Determine Weights Of Criteria Research Articles

A simplified neutrosophic multiplicative set‐based TODIM using water‐filling algorithm for the determination of weights

AbstractDue to the technological developments around the world, the amount of information that researchers work on increases continuously. This information density contains incomplete and uncertain data that cannot be fully expressed with crisp numbers. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are useful tools to manage such information, but these concepts use a symmetrical and uniform scale to express data, whereas real‐life problems contain nonsymmetrical and non‐uniform information. Intuitionistic multiplicative sets (IMSs) are effective tools for dealing with these real‐life problems. However, IMSs cannot handle real‐life problems completely because indeterminate information depends on membership and non‐membership information of IMSs, which is a restriction for decision makers and also for decision problems. To overcome this limitation, this paper generalizes the IMSs by using simplified neutrosophic set and introduces a novel approach that is called simplified neutrosophic multiplicative sets (SNMSs). Firstly, we define SNMS, show their set‐based operations, and then give a description of simplified neutrosophic multiplicative numbers (SNMNs). Based on SNMNs, we develop two simplified neutrosophic multiplicative aggregation operators on SNMNs that are called simplified neutrosophic multiplicative weighted arithmetic average operator and simplified neutrosophic multiplicative weighted geometric average operator. Furthermore, we define some simplified neutrosophic multiplicative distance measures. Finally, using a model based on water‐filling algorithm for determining criteria weights, we give a numerical example to demonstrate the effectiveness of the introduced concept with the proposed simplified neutrosophic multiplicative simplified neutrosophic multiplicative‐TODIM method.

Sustainable supplier selection for smart supply chain considering internal and external uncertainty: An integrated rough-fuzzy approach

This study proposes a novel framework to identify smart-sustainable SCMP (supply chain management practices) as supplier selection criteria for a smart supply chain. Supplier selection consists of two parts: criteria weights determination and suppliers ranking. DEMATEL (Decision Making Trial and Evaluation Laboratory) has been acknowledged as a relatively feasible method for determining the criteria weights due to its effectiveness in acquiring the interrelationships between criteria. TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) has been identified as the most frequently used method for supplier ranking due to its superiority in quickly finding the best alternatives. However, most existing research contains scant study of the simultaneous manipulation of internal uncertainty (individual linguistic vagueness) and external uncertainty (group preference diversity), which are involved in the supplier selection process. Therefore, this study proposes a hybrid rough-fuzzy DEMATEL-TOPSIS approach to sustainable supplier selection for a smart supply chain. The proposed method combines the strength of the fuzzy set in handling internal uncertainty and the advantages of the rough set in manipulating external uncertainty. The effectiveness and accuracy of the proposed methodology are illustrated through its application in sustainable vehicle transmission supplier selection and through comparisons with other methods.

Hydrogen energy storage method selection using fuzzy axiomatic design and analytic hierarchy process

This paper presents an integrated Fuzzy Analytical Hierarchy Process (fAHP) and Weighted Fuzzy Axiomatic Design (wfAD) methodology for a strategic level problem of hydrogen energy storage (HES) method selection for Turkey. Considering alternatives of tank, metal hydride and chemical storage, we design our decision problem with respect to five assessment criteria as weight, capacity, storage loss and leak, reliability, and total system cost. In the solution methodology, we first implement fAHP to determine criteria weights by incorporating linguistic judgement and vague information. Next, we define functional requirements and design parameters for the selection problem and use wfAD to compare alternatives. After implementing the proposed integrated approach, we perform additional sensitivity analysis experiments to test the robustness of the solution with respect to changes in functional requirements.

