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The purpose of this paper is to develop some picture uncertain linguistic aggregation operators based on Bonferroni mean operators, which is combined with multiple attribute decision-making (MADM) and has applied the proposed MADM model for selecting the service outsourcing provider of communications industry under picture uncertain linguistic environment.

The service outsourcing provider selection problem of communications industry can be regarded as a typical MADM problem, in which the decision information should be aggregated. In this paper, the authors investigate the MADM problems with picture uncertain linguistic information based on traditional Bonferroni mean operator.

The results show that the proposed model can solve the MADM problems within the context of picture uncertain linguistic information, in which the attributes are existing interaction phenomenon. Some picture uncertain aggregation operators based on Bonferroni mean have been developed. A case study of service outsourcing provider selection problem of communications industry is provided to illustrate the effectiveness and feasibility of the proposed methods. The results show that the proposed methods are useful to aggregate the picture uncertain linguistic decision information in which the attributes are not independent so as to select the most suitable supplier.

The proposed methods can solve the picture uncertain linguistic MADM problem, in which the interactions exist among the attributes. Therefore, it can be used to solve service outsourcing provider selection problems and other similar management decision problems.

This paper develops some picture uncertain aggregation operators based on Bonferroni mean and further presents two methods based on the proposed operators for solving MADM problems. It is useful to deal with multiple attribute interaction decision-making problems and suitable to solve a variety of management decision-making applications.

It is useful to deal with multiple attribute interaction decision-making problems and suitable to solve a variety of management decision-making applications.

The paper investigates the MADM problems with picture uncertain linguistic information based on traditional Bonferroni mean operator and develops the picture uncertain linguistic Bonferroni mean operator and picture uncertain linguistic geometric Bonferroni mean operator, picture uncertain linguistic weighted Bonferroni mean operator and picture uncertain linguistic weighted geometric Bonferroni mean operator for aggregating the picture uncertain linguistic information, respectively. Finally, a numerical example concerning the service outsourcing provider selection problem of communications industry is provided to illustrate the effectiveness and feasibility of the proposed methods.

The purpose of this paper is to develop a probabilistic uncertain linguistic (PUL) TODIM method based on the generalized Choquet integral, with respect to the interdependencies between criteria, for the selection of the best alternate in the context of multiple criteria group decision-making (MCGDM).

Owing to decision makers (DMs) do not always show completely rational and may have the preference of bounded rational behavior, this may affect the result of the MCGDM. At the same time, criteria interaction is a focused issue in MCGDM. Hence, a novel TODIM method based on the generalized Choquet integral selects the best alternate using PUL evaluation, where the generalized Choquet integral is used to calculate the weight of criterion. The generalized PUL distance measure between two probabilistic uncertain linguistic elements (PULEs) is calculated and the perceived dominance degree matrices for each alternate relative to other alternates are obtained. Furthermore, the comprehensive perceived dominance degree of each alternate can be calculated to get the ranking.

Potential application of the PUL-TODIM method is demonstrated through an evaluation example with sensitivity and comparative analysis.

As per author's concern, there are no TODIM methods with probabilistic uncertain linguistic sets (PULTSs) to solve MCGDM problems under uncertainty. Compared with the result of existing methods, the final judgment value of alternates using the extended TODIM methodology is highly corroborated, which proves its potential in solving MCGDM problems under qualitative and quantitative environments.

In many decision‐making problems under parameter uncertainty, the most popular stochastic approach is not used because of its serious drawbacks. The purpose of this paper is to present another approach, which copes with the uncertainty of parameters. It uses a precise criterion evaluating a decision with respect to uncertain parameters. This precision by the maximum operator is performed on a term based on the criterion and called the relative regret. The approach is applied to the allocation problems in a complex of operations.

The resource allocation problems in a complex of operations of independent and dependent structures to minimize a total execution time of all operations are investigated. Then, the results are extended for the problem of a task allocation in the complex of independent operations. The case is considered when the parameters in the functional models of the operations are uncertain, and their values belong to the intervals of known bounds. The solution algorithms for the uncertain problems are based on known solution algorithms for the corresponding deterministic problems. The solution algorithms for the latter problems are outlined in the paper.

The main contribution of the paper consists in presenting the property that it is possible for the uncertain problems considered to replace the solution of the uncertain allocation problems by solving a number of corresponding deterministic problems.

