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Handing computing assets to cloud service providers (CSPs) to obtain cloud services is one of the important strategies for enterprises to embrace the digital era, and CSP selection is a crucial decision‐making process for cloud deployment. However, there are many criteria involved in selecting an optimal CSP, not all of which can be accurately quantified. Therefore, CSP selection is a typical hybrid‐information decision‐making problem, in which criterion evaluation values are expressed in various forms. Meanwhile, the psychological behavior of the CSP selection team also has a significant impact on the decision‐making result, which is poorly considered in the existing research results on CSP selection. Thus, in this paper, a new group decision‐making support framework incorporating regret theory is constructed to select CSPs with hybrid information. Initially, various forms of hybrid information are processed separately to avoid the distortion of heterogeneous information caused by traditional conversion methods. Then, considering the psychology of regret aversion, the respective regret–rejoice functions for hybrid information are defined. Subsequently, regret–rejoice values are introduced into the evaluation of mixed data method framework, and a decision‐making support procedure based on it is established, in which an expert weight determination method based on the maximizing consensus model is proposed, and the group best–worst method is used to calculate criteria weights. Afterwards, an illustrative example of CSP selection is given to clarify the implementation process of the proposed method. Finally, the effectiveness and superiority of the proposed decision‐making framework in selecting CSPs are explained through parameter analysis and comparison with existing methods. [ABSTRACT FROM AUTHOR]

The main aim of the proposed work is to develop the new technique based on decision‐theoretical rough sets (DTRSs) and their applications in three‐way decision‐making problems. This study first develop a fractional fuzzy set (FFS) and their operations, the FFS is a more generalized and accurate tool for describing uncertainty in real‐life data information. A new form of decision technique for dealing with the issue of choice based on DTRSs is included in the three‐way decisions. The loss function of DTRSs is being used in the proposed decision method model. Initially, the idea of fractional fuzzy α‐covering (FF α‐covering), fractional fuzzy α–neighborhood (FF α–neighborhood) was introduced. Under the fractional fuzzy state, we integrated the loss function of DTRSs with covering‐based fractional fuzzy rough sets. Furthermore, we proposed and established performance characteristics for a new fractional fuzzy α‐covering decision‐theoretical rough sets model (FFCDTRSs). Then, according to the level of fractional fuzzy numbers (FFN's) positive and negative membership and related three‐way decision‐making, four methods to solve the expected loss expressed in the form of (FFNs) are described. We have developed a multicriteria decision algorithm (MCDM) based on FFCDTRS. Then an example is used to prove the feasibility of the four methods to solve the MCDM problem. Finally, the results of four distinct decision procedures with various loss functions are compared. The proposed three‐way decision‐making models are more accurate as compared with particular fuzzy sets. [ABSTRACT FROM AUTHOR]

The selection and evaluation of fresh food suppliers is the primary problem for supermarkets. This problem is solved by a new multiattribute group decision‐making method with multigranular unbalanced hesitant fuzzy linguistic term set, which is based on prospect theory and evidential theory. Then, a novel supermarket fresh food supplier evaluation index is constructed with 5 elements and 15 indicators. To get the reasonable weights, best–worst method, criteria importance through intercriteria correlation method, and game theory are applied. Moreover, three methods are compared to prove our proposed method's validity and superiority. Finally, this paper offers analysis and suggestions based on the results from strategy level and statics level, respectively. [ABSTRACT FROM AUTHOR]

Massive open online courses (MOOCs) are very popular in China, and it is very important to evaluate and improve them. In this paper, a new evaluation method for MOOCs based on multi‐attribute group decision‐making is proposed. First, an evaluation index system of MOOCs is constructed, which contains six elements and 16 indicators, and multigranular unbalanced hesitant fuzzy linguistic term set (MGUHFLTS) is adopted to describe these indicators. Then based on MGUHFLTS, the aggregation operators are developed, including the multigranularity unbalanced hesitant fuzzy linguistic weighted averaging operator and the multigranularity unbalanced hesitant fuzzy linguistic order weighted averaging operator, moreover, a novel multi‐attributive border approximation area comparison model based on MGUHFLTS is proposed. This model is testified validity and superiority by comparison with other three methods and is applied in evaluation of MOOCs. After ranking five MOOCs, each indicator is analyzed to show how they influenced each element and suggestions are given. [ABSTRACT FROM AUTHOR]

Normal wiggly hesitant fuzzy set (NWHFS) is a new fuzzy information form to help decision makers (DMs) express their evaluations, which can further dig the potential uncertain information hidden in the original data given by the DMs. Firstly, we define a new distance measure and new operational laws of NWHFSs. Then, for the situation where attribute weights are completely unknown, we propose an extended CCSD method to produce them objectively, which comprehensively uses standard deviation (SD) and correlation coefficient (CC). What's more, we introduce the MABAC (multiattributive border approximation area comparison) method, which takes the distance between alternatives and the border approximation area (BAA) into consideration for handling the complex and uncertain decision‐making problems. Meanwhile, we combine the MABAC method with prospect theory (PT), which considers DMs' psychological behavior, and propose a new NWHF‐CCSD‐PT‐MABAC method to cope with the multi‐attribute decision making problems under normal wiggly hesitant fuzzy environment. Lastly, we illustrate the validity and advantages of the proposed method through an example of college book supplier selection. [ABSTRACT FROM AUTHOR]

