The Compromise Ratio Method With Intuitionistic Fuzzy Distance for FMAGDM

The compromise ratio method (CRM) is an effective method to solve multiple attribute group decision making (MAGDM). Distance measure of intuitionistic fuzzy (IF) numbers (IFNs) is important for CRM. In this paper, according to the IF distance of IFNs, an extended compromise ratio method (CRM) is developed for (MAGDM) problems which attribute weights and evaluation values of alternatives on attributes are expressed in linguistic variables parameterized using TIFNs. Finally, the effectiveness and practicability of the extended CRM with IF distance are demonstrated by solving a software selection problem.

Multiple attribute group decision-making based on interval-valued q-rung orthopair uncertain linguistic power Muirhead mean operators and linguistic scale functions

Fuzzy set theory and its extended form have been widely used in multiple-attribute group decision-making (MAGDM) problems, among which the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) got a lot of attention for its ability of capturing information denoted by interval values. Based on the previous studies, to find a better solution for fusing qualitative quantization information with fuzzy numbers, we propose a novel definition of interval-valued q-rung orthopair uncertain linguistic sets (IVq-ROULSs) based on the linguistic scale functions, as well as its corresponding properties, such as operational rules and the comparison method. Furthermore, we utilize the power Muirhead mean operators to construct the information fusion method, and provide a variety of aggregation operators based on the proposed information description environment. A model framework is constructed for solving the MAGDM problem utilizing the proposed method. Finally, we illustrate the performance of the new method and investigate its advantages and superiorities through comparative analysis.

Some Trapezoid Intuitionistic Fuzzy Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple-Attribute Decision Making

In order to solve multiple-attribute group decision-making (MAGDM) problems under a trapezoid intuitionistic fuzzy linguistic (TIFL) environment and the relationships between multiple input parameters needed, in this paper, we extend the Maclaurin symmetric mean (MSM) operators to TIFL numbers (TIFLNs). Some new aggregation operators are proposed, including the trapezoid intuitionistic fuzzy linguistic Maclaurin symmetric mean (TIFLMSM) operator, trapezoid intuitionistic fuzzy linguistic generalized Maclaurin symmetric mean (TIFLGMSM) operator, trapezoid intuitionistic fuzzy linguistic weighted Maclaurin symmetric mean (TIFLWMSM) operator and trapezoid intuitionistic fuzzy linguistic weighted generalized Maclaurin symmetric mean (TIFLWGMSM) operator. Next, based on the TIFLWMSM and TIFLWGMSM operators, two methods are presented to deal with MAGDM problems. Finally, there is a numerical example to verify the effectiveness and feasibility of the proposed approaches.

Taxonomy method for multiple attribute group decision making based on interval-valued intuitionistic fuzzy with entropy

Interval-valued intuitionistic fuzzy set (IVIFS) is a flexible method to deal with uncertainty and fuzziness. For the past few years, extensive researches about the multi-attribute group decision making (MAGDM) problems based on IVIFSs has been extensively studied in many fields. In this study, the Taxonomy method based on IVIFSs (IVIF-Taxonomy) was proposed for MAGDM problems. For the sake of the objectivity of attribute weight, entropy is introduced into the proposed model. The IVIF-Taxonomy method fully considers the weight of the decision makers (DMs) and the homogeneity of the chosen alternatives, making it more realistic. In addition, we apply IVIF-Taxonomy method to fund selection to verify the validity of IVIF-Taxonomy method. Finally, the trustworthy of IVIF-Taxonomy method is proved by comparing with the aggregate operator, IVIF-TOPSIS method, IVIF-GRA method and modified IVIF-WASPAS method.

Correlation coefficients of credibility interval-valued neutrosophic sets and their group decision-making method in single- and interval-valued hybrid neutrosophic multi-valued environment

Although a single-valued neutrosophic multi-valued set (SVNMVS) can reasonably and perfectly express group evaluation information and make up for the flaw of multi-valued/hesitant neutrosophic sets in group decision-making problems, its information expression and group decision-making methods still lack the ability to express and process single- and interval-valued hybrid neutrosophic multi-valued information. To overcome the drawbacks, this study needs to propose single- and interval-valued hybrid neutrosophic multi-valued sets (SIVHNMVSs), correlation coefficients of consistency interval-valued neutrosophic sets (CIVNSs), and their multi-attribute group decision-making (MAGDM) method in the setting of SIVHNMVSs. First, we propose SIVHNMVSs and a transformation method for converting SIVHNMVSs into CIVNSs based on the mean and consistency degree (the complement of standard deviation) of truth, falsity and indeterminacy sequences. Then, we present two correlation coefficients between CIVNSs based on the multiplication of both the correlation coefficient of interval-valued neutrosophic sets and the correlation coefficient of neutrosophic consistency sets and two weighted correlation coefficients of CIVNSs. Next, a MAGDM method is developed based on the proposed two weighted correlation coefficients of CIVNSs for performing MAGDM problems under the environment of SIVHNMVSs. At last, a selection case of landslide treatment schemes demonstrates the application of the proposed MAGDM method under the environment of SIVHNMVSs. By comparative analysis, our new method not only overcomes the drawbacks of the existing method, but also is more extensive and more useful than the existing method when tackling MAGDM problems in the setting of SIVHNMVSs.

