Multiple attributes group decision making (MAGDM) is regarded as the process of determining the best feasible solution by a group of experts or decision makers according to the attributes that represent different effects. In assessing the performance of each alternative with respect to each attribute and the relative importance of the selected attributes, quantitative/qualitative evaluations are often required to handle uncertainty, imprecise and inadequate information, which are well suited to represent with fuzzy values. This paper develops a VIKOR method based on intuitionistic fuzzy sets with multi-judges and multi-attributes in real-life situations. Intuitionistic fuzzy weighted averaging (IFWA) operator is used to aggregate individual judgments of experts to rate the importance of attributes and alternatives. Then, an intuitionistic ranking index is introduced to obtain a compromise solution to solve MAGDM problems. For application and validation, this paper presents two application examples and solves the practical portfolio selection and material handling selection problems to verify the proposed method. Finally, the intuitionistic fuzzy VIKOR method is compared with the existing intuitionistic fuzzy MAGDM method for two application examples, and their computational results are discussed.

Generalized trapezoidal fuzzy numbers (GTFNs) have been widely applied in uncertain decision-making problems. The similarity between GTFNs plays an important part in solving such problems, while there are some limitations in existing similarity measure methods. Thus, based on the cosine similarity, a novel similarity measure of GTFNs is developed which is combined with the concepts of geometric distance, center of gravity, area and perimeter after analyzing the limitations of previous methods. Then comparative analysis is conducted with existing similarity measures, and the results show that the novel similarity measure has better distinguishability and lower invalidity. Furthermore, a general process, which combines the new similarity measure of GTFNs with compromise methods, is developed to deal with multi-attribute group decision making (MAGDM) problem. Finally, we combine fuzzy VIKOR with the general process as illustrated example, which proves the superiority of the developed similarity measure in solving MAGDM problem.

In a construction project, there are many factors that affect the project quality, such as people, materials, machinery, environment, etc. Among them, people have the greatest influence on the project quality, whether people participate directly or indirectly. This paper mainly evaluates human factors in the process of construction project management, such as workers proficiency, workers safety awareness, technical workers quality, and workers emergency capacity, with the purpose of helping Chinas construction project to proceed smoothly. In this manuscript, a multi-attribute group decision-making (MAGDM) technique based on Pythagorean interval 2-tuple linguistic numbers (PI2TLNs) and VIKOR method is proposed to evaluate human factors in construction projects. PI2TLNs are used to represent performance assessments of decision makers. Relying on Pythagorean interval 2-tuple linguistic weighted averaging (PI2TLWA)/Pythagorean interval 2-tuple linguistic weighted geometric (PI2TLWG) operator, the evaluation information given by experts is fused into a group decision matrix. Combined with the essential VIKOR method, PI2TLNVIKOR framework is established. The effectiveness of this method is verified by an example, and compared with two algorithms and PI2TLN-TODIM method.

Cyber security is a hot topic in recent years and one of the main performances in the decision-making is the choice of cyber security service providers (CSSPs). For enterprises and government units, the selection of appropriate NSSPs needs to be measured and evaluated from multiple perspectives, which is obviously a multiple attribute decision making (MADM) or multiple attribute group decision making (MAGDM). In this paper, the traditional MABAC method is improved by using the prospect theory, and the evaluation information is collected and sorted by using PULTS. The improved PUL-PT-MABAC method can not only deal with the uncertainty well, but also fully consider the influence of the psychological state of decision maker (DM) on the decision result. More importantly, we apply the improved PUL-PT-MABAC model to the selection of NSSPs and prove the reliability of this proposed method by taking advantage of comparative analysis with three existed methods. These results show that the model can deal with practical problems, and has good practicability and science.

In this paper, an interval-valued Pythagorean triangular fuzzy number (IVPTFN) as a useful tool to handle decision-making problems with vague quantities is defined. Then, their operational laws are developed. By introducing a novel method of making a decision on the concept of possibility theory, a multi-attribute group decision-making (MAGDM) problem is considered, in which the attribute values are expressed with the IVPTFN and the information on the decision makers’ (DM) weights is completely unknown. Two novel forms of a multi-attributive border approximation area comparison (MABAC) technique are proposed to solve the problem. One of them is applied to compute the weights of the decision makers, and the other is used to rank the preference order of alternatives, that is based on the possibility expected value and standard deviation and has no aggregation of information. Finally, to illustrate the practicality and effectiveness of proposed method in real-world problems, the proposed method is applied in a real case study of an Iranian transport complex to sustainability assessment of its transport projects.

