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Decision making is the task of selecting the most appropriate alternative among a finite set of possible alternatives with respect to some attributes. The attributes may be subjective or objective (or combination of both), depending upon the situation; requirements may also be conflicting. In practice, most of the real-world decision-making problems are based on subjective evaluation criteria which are basically ill-defined and vague. Since subjective human judgment bears ambiguity and vagueness in the decision making; application of grey numbers set theory may be proved fruitful in this context. The paper aims to discuss these issues.

Owing to the advantages of grey numbers set theory in tackling subjectivity in decision making; the crisp-TODIM needs to be extended by integrating with grey numbers set theory in order to facilitate decision making consisting of subjective data. Hence, the unified objective of this paper is to propose a grey-based TODIM approach in the context of decision making.

Application potential of grey-TODIM has been demonstrated through a case empirical robot selection problem. Result obtained thereof, has also been compared to that of existing grey-based decision support systems available in literature.

Application potential of grey-based decision support systems (grey-TOPSIS, grey analysis, grey-MOORA) have been highlighted in available literature resource. However, the shortcoming of these approaches is that they do not consider decision-makers’ risk attitude while decision making. TODIM method is derived from the philosophy of Cumulative Prospect Theory (CPT) which considers risk averting attitude of the decision maker in case of gain and risk seeking attitude in case of loss, while comparing dominance between two alternatives with respect to a particular criterion. Hence, this paper contributes a mathematical foundation of TODIM coupled with grey numbers set theory for logical decision making.

The main purpose of present study is to model the replacement policy under uncertainty for managerial application based on grey-reliability approach by considering the subjective views of quality control circle (QCC). The study objectively links the optimality between individual replacement and group replacement policies for determining the minimum operational costs. The integrated framework between QCC, replacement theory, grey set theory and supply chain management is presented to plan replacement actions under uncertainty.

The study proposes the concept of grey-reliability index and built a decision support model, which can deal with the imprecise information for determining the minimum operational costs to plan subsequent maintenance efforts.

The findings of the study establish the synergy between individual replacement and group replacement policies. The computations related to the numbers of failures, operational costs, reliability index and failure probabilities are presented under developed framework. An integrated framework to facilitate the managers in deciding the replacement policy based on operational time towards concerning replacement of assets that do not deteriorate, but fails suddenly over time is presented. The conceptual model is explained with a numerical procedure to illustrate the significance of the proposed approach.

A conceptual model under the framework of such items, whose failures cannot be corrected by repair actions, but can only be set by replacement is presented. The study provides an important knowledge based decision support framework for crafting a replacement model using grey set theory. The study captured subjective information to build decision model in the ambit of replacement.

Due to the limitation of acknowledgment, the complexity of software system and the interference of noises, this paper aims to solve the traditional problem: traditional software cost estimation methods face the challenge of poor and uncertain inputs.

Under such circumstances, different cost estimation methods vary greatly on estimation accuracy and effectiveness. Therefore, it is crucial to perform evaluation and selection on estimation methods against a poor information database. This paper presents a grey rough set model by introducing grey system theory into rough set based analysis, aiming for a better choice of software cost estimation method on accuracy and effectiveness.

The results are very encouraging in the sense of comparison among four machine learning techniques and thus indicate it an effective approach to evaluate software cost estimation method where insufficient information is provided.

Based on the grey rough set model, the decision targets can be classified approximately. Furthermore, the grey of information and the limitation of cognition can be overcome during the use of the grey rough interval correlation cluster method.

This paper proposed the grey rough set model combining grey system theory with rough set for software cost estimation method evaluation and selection.

The purpose of this paper is to explain the connotation of grey number, which is the basic unit of grey mathematics and the key to establish the mathematic framework of grey system theory.

From the grey hazy set, the paper re‐defines grey number and the operation of grey‐number element, then some properties are obtained. Based on them, the operation of grey‐matrix element is given. The general definition of grey function and its operation are also proposed.