The useful and interesting property of the solution algorithm for the allocation problems, in general, cannot be applied to the other decision‐making problems under uncertainty. As an example of such a problem, a simple routing‐scheduling problem is presented for which, however, a number of possible parameter scenarios can be substantially limited.

The allocation problems addressed in the paper have a variety of applications in computer systems and in manufacturing systems. Moreover, a lack of crisp values for the parameters in models of individual operations is rather common.

The paper extends previous results for the allocation problems in a complex of operations.

The purpose of this paper is to examine the problem of rate allocation (RA) in computer networks in cases when some parameters are unknown or their values are imprecise.

The application of uncertain variables for the RA problems in computer networks in the presence of uncertainty is proposed.

Decision‐making problem formulations for RA in computer networks with unknown parameters of the utility functions and bandwidths based on the network utility maximization concept are given. Solution algorithms for all these problems are proposed.

It is assumed that an expert can describe possible values of unknown network parameters in the form of a certainty distribution. Then, the formalism of uncertain variables is applied and the knowledge of an expert is modelled with certainty distributions.

The RA algorithms obtained can be useful for designing and planning computer networks.

The new approach to the RA problem in computer networks in the presence of uncertainty, in cases when the probabilistic approach cannot be applied, is proposed and discussed.

The purpose of this paper is to deal with a problem of admission control in computer networks when some of their parameters are uncertain. The case is considered when the most common probabilistic description of the uncertainty cannot be used and another approach should be applied.

The uncertain versions of admission control problem with quality of service requirements are considered. The uncertain variables are used to describe possible values of the unknown parameters in computer networks.

Given are formulations for the admission control problem in computer networks with unknown values of the capacities based on the network utility maximization concept. Solution algorithms for all these problems are proposed.

It is assumed that an expert can describe possible values of uncertain network parameters in the form of a certainty distribution. Then the formalism of uncertain variables is applied and the knowledge of an expert is modelled with the use of certainty distributions. Decisions strongly depends on the quality of an expert's knowledge.

Obtained admission control algorithms can be useful for planning and designing of computer networks.

A new approach to the admission control problem in computer networks in the presence of uncertainty, in the case when the uncertain variable can be applied, is proposed and discussed.

The purpose of the paper is to propose a new decision‐making method using grey systems theory with the attribute values of corresponding alternatives in the form of intuitionistic fuzzy numbers.

The uncertain degrees of different indices are determined by using the grey incidence analysis. Then, the mass functions of different alternatives in different indices are obtained by using the score function of intuitionistic fuzzy sets and the uncertain degrees of different indices. Information can be fused in accordance with the D‐S combination rule and the best alternative is calculated accordingly. Finally, a numerical example is utilized to illustrate that a satisfied solution can be obtained and the uncertainty can be decreased.

The results are convincing: the new decision‐making method, by combining the D‐S theory of evidence, can well deal with decision‐making problems with the attribute values of corresponding alternatives in the form of intuitionistic fuzzy sets. From the numerical example, it is seen that the uncertainty can be decreased by using the new method.

The method exposed in the paper can be used to help the decision maker make a fast and accurate decision when facing decision problems with the attribute values of corresponding alternatives in the form of intuitionistic fuzzy sets.

The paper succeeds in proposing a decision‐making method by using the D‐S theory of evidence and one of the newest developed theories: grey systems theory.

Currently, for the evaluation of enterprise credit, many specific values of indexes are difficult to obtain, so decision makers tend to give a form of uncertain linguistic variable. To solve this kind of problem, the purpose of this paper is to introduce an uncertain pure linguistic approach on evaluation of enterprise integrity based on grey information.

Initial uncertain linguistic variables given by experts are transferred into interval grey numbers, and their greyness of degree is computed. Then, the greyness of degree is applied to adjust the weights of experts. Moreover, the core of each interval grey number is calculated, and through giving the positive ideal point and negative ideal point, which are binary numbers, the comprehensive grey relational grade between the linguistic number and the two points is calculated, respectively, as well to get the ranking result of projects by considering both core and greyness of degree.

The model is applied to a case, and the result verifies the validity and practicability of the model which reveals high effectiveness.

