Proposed Multiattribute Decision Making Method Research Articles

Multiattribute decision making based on interval-valued intuitionistic fuzzy values, score function of connection numbers, and the set pair analysis theory

This paper proposes a new multiattribute decision making (MADM) method based on the proposed score function of connection numbers (CNs) and the set pair analysis (SPA) theory in the interval-valued intuitionist fuzzy (IVIF) context. Firstly, we develop a score function for ranking CNs. The various notable characteristics of the proposed score function of CNs are also presented. Then, we propose a new MADM method based on interval-valued intuitionist fuzzy values (IVIFVs), the proposed score function of CNs and the SPA theory, where we convert IVIFVs into CNs and the optimal weights of attributes are calculated from the IVIF weights of attributes. Finally, the proposed MADM method is applied for MADM in the IVIF context, where the preference orders (POs) of the alternatives obtained by the proposed MADM method are compared with the ones obtained by the existing MADM methods. The proposed MADM method can overcome the drawbacks of the existing MADM methods.

TDIFS: Two dimensional intuitionistic fuzzy sets

Intuitionistic fuzzy sets (IFS) are widely used in multi-attribute decision-making (MADM) because of its strong ability to express uncertainty in terms of membership degree, non-membership degree and hesitancy degree. Additionally, Z-number is a novel two-dimension framework to handle uncertainty problems by introducing the reliability of expert evaluation. However, a simple index in the framework of Z-number is not enough to express the evaluation of experts. In order to integrate the uncertainty and reliability expressions of IFS, inspired by Z-number, we propose a two-dimensional intuitionistic fuzzy set (TDIFS) model in this paper. In TDIFS model, the first dimensionality is the evaluation data from experts with regard to attributes, and the second dimensionality represents the reliability of expert in terms of the first component of TDIFS. Moreover, for each dimensionality, it is expressed as an ordered pair of intuitionistic fuzzy set, which can carry more information than a simple index. Furthermore, a novel combination rule is proposed for fusing TDIFSs. The TDIFS combination rule fully integrates expert evaluation and expert reliability, where it can reduce the uncertainty during combination process, so that more convincing results can be obtained. In addition, a new MADM method is proposed based on TDIFS model and TDIFS combination rule. Through comparing with the existing methods in an application of pattern recognition, it is demonstrated that the proposed MADM method is more effective, which can achieve higher robustness and better recognition results.

Multiattribute decision making based on U-quadratic distribution of intervals and the transformed matrix in interval-valued intuitionistic fuzzy environments

In this paper, we propose a new multiattribute decision making (MADM) method based on the U-quadratic distribution of intervals and the transformed matrix of the decision matrix given by the decision maker in interval-valued intuitionistic fuzzy (IVIF) environments. First, it gets the transformed matrix of the decision matrix. Then, it calculates the variances of the intervals appearing at each element of the obtained transformed matrix, respectively. Then, it calculates the standard deviations of the intervals appearing in the elements of each column of the obtained transformed matrix, respectively. Then, it calculates the middle points of the intervals appearing in the elements of each column of the obtained transformed matrix, respectively. Then, it calculates the average values of the intervals appearing in the elements of each column of the obtained transformed matrix, respectively. Then, it builds the z-score matrix. Then, it calculates the transformed weight of the IVIF weight of each attribute. Finally, according to the obtained z-score matrix and the obtained transformed weight of the IVIF weight of each attribute, it computes the weighted score of each alternative for ranking alternatives. The proposed MADM method can overcome the shortcomings of the existing MADM methods.

Multi-Attribute Decision Making Based on Stochastic DEA Cross-Efficiency with Ordinal Variable and Its Application to Evaluation of Banks’ Sustainable Development

Multi-attribute decision making (MADM) is a cognitive process for evaluating data with different attributes in order to select the optimal alternative from a finite number of alternatives. In the real world, a lot of MADM problems involve some random and ordinal variables. Therefore, in this paper, a MADM method based on stochastic data envelopment analysis (DEA) cross-efficiency with ordinal variable is proposed. First, we develop a stochastic DEA model with ordinal variable, which can derive self-efficiency and the optimal weight of each attribute for all decision making units (DMUs). To further improve its discrimination power, cross-efficiency as a significant extension is proposed, which utilizes peer DMUs’ optimal weight to evaluate the relative efficiency of each alternative. Then, based on self-efficiency and cross-efficiency of all DMUs, we construct corresponding fuzzy preference relations (FPRs) and consistent fuzzy preference relations (FPRs). In addition, we obtain the priority weight vector of all DMUs by utilizing the row wise summation technique according to the consistent FPRs. Finally, we provide a numerical example for evaluating operation performance of sustainable development of 15 listed banks in China, which illustrates the feasibility and applicability of the proposed MADM method based on stochastic DEA cross-efficiency with ordinal variable.