New model for determining criteria weights: Level Based Weight Assessment (LBWA) model

This paper presents new subjective model for determining weight coefficients in multi-criteria decision-making models. The new Level Based Weight Assessment (LBWA) model enables the involvement of experts from different fields with the purpose of defining the relations between criteria and providing rational decision making. The method can be applied in practical cases in specialized decision-making support systems, as well as in alternative dispute resolutions in virtual environment. The LBWA model has several key advantages over other subjective models based on mutual comparison of criteria, which include the following: (1) the LBWA model allows the calculation of weight coefficients with small number of criteria comparisons, only comparison; (2) The algorithm of the LBWA model does not become more complex with the increase of the number of criteria, which makes it suitable for use in complex multi-criteria (MCDM) models with a large number of criteria; (3) By applying the LBWA model, optimal values of weight coefficients are obtained with simple mathematical apparatus that eliminates inconsistencies in expert preferences, which are tolerated in certain subjective models (Best Worst Method - BWM and Analytic Hierarchy Process - AHP); (4) The elasticity coefficient of the LBWA model enables, after comparing the criteria, additional corrections of the values of the weight coefficients depending on the preferences of the decision makers. This feature of the LBWA model enables sensitivity analysis of the MCDM model by analyzing the effects of variations in the values of the weights of criteria on final decision.

Weighting methods for multi-criteria decision making technique

Determining criteria weights is a problem that arises frequently in many multi-criteria decision-making (MCDM) techniques. Taking into account the fact that the weights of criteria can significantly influence the outcome of the decision-making process, it is important to pay particular attention to the objectivity factors of criteria weights. This paper provides an overview of different weighting methods applicable to multi-criteria optimization techniques. There are a lot of concept been reported from the literature that are very useful in solving multicriteria problems. The present work emphasized on the use of these weighting methods in determining the criteria preference of each criterion to bring about desirable properties and in order to establish and satisfy a multiple measure of performance across all the criteria selected by identifying the best options possible. And from the results, it shows that subjective weighting methods are easy and straight forward in terms of their computations than the objective weighting methods which derived their information from each criterion by adopting a mathematical function to determine the weights without the decision-maker’s input,. This can be seen from the pairwise comparison which gives an internal storage and random access memory of a smart phone a weight value of 0.33 and 0.22 respectively as they have the highest criteria weights. Keywords: Multi-criteria, Decision-making, Relative importance, Alternative, Criteria

Multi-criteria decision making in Pythagorean fuzzy environment

Pythagorean fuzzy set, initially extended by Yager from intuitionistic fuzzy set, is capable of modeling information with more uncertainties in the process of multi-criteria decision making (MCDM), thus can be used on wider range of conditions. The fuzzy decision analysis of this paper is mainly built upon two expressions in Pythagorean fuzzy environment, named Pythagorean fuzzy number (PFN) and interval-valued Pythagorean fuzzy number (IVPFN), respectively. We initiate a novel axiomatic definition of Pythagorean fuzzy distance measurement, including PFNs and IVPFNs. After that, corresponding theorems are put forward and then proved. Based on the defined distance measurements, the closeness indexes are developed for both expressions, inspired by the idea of technique for order preference by similarity to ideal solution (TOPSIS) approach. After these basic definitions have been established, the hierarchical decision approach is presented to handle MCDM problems under Pythagorean fuzzy environment. To address hierarchical decision issues, the closeness index-based score function is defined to calculate the score of each permutation for the optimal alternative. To determine criterion weights, a new method based on the proposed similarity measure and aggregation operator of PFNs and IVPFNs is presented according to Pythagorean fuzzy information from decision matrix, rather than being provided in advance by decision makers, which can effectively reduce human subjectivity. An experimental case is then conducted to demonstrate the applicability and flexibility of the proposed decision approach. Finally, extension forms of Pythagorean fuzzy decision approach for heterogeneous information are briefly introduced to show its potentials on further applications in other processing fields with information uncertainties.

Decision making for portfolio selection by fuzzy multi criteria linear programming

In daily life events, there are many complexities arising from lack of information and uncertainty. Fuzzy linear programming model has been developed to reduce or eliminate this complexity. Fuzzy linear programming is the process of choosing the optimum solution from among the decision alternatives to achieve a specific purpose in cases where the information is not certain. One of the fields where the lack of information or uncertainty makes it difficult to decide is financial markets. Investors who have a certain amount of accumulations are aiming to increase in various ways as well as protecting the value of their income. While doing this, encounter the problem of deciding to which investment vehicle they need to invest in what extent. Therefore, investors apply to fuzzy linear programming model to eliminate this uncertainty and to create the optimal portfolio. In the portfolio selection process suggestions in the literature, the determination of criteria weights is based on triangular fuzzy numbers. In this study, as an alternative to the Enea and Piazza's portfolio selection model, which uses the triangular fuzzy numbers for criteria weighting, a new model that uses the trapezoidal fuzzy numbers for the same aim was proposed. With the solution of the linear programming model which is based on the determined weights, an alternative solution has been produced to the problem of which investment instrument will be invested at what proportion. The results obtained from the existing methods and the results obtained from the proposed model were compared.