The connotation of grey number is elaborated and the elementary framework of grey mathematics can be established.

The researched object, objective and techniques of grey system theory have not been logically proposed and they may influence the comprehension of grey system theory. The obtained results of grey mathematics may significantly promote its development.

The paper can enable managers to control the complex system with missing information by using the quantitative approaches.

Grey mathematics may become a branch of mathematics to deal with proximate calculation.

The purpose of this paper is to study the grey decision model and distance measuring method of general grey number.

First, intuitionistic grey number (IGN) set and an IGN are defined by grey number probability function. Second, each interval grey number in general grey number is represented by an IGN and converts the general grey number into an IGN set. Final, the operation of two general grey numbers is defined as the operation between IGN sets, and the distance measure of the general grey number is given.

Up to now, the method of measuring the distance and the grey decision model of general grey number is established. Thus, the difficult problem for set up decision mode of general grey number has been solved to a certain degree.

The method exposed in this paper can be used to integrate information form a different source. The method that a general grey number converted to a set of IGNs could be extended to the case of grey incidence analysis models, grey prediction models and grey clustering evaluation models, which includes general grey numbers, etc.

The concepts of IGN and IGN set are proposed for the first time in this paper; The operation of two general grey numbers can be defined as the operation between IGN sets. On this basis, the algorithm of IGN, the integration operator of IGN and the distance measure between IGN sets are given.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.

Risk management is one of the most influential parts of project management that has a major impact on the success or failure of projects. Due to the increasing use of information technology in all fields and the high failure rate of software development projects, it is essential to predict the risk level of each project effectively before starting. Therefore, the main purpose of this paper is proposing an expert system to infer about the risk of new banking software development project.

In this research, the risk of software developing projects is considered from four dimensions including risk of cost deviation, time deviation, quality deviation and scope deviation, which is examined by rough set theory (RST). The most important variables affecting the cost, time, quality and scope of projects are identified as condition attributes and four initial decision systems are constructed. Grey system theory is used to cluster the condition attributes and after data discretizing, eight rule models for each dimension of risk as a decision attribute are extracted using RST. The most validated model for each decision attribute is selected as an inference engine of the expert system, and finally a simple user interface is designed in order to predict the risk level of any new project by inserting the data of project attributes

In this paper, a high accuracy expert system is designed based on the combination of the grey clustering method and rough set modeling to predict the risks of each project before starting. Cross-validation of different rule models shows that the best model for determining cost deviation is Manual/Jonson/ORR model, and the most validated models for predicting the risk of time, quality and scope of projects are Entropy/Genetic/ORR, Manual/Genetic/FOR and Entropy/Genetic/ORR models; all of which are more than 90% accurate

It is essential to gather data of previous cases to design a validated expert system. Since data documentation in the field of software development projects is not complete enough, grey set theory (GST) and RST are combined to improve the validity of the rule model. The proposed expert system can be used for risk assessment of new banking software projects

The risk assessment of software developing projects based on RST is a new approach in the field of risk management. Furthermore, using the grey clustering for combining the condition attributes is a novel solution for improving the accuracy of the rule models.

Grey set is the important foundation of the grey mathematics and grey system theory, and the possibility function is the way of expressing grey set. This paper aims to establish the method of determining the possibility function of grey set and discusses its extended applications.

First, the grey kernel and the grey support set of grey set are defined, and the properties of grey kernel are analyzed. Second, according to the decomposition theorem of grey set, a method of determining the possibility function of grey set is put forward in this paper, which is called the method of increasing information and taking maximum and minimum (IITMM), and then it is further simplified as the method of increasing information and taking maximum (IITM), and an simple example is given to illustrate the calculation procedure. Finally, the grey information cluster method (GICM) based on IITM is proposed and applied to the ecological and geographical environment analysis of pine caterpillar.