CPT-MABAC-Based multiple attribute group decision making method with probabilistic hesitant fuzzy information

Facing with a sea of fuzzy information, decision makers always feel it difficult to select the optimal alternatives. Probabilistic hesitant fuzzy sets (PHFs) utilize the possible numbers and the possible membership degrees to describe the behavior of the decision makers. though this environment has been introduced to solve problems using different methods, this circumstance can still be explored by using different method. This paper’ s aim is to develop the MABAC (Multi-Attributive Border Approximation area Comparison) decision-making method which based on cumulative prospect theory (CPT) in probabilistic hesitant fuzzy environment to handle multiple attributes group decision making (MAGDM) problems. Then the weighting vector of attributes can be calculated by the method of entropy. Then, in order to show the applicability of the proposed method, it is validated by a case study for buying a house. Finally, through comparing the outcome of comparative analysis, we conclude that this designed method is acceptable.

An interval type-2 fuzzy TOPSIS for MAGDM applied to solar power systems

This article proposes a new version of the technique of order preference by similarity to an ideal solution (TOPSIS) to solve fuzzy multi-attribute group decision making (MAGDM) problems using trapezoidal interval type-2 fuzzy sets (IT2FSs). The traditional TOPSIS ranks the alternatives according to their relative degree of closeness to the ideal solutions. On the other hand, TOPSIS based on similarity measure ranks the alternatives according to their total degree of similarity to the ideal solutions. This study extends TOPSIS using similarity measure using map distance to IT2FSs. First, the similarity measure based on map distance for interval-valued fuzzy sets (IVFSs) is extended to encompass IT2FSs due to the deficiency in IT2FSs similarity measures. Then, TOPSIS using similarity measure is applied. Hence, fuzzy MAGDM problems can be handled in a more flexible intelligent manner and avoiding defuzzification with its drawbacks. An illustrative example is given to explain the approach. Then, a practical problem in assessing thermal energy storage technologies in solar power systems is solved, where the weights of the attributes and the performance of the qualitative attributes are linguistic variables modeled by IT2FSs. The reliability of two normalization techniques is examined and the impact of the theoretical and empirical reference points on the solution is investigated.

Interval-valued intuitionistic pure linguistic entropy weight method and its application to group decision-making

In recent years, the problem of complex multi-attribute group decision-making (MAGDM) in uncertain environments has received increasing attention. In evaluating MAGDM problems, obtaining the objective attribute weights is very important. Considering the excellent performance of intuitive fuzzy linguistic sets in dealing with uncertain information, this paper introduces a new interval-valued intuitionistic pure linguistic entropy weight (IVIPLEW) method for determining attribute weights and evaluating MAGDM problems. The IVIPLEW method considers the cases of missing values, and uses the conventional interval-valued intuitionistic pure linguistic (IVIPL) expectations to supplement the missing values. This method of dealing with missing values not only considers the expectations of experts, but also prevents fluctuations in linguistic variables from impacting the decision results. This paper establishes an analysis framework that allows the IVIPLEW method to be applied to MAGDM problems, and presents a practical case study that illustrates the practicality and effectiveness of IVIPLEW. The results are quite satisfactory. The effectiveness of the proposed method is demonstrated through a comparison with the IVIPL information aggregation method. Furthermore, the robustness of the IVIPLEW method is verified through a sensitivity analysis. The results presented in this paper show that the IVIPLEW method is applicable to a wide range of MAGDM problems.

Some self-evaluation models of enterprise’s credit based on some probabilistic double hierarchy linguistic aggregation operators

Probabilistic double hierarchy linguistic term set (PDHLTS) can not only express the complex linguistic information that the probabilistic linguistic term set (PLTS) cannot express, but also reflect the frequency or importance of linguistic term set (LTS)that cannot be reflected by the double hierarchy linguistic term set (DHLTS). It is an effective tool to deal with multiple attribute group decision making (MAGDM) problems. Therefore, in this paper, we propose several aggregation operators which can aggregate PDHLTS information and apply them to MAGDM problems. Firstly, the basic notion of PDHLTS is reviewed, and the distance formula and algorithm of PDHLTS are defined; then, extant weighted averaging (WA) operator, weighted geometric(WG) operator and power weighted averaging (PWA) operator, power weighted geometric(PWG) operator to PDHLTS, and establish probability double hierarchy linguistic weighted averaging (PDHLWA) operator, probability double hierarchy linguistic weighted geometric (PDHLWG) operator, probability double hierarchy linguistic power weighted averaging (PDHLPWA) operator, probability double hierarchy linguistic power weighted geometric (PDHLPWG) operator; in addition, The idempotency, boundedness and monotonicity of these aggregation operators are studied; what’s more, those aggregation operators are proposed to establish the enterprise credit self-evaluation model; Finally, compared with the available probabilistic double hierarchy linguistic MAGDM methods, the defined model is proved to be scientific and effective.