPSIS (LDF‐TOPSIS)

AbstractThe literature of multiple attribute decision making (MADM) is fruitful since there are various and successful applications of different fuzzy set extensions such as intuitionistic, Pythagorean and q‐Rung orthopair fuzzy sets (IFS, PFS and q‐ROFS). Besides their powerful aspects, some definitional limitations are known. In order to eradicate these boundaries regarding the definitions of membership and non‐membership degrees, linear Diophantine fuzzy set (LDFS) concept has been recently emerged. By considering two parameters, LDFS extends the representation area of the previous fuzzy set definitions and provides more extensive human judgement coverage field. In this study, the first distance and entropy measures in the literature have been developed for LDFSs. Their axiomatic definitions are given, and the proofs are shown. Also, thanks to our extensive literature review, we became aware that there is no MADM extension dedicatedly proposed for LDFS. So, the first MADM method extension for LDFS environment has also been developed in this study. A very well‐known MADM approach, TOPSIS, has been extended into LDFS environment for the first time in the literature. The applicability is shown in a healthcare management decision problem and the validity is checked and approved by comparing the alternative rankings LDF‐TOPSIS and the aggregation operators that were obtained from the literature produced.

Extended EDAS method for multiple attribute decision making in mixture z-number environment based on CRITIC method

In multiple attribute decision making (MADM) issues, the ambiguity, imprecision, and imperfection of assessment information may lead to inadequate decision-making results. However, the Z-number suggested by Zadeh in 2011 could somehow prevent this problem. For MADM issues with unknown attributes weights, an extended Distance from the Average Solution (EDAS) method is proposed under a mixture Z-number environment. In addition, the Criteria Importance Through Inter-criteria Correlation (CRITIC) method is used to estimate the weights of the criterion, which is easy to calculate and avoids subjective forecasts. A novel illustrative example is provided to demonstrate the feasibility, validity, and practicability of the presented method, and is compared with existing decision methods. The outcome indicates that the suggested method can solve complicated decision-making problems.

Information volume of Z-number

Given a probability distribution, Shannon entropy can be used to measure its corresponding information volume. However, it is still an open issue to calculate the information volume of Z-number. In this paper, the information volume of the Z-number is presented using the proposed transformation of a Z-number into a mass function. In our proposed method, the mass function degenerates into probability distribution under the circumstance that the uncertainty of the Z-restriction is 0. In this case, the information volume degenerates into Shannon entropy. The information volume of a given Z-number increases approximately linearly with the unreliability of its Z-restriction. In addition, the information volume varies with the value of Z-restriction and fuzzy number A. Some illustrative examples are shown to demonstrate the properties of the proposed information volume of Z-number. A new Weighted Multiple Attribute Decision Making (WMADM) method is also proposed to illustrate the practical advantage of the proposed information volume.

Synchromodal transport planning considering heterogeneous and vague preferences of shippers

In synchromodal transport, a freight forwarder usually serves multiple shippers with heterogeneous and vague preferences, such as low-cost, fast, or reliable transport. Ignoring shippers’ preferences will negatively impact the satisfaction of shippers and lead to the loss of them in the longer run. In order to incorporate these preferences, a Synchromodal Transport Planning Problem with Heterogeneous and Vague Preferences (STPP-HVP) is proposed and formulated as a mathematical model. Heterogeneous and Vague Preferences (HVP) are modeled through Multiple Attribute Decision Making approaches that integrate fuzzy set theory. The proposed model has two objectives, i.e., maximizing the number of served requests and minimizing the transportation cost. Preferences of shippers are set as constraints such that the freight forwarder needs to satisfy the preferred levels for each attribute. A heuristic algorithm (Adaptive Large Neighborhood Search) is proposed to find (near) optimal solutions. The case study in the European Rhine–Alpine corridor demonstrates that the proposed model can provide more attractive solutions to shippers compared with optimization which ignores preferences. Under various scenarios, the attributes, such as cost, time, emissions, reliability, and risk of damage, are analyzed and the (near) optimal modes and routes are suggested according to HVP. Moreover, the results show that the conflicts among attributes, conflicts among shippers, and conflicts between the freight forwarder and shippers are resolved by making one actor more satisfied without compromising any other actor’s preferences.