Linguistic q‐rung orthopair fuzzy numbers (Lq‐ROFNs) are a qualitative form of q‐rung orthopair fuzzy numbers (q‐ROFNs) where the membership and nonmembership degrees are represented by linguistic variables. The Lq‐ROFNs can describe a broader range of linguistic assessment information flexibly by adjusting the parameter q based on different situations, so they are more superior to the linguistic intuitionistic fuzzy numbers and linguistic Pythagorean fuzzy numbers in real application. Based on the Lq‐ROFNs, we introduce the entropy measure which can be used to determine the indefiniteness of the assessment information. Then, based on the linguistic entropy measure, we further propose a method to obtain the attribute weights when the weight information is incomplete known. For aggregating the assessment information, the power average (PA) operator can reduce the influence of extreme data caused by the biased decision‐makers by considering the support degree of different evaluation individuals, and the Muirhead mean (MM) operator can take the interrelationship of different numbers of attributes into account by adjusting the parameter vector based on the real situations. In this paper, based on these two operators, we firstly propose the linguistic q‐rung orthopair fuzzy PA operator and linguistic q‐rung orthopair fuzzy weighted PA operator. Further, for combing the advantages of the MM operator and PA operator, we propose the linguistic q‐rung orthopair fuzzy power MM (PMM) operator and linguistic q‐rung orthopair fuzzy weighted PMM operator, and then investigate some properties of them. Finally, a new multiple‐attribute group decision‐making (MAGDM) method is proposed to process the Lq‐ROFNs, and some practical examples are given to illustrate the effectiveness and superiority of this new method in comparison with other existing MAGDM methods. [ABSTRACT FROM AUTHOR]

In this paper, a new conception of linguistic q‐rung orthopair fuzzy number (Lq‐ROFN) is proposed where the membership and nonmembership of the q‐rung orthopair fuzzy numbers (q‐ROFNs) are represented as linguistic variables. Compared with linguistic intuitionistic fuzzy numbers and linguistic Pythagorean fuzzy numbers, the Lq‐ROFNs can more fully describe the linguistic assessment information by considering the parameter q to adjust the range of fuzzy information. To deal with the multiple‐attribute group decision‐making (MAGDM) problems with Lq‐ROFNs, we proposed the linguistic score and accuracy functions of the Lq‐ROFNs. Further, we introduce and prove the operational rules and the related properties characters of Lq‐ROFNs. For aggregating the Lq‐ROFN assessment information, some aggregation operators are developed, involving the linguistic q‐rung orthopair fuzzy power Bonferroni mean (BM) operator, linguistic q‐rung orthopair fuzzy weighted power BM operator, linguistic q‐rung orthopair fuzzy power geometric BM (GBM) operator, and linguistic q‐rung orthopair fuzzy weighted power GBM operator, and then presents their rational properties and particular cases, which cannot only reduce the influences of some unreasonable data caused by the biased decision‐makers, but also can take the interrelationship between any two different attributes into account. Finally, we propose a method to handle the MAGDM under the environment of Lq‐ROFNs by using the new proposed operators. Further, several examples are given to show the validity and superiority of the proposed method by comparing with other existing MAGDM methods. [ABSTRACT FROM AUTHOR]

The two‐dimensional uncertain linguistic variables (2DULVs) add a self‐evaluation on the reliability of the assessment results given by decision makers (DMs), so they can better describe some uncertain information, and the partition Bonferroni mean (PBM) operator has the advantages, which assumes that all aggregated arguments are partitioned into several subparts, and members in the same subpart are interrelated and members in different subparts are no interrelationships. However, the traditional PBM can only deal with the crisp numbers and cannot aggregate the 2DULVs. In this paper, we extend the PBM operator to deal with the 2DULVs and propose some PBM operators for 2DULVs. First, we introduce the concepts, properties, operational laws, and comparison methods of 2DULVs, and then we propose the PBM operator for 2DULVs (2DULPBM), the weighted PBM operator for 2DULVs (2DULWPBM), the partitioned geometric Boferroni mean (PGBM) operator for 2DULVs (2DULPGBM), and weighted PGBM operator for 2DULVs (2DULWPGBM). Further, we develop a method to solve multiattribute group decision‐making (MAGDM) problems with the 2DULVs. Finally, we give an example to verify that the method based on the proposed operators is effective and influential. [ABSTRACT FROM AUTHOR]

The q-rung orthopair fuzzy sets (q-ROFs) are an important way to express uncertain information, and they are superior to the intuitionistic fuzzy sets and the Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the membership degree and the qth power of the degrees of non-membership is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we propose the q-rung orthopair fuzzy weighted averaging operator and the q-rung orthopair fuzzy weighted geometric operator to deal with the decision information, and their some properties are well proved. Further, based on these operators, we presented two new methods to deal with the multi-attribute decision making problems under the fuzzy environment. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods. [ABSTRACT FROM AUTHOR]

In the real multi-attribute group decision making (MAGDM), there will be a mutual relationship between different attributes. As we all know, the Bonferroni mean (BM) operator has the advantage of considering interrelationships between parameters. In addition, in describing uncertain information, the eminent characteristic of q-rung orthopair fuzzy sets ( q-ROFs) is that the sum of the qth power of the membership degree and the qth power of the degrees of non-membership is equal to or less than 1, so the space of uncertain information they can describe is broader. In this paper, we combine the BM operator with q-rung orthopair fuzzy numbers ( q-ROFNs) to propose the q-rung orthopair fuzzy BM ( q-ROFBM) operator, the q-rung orthopair fuzzy weighted BM ( q-ROFWBM) operator, the q-rung orthopair fuzzy geometric BM ( q-ROFGBM) operator, and the q-rung orthopair fuzzy weighted geometric BM ( q-ROFWGBM) operator, then the MAGDM methods are developed based on these operators. Finally, we use an example to illustrate the MAGDM process of the proposed methods. The proposed methods based on q-ROFWBM and q-ROFWGBM operators are very useful to deal with MAGDM problems. [ABSTRACT FROM AUTHOR]