The results show that the grey kernel of grey set still has grey uncertainty; the method of IITM has simple calculation and strict mathematical basis, and it can synthesize the information of the research object and accords with the principle of using minimum information; the GICM and the fuzzy cluster method have the same classification effect.

The researches show that method of IITM can be used not only to determine the possibility function of the grey set effectively, but also be used for the evaluation and cluster analysis of connotative objects. The classification result of the GICM presented in this paper is more precise than that of the fuzzy cluster method.

The paper succeeds in realizing both the IITM method for determining the possibility function of grey set and the GICM based on IITM for the connotative objects.

The purpose of this paper is to design an inference engine to measure the level of readiness of each bank before starting the corporate sustainability auditing process. Based on the output of the designed inference engine, the audition team can decide about the audition resources and the auditing process.

In this paper, the hybrid rough and grey set theory are used to design and create a rule model system to measure the sustainability level of banks. First, 16 rule models are extracted using rough set theory (RST), and the cross-validation of each model is done. Then, the grey clustering is used to combine the same condition attributes and improve the validity of the final model. A total of 16 new rule models are extracted based on the decreased condition attributes, and the best model is selected based on the cross-validation results.

By comparing the accuracy of rough-gray’s rule models and as a result of decreasing the condition attributes, a proper increase in the accuracy of all models is obtained. Finally, the Naive/Genetic/object-related reducts model with 95.6% accuracy is selected as an inference engine to measure new banks’ readiness level.

Sustainability measurement of banks based on RST is a new approach in the field of corporate sustainability. Furthermore, using the grey clustering for combining the condition attributes is a novel solution for improving the accuracy of the rule models.

The oil and gas industry is a crucial economic sector for both developed and developing economies. Delays in extraction and refining of these resources would adversely affect industrial players, including that of the host countries. Supplier selection is one of the most important decisions taken by managers of this industry that affect their supply chain operations. However, determining suitable suppliers to work with has become a phenomenon faced by these managers and their organizations. Furthermore, identifying relevant, critical and important criteria needed to guide these managers and their organizations for supplier selection decisions has become even more complicated due to various criteria that need to be taken into consideration. With limited works in the current literature of supplier selection in the oil and gas industry having major methodological drawbacks, the purpose of this paper is to develop an integrated approach for supplier selection in the oil and gas industry.

To address this problem, this paper proposes a new uncertain decision framework. A grey-Delphi approach is first applied to aid in the evaluation and refinement of these various available criteria to obtain the most important and relevant criteria for the oil and gas industry. The grey systems theoretic concept is adopted to address the subjectivity and uncertainty in human judgments. The grey-Shannon entropy approach is used to determine the criteria weights, and finally, the grey-EDAS (evaluation based on distance from average solution) method is utilized for determining the ranking of the suppliers.

To exemplify the applicability and robustness of the proposed approach, this study uses the oil and gas industry of Iran as a case in point. From the literature review, 21 criteria were established and using the grey-Delphi approach, 16 were finally considered. The four top-ranked criteria, using grey-Shannon entropy, include warranty level and experience time, relationship closeness, supplier’s technical level and risks which are considered as the most critical and influential criteria for supplier evaluation in the Iranian oil and gas industry. The ranking of the suppliers is obtained, and the best and worst suppliers are also identified. Sensitivity analysis indicates that the results using the proposed methodology are robust.

The proposed approach would assist supply chain practicing managers, including purchasing managers, procurement managers and supply chain managers in the oil and gas and other industries, to effectively select suitable suppliers for cooperation. It can also be used for other multi-criteria decision-making (MCDM) applications. Future works on applying other MCDM methods and comparing them with the results of this study can be addressed. Finally, broader and more empirical works are required in the oil and gas industry.

This study is among the first few studies of supplier selection in the oil and gas industry from an emerging economy perspective and sets the stage for future research. The proposed integrated grey-based MCDM approach provides robust results in supplier evaluation and can be used for future domain applications.