Decision Support System Scholarship Selection Using Simple Additive Weighting (SAW) Method

Scholarships are given to students to motivate students and compete with each other in pursuit of the best grades and achievements during their studies. As the name implies, factors such as GPA, competition participation, lecturer recommendations, and organizational participation are the criteria that will be considered for the selection process. In addition, parental income will also be an additional criterion. To minimize errors and reduce bias in the selection process, students who are eligible for scholarships will be assisted by using a Decision Support System (DSS). DSS will support decision making in selecting outstanding scholarship recipients from a pool of alternatives, namely students who register for the outstanding scholarship program by calculating student eligibility based on consideration of the criteria that students have in accordance with predetermined criteria. This calculation is carried out using the Simple Additive Weighting (SAW) method which is suitable for use in Multiple Attribute Decision Making (MADM) problems. As a result, each student will get an eligibility score which will influence the final decision. After the ranking of students who are most entitled to a scholarship according to the system calculations are obtained, the final decision will still be taken by the university.

Algorithms for multiple attribute group decision making with intuitionistic 2-tuple linguistic information and its application

Recently, the TODIM has been used to deal with multiple attribute decision making (MADM) problems. The intuitionistic 2-tuple linguistic sets (I2TLSs) are useful tools to depict uncertainty in MADM. This paper use TODIM method to solve MADM with the intuitionistic 2-tuple linguistic numbers (I2TLNs). Firstly, the concepts of I2TLNs are briefly presented, and classical TODIM for MADM are introduced. Then, the classical TODIM method is used to solve MADM with I2TLNs, and its important characteristic is to fully consider the decision makers’ bounded rationality which is a real action in MADM. And a comparative analysis is also given. Finally, a numerical example for service outsourcing providers selection is proposed.

A multiple attribute decision-making three-way model at four-branch fuzzy environment

Three-way decisions (TWDs) theory is one of the core ideas of decision-theoretic rough sets (DTRSs). Reviewing the existing research results, we find that TWDs provides us with more flexible decision choices. And the traditional fuzzy number does not take into account the absence of information (indifference) in the evaluation process. In order to construct a new model which can get flexible decision results in complex decision environment, we introduce four-branch fuzzy numbers (FBFNs) to describe the evaluation information, so that the decision-makers can express the evaluation information more comprehensively. In this paper, a novel TWDs model in four-branch fuzzy environment is proposed to solve multiple-attribute decision-making (MADM) problem. The first challenge is to construct a TWDs model based on FBFNs and to develop a new linguistic interpretation of the loss functions. Then, we extend a method for aggregating the loss functions obtained from the attribute evaluation values. Finally, we use the nonlinear solution to solve the threshold, and apply TOPSIS method to solve the conditional probability of FBFNs. The effectiveness of this method is illustrated by an example, and the decision results are compared with a MADM method based on OWGA operator.

Thermal performance revival of composite PCM for hybrid BTMSs by architecture and formula integrated optimization

Composite phase change material (CPCM) cooling is an essential method to ensure better performance of battery thermal management system (BTMS) due to high latent heat. However, long recovery time of CPCM makes it unaffordable especially during continuous high rate discharge–charge cycles. In order to reduce the energy consumption while enhancing the latent heat recovery efficiency, a novel hybrid BTMS architecture coupling with CPCM and liquid cooling is proposed. Liquid cooling is employed to recover the latent heat of PCM. To enhance the heat transfer in BTMS, the structural layout of liquid cooling arrangement is investigated. Meanwhile, mass fraction of expanded graphite (EG) and bulk density of CPCM are considered. Specially, the experiments are conducted to verify the effectiveness of present hybrid BTMS. In solidification, temperature performance especially temperature uniformity is not ideal. Therefore, a novel successive multiple attribute decision making (MADM) algorithm is employed to achieve optimized temperature difference, maximum temperature, solidification rate and mass of CPCM. In MADM algorithm, the order preference by similarity to ideal solution (TOPSIS) is coupled with the analytic hierarchy process (AHP) to solve the multi-objective discrete optimization problem. Results indicate that the optimal solution can make the maximum temperature and temperature difference at the lowest level of 317.51 K and 3.45 K at discharge rate of 4C. Meanwhile, the latent heat of CPCM is improved by about 27.5% at charge rate of 2C. The solution can improve the long-term reliability for the BTMS and the safety and service life for battery module.