TOPSIS method based on a fuzzy covering approximation space: An application to biological nano-materials selection

The applications of nanomaterials in biomedicine have received increasing attentions. Therefore, how to choose the most suitable material among a variety of bio-nanomaterials with similar properties is a significant problem. Aiming at this problem, we describe it as a multi-criteria decision-making problem in a fuzzy covering approximation space and solve it via the TOPSIS method. Firstly, combining fuzzy neighborhood operators with fuzzy rough set models, we propose two pairs of covering-based fuzzy rough set models and study the basic properties together with classifications of these two pairs of models. Subsequently, we reveal a new method for determining objective weights using the first pair of covering-based fuzzy rough set models. Combining the objective criteria weight determination method with the TOPSIS method, we provide a solution to solve the problem of bone transplant replacement materials selection. Then, we discuss the experimental effects of our proposed method and the other eight different decision-making methods in practical problems to explain the rationality and enforceability of our approach. Finally, we validate the performance of our approach with the support of ideas of cross-validation and hypothesis testing.

A multicriteria decision making–based methodology to identify accident-prone road sections

Accident-prone road section (APRS) treatment is the most effective strategy for accident reduction. Because use of multicriteria decision making (MCDM) in the decision process improves the quality of the decision, especially in problems involving multiple criteria, MCDM approach may be the appropriate approach for APRS determination. In this study, an MCDM-based methodology was developed for the determination of APRSs. Weighted linear combination method was used to combine criteria. Because use of experts' opinion for criteria weight determination in MCDM studies may bring subjective results, all possible criteria weight combinations (with some simplifications) were tried to determine the best weight combination. “Relative risk” was used as common unit for criteria standardization and past accident data is utilized to express the “relative risk”. The methodology was tested on D850 State Highway, Tokat, Turkey. Five criteria (horizontal alignment, vertical alignment, intersections, significant places, shoulder width) were used in the process. At the end, although 63 out of 94 sections (67.02%) were labeled as “accident prone”, 173 out of 206 accidents (83.98%) take place in these sections. Therefore, the methodology can be used for APRS determination. Also, the effect of any change in the road properties on the accident-proneness can be simulated by simply changing the criterion values.

Development of an ITARA-based hybrid multi-criteria decision-making model for material selection

The optimum selection of material in manufacturing environment should be investigated using a strategic perspective because of its complex nature. The ideal alternative cannot be found easily due to the different criteria, so the decision maker has to consider several factors for selecting the appropriate material. As a result, the decision maker should design a proper form of decision support system to solve the given problem. From decision-maker perspective, it is not easy to determine criteria weights of materials selection problem. Especially, several criteria cause inadequate subjective evaluation. In order to prevent this, different novel hybrid models were developed by using indifference threshold-based attribute ratio analysis (ITARA), VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) technique for order of preference by similarity to ideal solution (TOPSIS) and multi-objective optimization on the basis of ratio (MOORA) methods. Two case studies (material selection of flywheel and cryogenic storage tank) were taken from the literature to test these models. ITARA is used to calculate the criteria weights in the problems, and the final rankings are obtained by using VIKOR, TOPSIS and MOORA. The results indicate that the proposed methods produced successful results in terms of material selection perspective.