Q-rung Orthopair Normal Fuzzy Aggregation Operators and Their Application in Multi-Attribute Decision-Making

Q-rung orthopair fuzzy set (q-ROFS) is a powerful tool to describe uncertain information in the process of subjective decision-making, but not express vast objective phenomenons that obey normal distribution. For this situation, by combining the q-ROFS with the normal fuzzy number, we proposed a new concept of q-rung orthopair normal fuzzy (q-RONF) set. Firstly, we defined the conception, the operational laws, score function, and accuracy function of q-RONF set. Secondly, we presented some new aggregation operators to aggregate the q-RONF information, including the q-RONF weighted operators, the q-RONF ordered weighted operators, the q-RONF hybrid operator, and the generalized form of these operators. Furthermore, we discussed some desirable properties of the above operators, such as monotonicity, commutativity, and idempotency. Meanwhile, we applied the proposed operators to the multi-attribute decision-making (MADM) problem and established a novel MADM method. Finally, the proposed MADM method was applied in a numerical example on enterprise partner selection, the numerical result showed the proposed method can effectively handle the objective phenomena with obeying normal distribution and complicated fuzzy information, and has high practicality. The results of comparative and sensitive analysis indicated that our proposed method based on q-RONF aggregation operators over existing methods have stronger information aggregation ability, and are more suitable and flexible for MADM problems.

Multiattribute decision making based on probability density functions and the variances and standard deviations of largest ranges of evaluating interval-valued intuitionistic fuzzy values

In this paper, we propose a new multiattribute decision making (MADM) method based on probability density functions (PDFs) and the variances and standard deviations of the largest ranges of evaluating interval-valued intuitionistic fuzzy values (IVIFVs). First, the proposed MADM method gets the largest range of each evaluating IVIFV in the decision matrix and calculates the average value of the largest ranges of each attribute. Then, it gets the PDF of the largest range of each evaluating IVIFV in the decision matrix, calculates the variance of each largest range and calculates the standard deviation of the largest ranges of each attribute. Then, it constructs the z-score decision matrix and gets the transformed weight of the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute. Finally, it calculates the weighted score of each alternative based on the obtained z-score decision matrix and the transformed weight of the IVIF weight of each attribute. The larger the value of the weighted score, the better the preference order (PO) of the alternative. The proposed MADM method can overcome the drawbacks of the existing MADM methods.

Multiattribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed new score function of intuitionistic fuzzy values (IFVs) and the proposed modified VIKOR method. The proposed new score function can overcome the drawbacks of the existing score functions, the existing accuracy functions and the existing measure methods for ranking IFVs. The proposed modified VIKOR method is based on the proposed new score function of IFVs, which not only calculates the closest ideal score value of each alternative, but also calculates the farthest worst score value of each alternative. Moreover, the proposed MADM method uses the concept of the TOPSIS method to rank alternatives. The smaller the degree of relative closeness, the better the preference order of the alternative. The proposed MADM method can overcome the drawbacks of the existing MADM methods for MADM in intuitionistic fuzzy environments.

Multiple attribute decision making method under linguistic cubic information

In this paper, the concept of linguistic cubic number (LCN) is introduced which further extends the concept of linguistic intuitionistic fuzzy number (LIFN). More specifically, the notions of internal (external) developed and (P-)R-order for LCN are studied. For a given LCN, some basic operational laws, score and accuracy function are proposed. Also, some generalized aggregation operators based on the operational rules are developed and their related properties are investigated. As application, a multi-attribute decision-making (MADM) method is established based in the environment of LCNs and with the help of defined aggregation operators. Finally, an illustrative example is provided to show the effectiveness of the proposed MADM method.

Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making

The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter.

A Multi-Attribute Expansion Planning Model for Integrated Gas–Electricity System

Gas-fired power plants are environmentally friendly because of their high efficiency rates and low CO2 emissions. On the other hand, the output power of renewable generators is stochastic, meaning that additional capacity must be held in reserve throughout the system. Gas-fired power plants are ideally suited to mitigate renewable uncertainties as they are more flexible and can easily be fired up in just a few minutes, and subsequently be shut down. Increased use of gas-fired power plants makes gas and electricity networks more dependent, so that adequacy in fuel supply of electricity network becomes a majority. However expansion planning of gas and electricity systems is accomplished by private gas and electricity companies, having no effective data exchange mechanism together. So there is a need to provide a model that coordinates the expansion planning of gas and electricity networks. On the other hand, expansion cost of either gas or electricity network and risk criteria of integrated energy system may have priority in decision-making process. With different challenging attributes, there is a gap in the literature to provide a model that takes into account the privacy of energy parties with a minimum data exchange, while considering different attributes in decision-making process. In this paper a multi-attribute decision-making (MADM) method for co-expansion planning of gas and electricity systems is introduced. The proposed MADM method supposes that a central entity as Ministry of Energy (ME) is responsible for coordinated expansion planning of gas and electricity networks, while taking into account the privacy of gas and electricity energy parties. Decision-making attributes are conflicting and the proposed method selects the best plan based on a compromise among the attributes. Different attributes including gas expansion cost (GEC), electricity expansion cost (EEC), minimum of maximum regret (MMR) and β-robustness (β_R) are considered to find the best plan with regard to the preferences of independent gas and electricity network operators. In this regard, two multi-attribute decision analysis methodologies are employed: analytical hierarchy process (AHP) is used as a simple way to weight and rank all the attributes objectively and find the relative importance of various plans, and the weighted sum method to provide a general composite index and finding the final appropriate plan. A real case study in the Khorasan province of Iran, which has a high penetration level of gas-consuming generation units (GCGU), is utilized to demonstrate the effectiveness of proposed MADM method. Results are compared with a Pareto optimal method to qualify the accuracy of proposed method.

Multiattribute decision making based on nonlinear programming methodology, particle swarm optimization techniques and interval-valued intuitionistic fuzzy values

In this paper, we propose a new multiattribute decision making (MADM) method by applying the nonlinear programming (NLP) methodology and particle swarm optimization (PSO) techniques using interval-valued intuitionistic fuzzy values (IVIFVs) to conquer the drawbacks of Chen and Huang's MADM method (2017), which has three drawbacks, i.e., (1) multiple different preference orders (POs) of alternatives are obtained in some situations, (2) the PO of alternatives cannot be distinguished in some circumstances, and (3) the PO of alternatives cannot be obtained in some circumstances. Moreover, the proposed MADM method also can conquer the shortcomings of Chen and Chiou's MADM method (2015), Li's MADM method (2010) and Zhitao and Yingjun's method (2011).

An improved MADM method using interval-valued intuitionistic fuzzy values

In this paper, we modify Chen and Han's multiattribute decision making (MADM) method (2018) to propose a novel MADM method based on the nonlinear programming (NLP) methodology, Xu's score function (SF) (2007) and Xu's accuracy function (AF) (2007) of interval-valued intuitionistic fuzzy values (IVIFVs), the membership uncertainty (MU) index (2009) and the hesitation uncertainty (HU) index (2009) of IVIFVs, and Wang et al.’s ranking method (2009) of IVIFVs. The proposed MADM method can conquer the shortcomings of Chen and Chiou's MADM method (2015), Chen and Han's MADM method (2018), Chen and Huang's MADM method (2017), Li's MADM method (2010) and Zhitao and Yingjun's MADM method (2011).