Analysis of Interval-Valued Intuitionistic Fuzzy Aczel–Alsina Geometric Aggregation Operators and Their Application to Multiple Attribute Decision-Making

When dealing with the haziness that is intrinsic in decision analysis-driven decision making procedures, interval-valued intuitionistic fuzzy sets (IVIFSs) can be quite effective. Our approach to solving the multiple attribute decision making (MADM) difficulties, where all of the evidence provided by the decision-makers is demonstrated as interval-valued intuitionistic fuzzy (IVIF) decision matrices, in which all of the components are distinguished by an IVIF number (IVIFN), is based on Aczel–Alsina operational processes. We begin by introducing novel IVIFN operations including the Aczel–Alsina sum, product, scalar multiplication, and exponential. We may then create IVIF aggregation operators, such as the IVIF Aczel–Alsina weighted geometric operator, the IVIF Aczel–Alsina ordered weighted geometric operator, and the IVIF Aczel–Alsina hybrid geometric operator, among others. We present a MADM approach that relies on the IVIF aggregation operators that have been developed. A case study is used to demonstrate the practical applicability of the strategies proposed in this paper. By contrasting the newly developed technique with existing techniques, the method is capable of demonstrating the advantages of the newly developed approach. A key result of this work is the discovery that some of the current IVIF aggregation operators are subsets of the operators reported in this article.

Multiple Attribute Decision Making Based on Interval-Valued Neutrosophic Trapezoidal Fuzzy Numbers and its Application in the Diagnosis of Viral Flu

Decision-making technique (DMT) is mostly used in artificial intelligence and cognitive sciences to elaborate individual and social perception. So, one of the most important strategies in DMT evolved in medical diagnosis scrutiny regarding the connection of symptoms and diagnosis of diseases due to uncertainty and fuzziness in the relevant information. The focus of this article is to develop a diagnostic decision making strategy for the diagnosis of Viral diseases with close related symptoms using the Interval-valued trapezoidal neutrosophic fuzzy Numbers (IVTrNFN) w.r.t multiple attribute decision making (MADM) strategy where, the attribute value is evolved to Interval-valued trapezoidal neutrosophic fuzzy number and the attribute weight is unknown and can be related to the GRA (Grey relational analysis projection) technique. In this research several operational laws are developed as well as the expected value and the hamming distance between two IVTrFNs are introduced. Moreover, the information entropy method is used to determine the attributes weights and the grey relational analysis as well as the projection method are involved too in the proposed framework. The ranks of the alternative decisions are evaluated by their relative closeness to PIS (Positive Ideal Solutions), which combine the grey relational projection values from positive and negative ideal solutions associated with each alternative. Finally, a Viral disease example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Fuzzy Nano z-locally Closed Sets, Extremally Disconnected Spaces, Normal Spaces, and Their Application

In this paper, we introduce fuzzy nano (resp. δ, δS, P and Z) locally closed set and fuzzy nano (resp. δ, δS, P and Z) extremally disconnected spaces in fuzzy nano topological spaces. Also, we introduce some new spaces called fuzzy nano (resp. δ, δS, P and Z) normal spaces and strongly fuzzy nano (resp. δ, δS, P and Z) normal spaces with the help of fuzzy nano (resp. δ, δS, P and Z)-open sets in fuzzy nano topological space. Numerical data is used to quantify the provided features. Furthermore, using fuzzy nano topological spaces, an algorithm for multiple attribute decision-making (MADM) with an application in medical diagnosis is devised.

Selecting an Appropriate Configuration in a Construction Project Using a Hybrid Multiple Attribute Decision Making and Failure Analysis Methods

To successfully complete a project, selecting the most appropriate construction method and configuration is critical. There are, however, plenty of challenges associated with these complex decision-making processes. Clients require projects with the desired cost, time, and quality, so contractors should trade-off project goals through project configuration. To address this problem, in this study, an integrated FTA-DFMEA approach is proposed that implements the integrated AHP-TOPSIS method to improve construction project configuration. The proposed approach applies quality management techniques and MADM methods concurrently for the first time to improve construction project configuration considering project risks, costs and quality. At first, the Client’s requirements and market feedback are considered to identify potential failures in fulfilling project goals, and an integrated AHP-TOPSIS is used to select the most critical potential failure. Then fault tree analysis is used to indicate minimal paths. An inverse search in the operational model is performed to determine relevant tasks and identify defective project tasks based on WBS. Afterward, failure modes and effect analysis are applied to identify failure modes, and an integrated AHP-TOPSIS is used to rank failure modes and select the most critical one. Then Corrective actions are carried out for failure modes based on their priority, and project configuration is improved. This study considers construction resource suppliers with different policies, delivery lead times, warranty costs, and purchasing costs. Moreover, redundancy allocation and different configuration systems such as series and parallel are taken into account based on the arrangement and precedence of tasks. Finally, a case study of a building construction project is presented to test the viability of the proposed approach. The results indicate that the proposed approach is applicable as a time-efficient and powerful tool in the improvement of construction project configuration, which provides the optimal output by considering various criteria with respect to the client’s requirements and contractor’s obligations. Moreover, the algorithm provides various options for the contractor to improve the implementation of construction projects and better respond to challenges when fulfilling project goals.