Stochastic KEMIRA-M Approach with Consistent Weightings

This study proposes an advanced Modified KEmeny Median Indicator Rank Accordance (KEMIRA-M) approach based on stochastic evaluation process considering consistent weights to improve effective usage of KEMIRA-M. In the proposed approach, tasks related to the decision issue are performed by decision makers to ensure the understanding sufficiency of alternatives in terms of criteria more clearly. The weighting procedure of Analytic Hierarchy Process (AHP) is implemented in a stochastic manner benefited from discrete uniform distribution to provide obtaining consistent criteria weights considering median priority components. Therefore, different trials including different number of replications that shows the number of decision makers are performed and the most consistent weightings are determined for each trial in the stochastic process. In this way, the dependency to the limited numbers of decision makers and to determine criteria weights in a heuristic manner in KEMIRA-M is prevented. Additionally, the effect of the number of decision makers on criteria weightings and alternatives’ ranking process is shown. To obtain the most consistent weighting results, this stochastic process is utilized until acquiring approximate consistency ratios. The proposed stochastic KEMIRA-M approach is utilized to rank nine shopping malls (SMs) in Ankara in terms of technical criteria (TC) and universal design criteria (UDC). It was seen from the ranking results that the first SM (SM1) is the best one.

Integrated MCDM model for processes optimization in the supply chain management in the wood company

Supply chain management (SCM) is a global strategy in nowadays business environment. It is needed It is necessary to manage a number of processes and activities on a daily basis in order to achieve a competitive advantage. In order to achieve adequate bases for successful functioning, it is necessary to know their abilities and weaknesses. In order to achieve this, it is necessary to perform the decomposition of the complete system. In this paper decomposition in wood company and supplier selection in subsystem of procurement has performed. For determining criteria weights are applied Full Consistency Method (FUCOM), while the ranking of supplier is performed using Weighted Aggregated Sum Product ASsessment (WASPAS) method. Obtained results are checked through sensitivity analysis that is formed with modeling of criteria weights. In sensitivity analysis it was found that changes in the significance of the criteria could influence the decision making and ranking of suppliers.

Criteria Assessment in Sustainable Macromanagement of Housing Provision Problem by a Multi-phase Decision Approach with DEMATEL and Dynamic Uncertainty

Macromanagement of housing provision based on sustainable development characteristics may be required for applying some different strategies to ensure the housing preparation regarding economic, environmental, and social competencies. In this regard, there are some challenges, including defining the criteria in a hierarchical structure to check the problem in all aspects, computing experts’ weights for reducing judgments’ errors, computing interdependencies effects among criteria to increase the precise of criteria weight determination, dynamic criteria’ weights evaluation to analyze the criteria importance in some different periods, and uncertainty modeling of criteria weights computations in the research area, in which recent studies did not focus them simultaneously. To address the issue, this study proposes a multi-phase weighting approach by combining the collective index and decision-making trial and evaluation laboratory (DEMATEL) methodologies via dynamic interval-valued hesitant fuzzy sets (DIVHFSs) theory. Considering dynamic uncertainty is needed for covering the incomplete information in various periods because the significance and impact of evaluation criteria may be changed in each period. On the other hand, DIVHFSs theory could assist the experts by assigning some dynamic interval-valued hesitant fuzzy (DIVHF)-membership degrees for an element under a set to decrease the errors. In proposed DIVHF-collective index method, criteria local weights are obtained based on correlation and standard deviation approaches under a DIVHF-environment. In addition, the extended DEMATEL methodology is prepared for taking account of hierarchical structure and criteria interdependencies relations. Moreover, a novel DIVHF-utility degree method is presented to compute the weight of each expert. Then, experts’ weights are taken into account in the presented multi-phase weighting approach. In addition, the DIVHF-multi-phase weighting approach based on collective index and DEMATEL (DIVHF-MPW-CI–DEMATEL) methodologies is proposed via a last aggregation approach to keep away from the data loss. Meanwhile, some needed operations on DIVHFS theory for presenting DIVHF-MPW-CI–DEMATEL methodology are extended. Finally, a real case study about the determining criteria’ weights for strategy selection in macromanagement of housing provision problem based on sustainable development properties is prepared to indicate the feasibility and applicability of proposed DIVHF-MPW-CI–DEMATELs approach.