In this article, we introduce the interval-valued intuitionistic fuzzy set (\textbf{IVIFS}), which are generalized forms of intuitionistic fuzzy set (\textbf{IFS}) and fuzzy set, this is because in intuitionistic fuzzy sets the non-membership function also applies to evaluations, and these sets are useful for modelling ambiguous concepts that abound in real problems. Here we try to look for new methods for more practical solutions in optimization problems for various sciences such as computer science, mathematics, engineering, medicine, psychology, climate and etc. First, with the introduction of t-norm Frank, an action we construct some Frank aggregation operators on interval-valued intuitionistic fuzzy numbers (\textbf{IVIFN}s), including the Frank weighted averaging operator, Frank-ordered weighted averaging operator, Frank hybrid weighted averaging operator, Frank geometric weighted averaging operator, Frank geometric-ordered weighted averaging operator, and Frank geometric hybrid weighted averaging operator. Also, examine some of the characteristics of these operators. In the following, we introduce two multiple attribute group decision-making methods (\textbf{MAGDM}) based on such operators. Finally, we provide illustrative examples of these methods.

Linguistic variables (LVs) provide a reliable expression of cognitive information. By inheriting the advantages of LVs, we can express uncertain and incomplete cognitive information in multiple attribute decision-making (MADM), and they do so better than existing methods.  In the decision-making process, we can consider decision experts’ (DEs’) bounded rationality, such as cognition toward loss caused by the DEs’ cognitive limitations during the decision process. Therefore, it is necessary to propose a novel cognitive decision approach to handle MADM problems in which the cognitive information is expressed by LVs. In this paper, we employ LVs to represent uncertain and hesitant cognitive information. Then, we propose a mathematical programming approach to solve the MADM problems where attributes or cognitive preferences are not independent.  Moreover, the validity and superiority of the presented approach are verified by dealing with a practical problem.

The Bonferroni mean (BM) has the advantages that it can capture the interrelationship among the input arguments, and the Harmonic mean is a conservative average lying between the max and min operators. The 2-dimension uncertain linguistic variables add a subjective evaluation on the reliability of the evaluation results given by decision makers, so they can better express fuzzy information. In this paper, in order to combine the advantages of them, we first propose the 2-dimensional uncertain linguistic weighted Bonferroni mean (2DULWBM) operator. However, it cannot consider the case when the given arguments are too high or too low. So we further proposed the 2-dimensional uncertain linguistic improved weighted Bonferroni harmonic mean (2DULIWBHM) operator, which combine the 2DULWBM with Harmonic Mean. Furthermore, we study some desirable properties and some special cases of them. Further, we develop a new method to deal with some multi-attribute group decision making (MAGDM) problems under 2-dimension uncertain linguistic environment based on the proposed operators. Finally, an illustrative example is given to testify the validity of the developed method by comparing with the other existing methods.

This paper introduces a new decision support framework for transport projects appraisal, which is based on the multi-criteria decision analysis (MCDA) and the cost-benefit analysis (CBA) to address both monetary and non-monetary characteristics of the problem at the same time. Substantial inaccuracies are present while obtaining non-monetary and monetary inputs to the MCDA and the CBA, respectively. To provide the MCDA part of the framework with uncertainty, an interval-valued Pythagorean fuzzy set (IVPFS) is used as an attractive uncertain modeling tool. Additionally, a new multi-attribute group decision-making (MAGDM) method with partially known attribute weights and unknown expert weights under the IVPFS environment is proposed to find the best sustainable transport project from the non-monetary criteria point of view. Furthermore, a novel uncertainty modeling tool, namely an interval-valued Pythagorean trapezoidal fuzzy set, is introduced to address ill-known quantities and inaccuracies that exist in the estimation of monetary impacts. Finally, this framework is used to handle a real case study of a complex decision process of finding the best transport project to fund several candidate projects. This approach has made it possible to handle the decision process from economic, social, environmental points of view at the same time. The result of this case study shows that the decision-making framework can be used as a valuable decision support tool. Moreover, it is shown that the presented framework can be applied to effectively support appraisals of transport projects.