Polytopic Fuzzy Sets and Their Applications to Multiple-Attribute Decision-Making Problems

Polytopic Fuzzy Sets and Their Applications to Multiple-Attribute Decision-Making Problems

Fuzzy Multiple Attribute Decision Making Menggunakan TOPSIS Pada Sistem Pendukung Keputusan Pemilihan Wireless Router

Selection of the right wireless router can maximize the performance of the internet network. Especially for a company whose business is very dependent on the internet network, choosing the right wireless router is an important factor. The purpose of this study is to implement one of the Fuzzy Multiple Attribute Decision Making (FMADM) approaches, namely the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method in a decision support system for selecting wireless router devices to help individuals and companies determine the right wireless router and according to what the user wants. The TOPSIS method is used because it is practical in its use, and has simplicity in concept, efficiency in the computational process and the best alternative is obtained by paying attention to the distance of the closest positive ideal solution and the farthest negative ideal solution distance. The system is built with software development techniques using the Extreme Programming (XP) method which begins with the planning, design, coding and testing stages. The developed system has functions such as being able to manage alternative data, criteria data, weight data, alternative values for each criterion, perform calculations using the TOPSIS method and can display the best alternative results. The results of the black-box testing show that the developed system can function and run well. In addition, the results by calculating manually with the system show the same results.

Interaction power Heronian mean aggregation operators for multiple attribute decision making with T-spherical fuzzy information

The interaction operation laws (IOLs) between membership functions can effectively avoid the emergence of counterintuitive situations. The power average (PA) operator can eliminate the negative effect of extremely or improperly assessments on the decision results. The Heronian mean (HM) operator is capable of examining the interrelationship between the two attributes. To synthesize the powers of the IOLs, PA and HM operators in this paper, the PA and HM operators are extended to process T-spherical fuzzy evaluation information perfectly based on the IOLs, and the T-spherical fuzzy interaction power Heronian mean (T-SFIPHM) operator and its weighted form are proposed. We further present some properties of these proposed AOs and discuss several special cases. Moreover, a novel method to T-spherical fuzzy multiple attribute decision making (MADM) problems applying the proposed AO is developed. Lastly, we present a numerical example to validate its feasibility and reasonableness, and the superiority of the developed method is further illustrated by sensitivity analysis of parameters and comparison with existing methods. The results show that proposed AOs not only can capture the interactivity among membership degree (MD), abstinence degree (AD) and non-membership degree (NMD) of T-spherical fuzzy numbers (T-SFNs), bust also ensure the overall balance of variable values in the process of information fusion and realize the interrelationship between attribute variables, so the decision results can be closer to reality and more reliable.

2DLIF-PROMETHEE based on the hybrid distance of 2-dimension linguistic intuitionistic fuzzy sets for multiple attribute decision making

2-dimension linguistic intuitionistic fuzzy set (2DLIFS) includes two classes of linguistic intuitionistic fuzzy variables, which has a more powerful and flexible ability in representing and handling uncertainty than 2-dimension linguistic fuzzy set (2DLFS) and intuitionistic fuzzy set (IFS). Distance and similarity are two important tools to quantify the difference and closeness of 2DLIFSs. This paper proposes the Euclidean distance and the cosine similarity measures for 2DLIFSs, respectively. Due to the limitation of the Euclidean distance and the cosine similarity measures for 2DLIFSs, a hybrid distance for 2DLIFSs is introduced by integrating these two measures. Further, based on the hybrid distance for 2DLIFSs, 2DLIF-PROMETHEE methods are introduced to deal with the multiple attribute decision making (MADM) problems under 2DLIF environment. Finally, a numerical example is provided to demonstrate the advantages and practicality of 2DLIF-PROMETHEE methods.