This model provides a new feasible method in a growing number of fuzzy evaluation schemes in the fields of enterprise integrity and contributes to getting better and more accurate results.

In this paper, the greyness of degree is introduced to the model to adjust the experts’ weights, and it reflects the thought of “making full use of the information” in grey system theory and further enriches the system of grey decision-making theory as well as expanding its application scope.

The concept of agile supply chain (ASC) has become increasingly important as means of achieving a competitive edge in turbulent business environments. An ASC is a dynamic alliance of member enterprises, the adaptation of which is likely to introduce velocity, responsiveness and flexibility into the manufacturing system. In ASC management, supplier/partner selection is a key strategic concern; influenced by various agility-related criteria/attributes. Therefore, evaluation and selection of potential supplier in an ASC has become an important multi-criteria decision-making problem. The purpose of this paper is to report, a supplier selection procedure (module) in the context of ASC.

During supplier selection, subjectivity of evaluation information (human judgment) often creates conflict and bears some kind of uncertainty. To overcome this, the present work attempts to explore vague set theory to deal with uncertainties in the supplier selection decision-making process. Since, vague sets can provide more accurate information as compared to fuzzy sets. It considers true membership function as well as false membership function which give more superior results for uncertain information. In this procedure, first, linguistic variables have been used to assess appropriateness rating (performance extent) as well as priority weights for individual quantitative or qualitative criterions. Second, the concept of degree of similarity and probability of vague sets has been used to determine appropriate ranking order of the potential supplier alternatives.

A case empirical example has been provided. It has been proved that the methodology would be fruitful in considering different evaluation criterion (indices); may be contradicting in nature like beneficial and cost criterions. The application of vague set theory has also been proved as a better option to work under uncertain (fuzzy) decision-making environment in comparison to fuzzy set theory.

The application of vague set theory in multi-criteria group decision making has been reported in literature to a limited extent. Application of vague set as a decision-making tool in agile supplier selection appears relative new and unexplored work area. The work has got remarkable managerial implications.

The purpose of this paper is to select the best scaling coefficient during the quantitative-qualitative conversion.

Cloud model can describe the qualitative concept of randomness and fuzziness, achieve uncertain transition between qualitative and quantitative in the field of multi-criteria group decision and has been receiving widespread attention. This paper discusses scale conversion issues of the cloud model when evaluating qualitative information. In order to improve the accuracy of the evaluation on multi-attribute decision problems based on uncertainty of natural linguistic information, this paper proposes a method of self-testing cloud model based on a composite scale (with the exponential scale and the scale as a basis).

Through experimental verification results show that under composite scale, the best suitable selection of can effectively improve the accuracy and reliability of decision results.

This research presents a new approach to determine the suitable value for coefficient based on uncertain knowledge of natural multi-criteria group decision making, and gives concrete steps and examples. This method has positive significance to improve the quality of qualitative and quantitative conversion based on cloud model.

In order to solve the decision-making problem that the attributive weight and attributive value are both interval grey numbers, this paper tries to construct a multi-attribute grey decision-making model based on generalized greyness of interval grey number.

Firstly, according to the nature of the generalized gresness of interval grey number, the generalized weighted greyness distance between interval grey numbers is given, and the transformation relationship between greyness distance and real number distance is analyzed. Then according to the objective function that the square sum of generalized weighted greyness distances from the decision scheme to the best scheme and the worst scheme is the minimum, a multi-attribute grey decision-making model is constructed, and the simplified form of the model is given. Finally, the grey decision-making model proposed in this paper is applied to the evaluation of technological innovation capability of 6 provinces in China to verify the effectiveness of the model.

The results show that the grey decision-making model proposed in this paper has a strict mathematical foundation, clear physical meaning, simple calculation and easy programming. The application example shows that the grey decision model in this paper is feasible and effective. The research results not only enrich the grey system theory, but also provide a new way for the decision-making problem that the attributive weights and attributive values are interval grey numbers.

The decision-making model proposed in this paper does not need to seek the optimal solution of the attributive weight and the attributive value, and can save the decision-making labor and capital investment. The model in this paper is also suitable for the decision-making problem that deals with the coexistence of interval grey numbers and real numbers.

The paper succeeds in realizing the multi-attribute grey decision-making model based on generalized gresness and its simplified forms, which provide a new method for grey decision analysis.