Multiple attribute decision-making approach based on dual hesitant fuzzy Frank aggregation operators

Real-world decision-making problems are often complex and indeterminate. Thus, uncertainty and hesitancy are usually unavoidable issues being experienced by decision makers. Dual hesitant fuzzy sets (DHFSs) which are described in terms of the two functions, namely the membership hesitancy function and the non-membership hesitancy function, have been developed. In light of their properties, they are considered as a powerful vehicle to express uncertain information in the process of multi-attribute decision-making (MADM). In accordance with the practical demand, this study proposes a new MADM approach with dual hesitant fuzzy (DHF) assessments based on Frank aggregation operators. First, original score and accuracy functions of DHFS are developed to construct a new comparison method of DHFSs. The properties of the developed score and accuracy functions are analyzed. Second, we investigate the generalized operations of DHFS based on Frank t-norm and t-conorm. The generalized operations are then used to build the generalized arithmetic and geometric aggregation operators of DHF assessments in the context of fuzzy MADM. The monotonicity of arithmetic and geometric aggregated assessments with respect to a parameter in Frank t-norm and t-conorm and their relationship are also demonstrated. In particular, the monotonicity is employed to associate the parameter with the risk attitude of a decision maker, by which a method is designed to determine the parameter. A procedure of the proposed MADM method is presented. Finally, an investment evaluation problem is discussed by the proposed approach to demonstrate its applicability and validity. A detailed sensitivity analysis and a comparative study are also conducted to highlight the validity and advantages of the approach proposed in this paper. More importantly, we discuss the situations where Frank aggregation operators are replaced by Hamacher aggregation operators at the second step of the proposed approach, through re-considering the investment evaluation problem.

Multiattribute decision making based on non-linear programming methodology with hyperbolic function and interval-valued intuitionistic fuzzy values

In this paper, we present a novel multiattribute decision making (MADM) method based on the non-linear programming (NLP) methodology with the hyperbolic tangent function and interval-valued intuitionistic fuzzy values (IVIFVs). Both the attributes’ weights and the decision matrix (DM) are expressed by IVIFVs. First, the proposed MADM method constructs the transformed decision matrix (TDM) of the DM. Then, it constructs a NLP model with the hyperbolic tangent function to get the optimal weights of the attributes. Then, it uses the interval-valued intuitionistic fuzzy weighted averaging (IVIFWA) operator to calculate the weighted evaluating IVIFVs of the alternatives. Finally, it uses Wang et al.’s method (2009) for comparing IVIFVs to obtain the preference order (PO) of the alternatives. It can conquer the shortcomings of Chen and Huang's MADM method (2017).

Commercially Available Materials Selection in Sustainable Design: An Integrated Multi-Attribute Decision Making Approach

This paper presents an integrated multi-attribute decision-making (MADM) approach to aid selection of commercially available materials in the context of sustainable design. The MADM couples grey relational analysis (GRA) with an analytic hierarchy process (AHP) to rank alternative materials in terms of their economic, environmental, and social performance. AHP is used to determine the corresponding weighting values for the selected indicators. In addition, a case example is used to verify the proposed MADM method and demonstrate its practical application. Three alternative polymer materials, i.e., poly(vinyl chloride) (PVC), polypropylene (PP), and polyethylene (PE), are examined to determine their sustainability for plastic pipe design. The associated MADM result and the limitations of the approach are discussed to lay the foundation for further improvement.

Multiattribute Decision Making Based on Entropy under Interval-Valued Intuitionistic Fuzzy Environment

Multiattribute decision making (MADM) is one of the central problems in artificial intelligence, specifically in management fields. In most cases, this problem arises from uncertainty both in the data derived from the decision maker and the actions performed in the environment. Fuzzy set and high-order fuzzy sets were proven to be effective approaches in solving decision-making problems with uncertainty. Therefore, in this paper, we investigate the MADM problem with completely unknown attribute weights in the framework of interval-valued intuitionistic fuzzy (IVIF) set (IVIFS). We first propose a new definition of IVIF entropy and some calculation methods for IVIF entropy. Furthermore, we propose an entropy-based decision-making method to solve IVIF MADM problems with completely unknown attribute weights. Particular emphasis is put on assessing the attribute weights based on IVIF entropy. Instead of the traditional methods, which use divergence among attributes or the probabilistic discrimination of attributes to obtain attribute weights, we utilize the IVIF entropy to assess the attribute weights based on the credibility of the decision-making matrix for solving the problem. Finally, a supplier selection example is given to demonstrate the feasibility and validity of the proposed MADM method.