Location selection of seawater pumped hydro storage station in China based on multi-attribute decision making

With the urgent need for energy conservation and intrinsic intermittence optimization, seawater pumped hydro energy storage (SPHS) is developing rapidly in the foreign countries but no one has been built in China. Nevertheless, with vast resources, our country pays much attention on SPHS site selection lately since its superiority and the need for long-term energy development. To select the most ideal SPHS site from numerous candidate alternatives, 18 evaluation criteria are set in this paper. Due to vague relevance among criteria, λ-fuzzy measure combining Analytic Hierarchy Process (AHP) and entropy weight method are proposed to determine criteria weights. Later, fuzzy Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method is applied to sort an optimal solution for the SPHS construction. Simultaneously, the published data from National Energy Administration (NEA) combining experts' scoring and public opinions are calculated as a case and the Fu Ying Island in Ning De is proved to be the best. In order to ensure the validity and stability of the result, comparative and sensitive analysis are proposed. Overall, the proposed model can provide a reference to the government and electricity grid for further evaluation since SPHS site selection has not been deeply studied in China.

An Integrated Multi-Criteria Decision Making Approach to Location Planning of Electric Vehicle Charging Stations

Electric vehicles (EVs) are recognized as one of the most promising technologies worldwide to address the fossil fuel energy resource crisis and environmental pollution. As the initial work of EV charging station (EVCS) construction, site selection plays a vital role in its whole life cycle, which, however, is a complicated multiple criteria decision making (MCDM) problem involving many conflicting criteria. Therefore, this work aims to propose a novel integrated MCDM approach by a grey decision making trial and evaluation laboratory (DEMATEL) and uncertain linguistic multi-objective optimization by ratio analysis plus full multiplicative form (UL-MULTIMOORA) for determining the most suitable EVCS site in terms of multiple interrelated criteria. Specifically, the grey DEMATEL method is used to determine criteria weights and the UL-MULTIMOORA model is employed to evaluate and select the optimal site. Finally, an empirical example in Shanghai, China, is presented to demonstrate the applicability and effectiveness of the proposed approach. The results show that the proposed approach is a useful, practical, and effective way to find the optimal location of EVCSs.

A GRA-Based Method for Evaluating Medical Service Quality

Medical service quality is the foundation and core of the medical institution’s management. However, the abstraction of service quality makes it difficult to measure by general measurement approaches. This paper proposes a new fuzzy multi-attribute decision-making model to evaluate hospital service performance based on a grey relational analysis. First, the Delphi method is used to determine criteria and establish an evaluation system. Then, the existing uncertainty and ambiguity are quantified by the interval-valued intuitionistic trapezoidal fuzzy numbers. Second, the subjective and objective information is aggregated to determine criteria weights, and then the grey relational analysis method is proposed to evaluate alternatives. Finally, a case is provided to illustrate an application of the proposed model. In addition, comparative analysis and sensitivity analysis are performed to verify the feasibility and effectiveness. The results show that the proposed model is an effective tool for evaluating medical service quality.

Evaluation of ERP softwares with fuzzy AHP integrated TODIM method

Since enterprise resource planning process is important for growing and developed private companies due to productivity, in the business world it has found effectively its place. ERP system softwares those are fundamental interest area of industrial engineering, have gained much importance in recent years according to doing the jobs productivity needs. In this study, a solution method is proposed for a private organization that desires to re-evaluate the distributed ERP softwares of it owns. For this, most used multi-criteria decision-making method named analytic hieararchy process is utilized for determination of criteria weights. In addition a risk involving process called TODIM (an MCDM method), which is based on prospect theory, was chosen for risky and dynamic conditions in the study. Since the Nobel prize-winning prospect theory including risk avoidance and risk taking situations in decision-making behaviors has been integrated in TODIM's decision-making process. This process involves ambiguities as well as risk. Furthermore, the company's data privacy policy has been incorporated into the solution procedure with the fuzzy logic, which takes into account these drawbacks. Besides, it has been ensured that the cost criterion is integrated in a detailed manner. In the real world application, a selection is made between the renovation of the existing system alternative consisting of the scattered and different softwares –especially stressed on built-in software that only a majority uses-; this software’s cloud alternative and a completely different rival software alternatives. The result of this study, which examines ERP software selection under uncertainties by adding risk and cost measures, has been influential on enterprise’s preferences about this project.

A Three-Dimensional Fuzzy Linguistic Evaluation Model

A probabilistic linguistic-based model is an effective tool to express preferences with different weights for different linguistic terms. This paper aims at introducing a new model for determining criteria weights in group decision-making problems, which is based on the concept of probabilistic linguistic terms. Different linguistic weights of respondents are also incorporated into the proposed model. Fuzzy numbers are used to quantify the linguistic terms. Using this model, first, a new concept called three-dimensional fuzzy linguistic representation is proposed to serve as an extension of the existing models. Then, a normalization process, an aggregation process, and a defuzzifying process for three-dimensional fuzzy linguistic representation are investigated. Next, a model for determining criteria weights is formulated. A case study of a beverage product in Thailand is provided to demonstrate the applicability of the proposed model. Finally, the results are compared with the existing models.

Special Issue on the Power of Fuzzy—Dedicated to the Father of Fuzzy Logic

On September 6, 2017, we lost a great researcher, Prof. Lotfi A. Zadeh, the one who introduced one of the most important mathematical concepts that gets a good rapport with reality. “Fuzzy Sets” was the paper he published in 1965. Many researchers and practitioners of mathematics, science, engineering, medicine, and economics found it fascinating. In Japan, consumer electronics incorporating ambiguity in human thought and behavior became popular. As these products became big topics, the term “fuzzy” also became popular in the 1990s. This set of papers offers a sample of the expanding development of fuzzy logic and soft computing. One review paper is written by Prof. Takeshi Yamakawa, an internationally famous fuzzy researcher of fuzzy hardware systems. Four of these papers were selected through a peer review process. One, “Design of Fuzzy Logic Controller and its Distinctive Features” by Prof. Takeshi Yamakawa, describes the design of a fuzzy logic controller and its application to controlling mouse-platform stabilization. The distinctive features of fuzzy logic control are also discussed. The first original paper, “MMMs-Induced Possibilistic Fuzzy Co-Clustering and its Characteristics” by Ubukata et al., describes an NPCCMM scheme by considering variable cluster volumes and the fuzziness degree of item memberships to investigate the specific aspects of fuzzy rather than probabilistic nature in co-clustering tasks. The second original paper, “Inner Evaluation of Writing in a Foreign Language Based on Expert Judgment for Correction” by Entani et al., proposes a method of numerically deriving each writer’s writing preference from an expert’s initial evaluation. Third, “A 3-Dimensional Fuzzy Linguistic Evaluation Model” by Suprasongsin et al., describes a new model for determining criteria weights in group decision-making problems, a model based on the concept of probabilistic linguistic terms. The fourth original paper, “Natural Language Generation Using Monte Carlo Tree Search” by Kumagai et al., proposes a method for generating simulation-based natural language. The method accounts for both building a correct syntactic structure and reflecting the given situational information as input in the sentences generated. We appreciate Prof. Takeshi Yamakawa for the excellent review of fuzzy controllers. We also thank all of the authors who submitted original articles and all of the reviewers who offered their valuable comments and suggestions.

Sustainable site selection for photovoltaic power plant: An integrated approach based on prospect theory

Site selection is one of the critical steps in building photovoltaic power plants which influences electricity-generating capacity and socio-economic benefits in the future. It needs to consider many factors in site selection, such as climate, geology, and social acceptance, etc. Thus, photovoltaic power plants site selection is a complex problem of multiple-criteria decision-making. However, most of the previous studies consider less about the subjectivity and vagueness of decision-making information and assume that decision makers are totally rational without considering their psychological factors. To deal with the problem, a novel integrated method based on variable precision rough number, Technique for Order Performance by Similarity to Ideal Solution and prospect theory is developed in this paper. Basically, the method includes two stages: one is determination of criteria weights based on variable precision rough number, and the other is selecting the most suitable photovoltaic power plant site with a prospect theory-based approach. The novel method integrates the advantage of variable precision rough number in flexibly dealing with vague information and the merit of prospect theory in manipulating decision maker’s bounded rationality. Finally, a case study of a 10-megawatt photovoltaic power plant site selection in China is used to demonstrate the effectiveness and efficiency of the proposed method.