A novel group decision making approach based on the cumulative belief degrees

In recent years, the interest in the research activities in group decision making have dramatically increased. A group decision making (GDM) problem is defined as a decision situation in which there is more than one individual involved. These individuals (e.g. experts, stakeholders, voters) have their own viewpoints and motivations, realize the existence of a common problem, and attempt to reach a collective decision. The GDM process is extremely difficult due to the presence of multiple decision makers who have their own viewpoints and motivations. The application of multiple attribute decision-making (MADM) methods to GDM problems covers a wide area in the related literature. However, there is no systematic classification scheme for these studies. This thesis introduces a general conceptual framework and a classification scheme for multiple attribute group decision making methods (MAGDM). The proposed framework consists of three main stages: the structuring and construction stage, the assessment stage, and the selection/ranking stage. This framework provides not only an outline for classification but also a roadmap for the researchers working on this subject. Additionally, most cited studies are categorized based on this classification scheme in order to clarify the state-of-the-art and to identify future research trends. As a result, eight key suggestions for future research are stated. These are, (1) use of fuzzy set theory along with its extensions for solving real-life group decision-making problems; (2) greater importance within the MAGDM literature for methods offering consensus process since consensus is necessary to obtain a final ranking with a certain level of agreement between group members; (3) important contribution to the literature by applications of methods to real life problems, as they will highlight the practical advantages, disadvantages, and limitations of the methods; (4) requirement for methods that permit individual criteria instead of a common list of agreed criteria; (5) possible increase in the use of pairwise comparisons as preference information type in future studies; (6) requirement for methods that can process evaluations provided in different formats; (7) development of a more universal software for group decision support systems and the application of different methods in different problems; (8) research into the question of how to determine importance weights for experts. In most complex real-life group decision-making problems, information can be heterogeneous. Heterogeneous information may arise when decision makers use their own set of criteria, evaluations presented in different formats, incomplete and/or unreachable information, and use of a combination of subjective and objective criteria. In this thesis, a Cumulative Belief Degree (CBD) based approach is developed to deal with heterogeneous information in MAGDM problems. The CBD approach was first developed in the evaluation of nuclear safeguards. It has been further applied to multiple criteria decision making problems, such as nuclear safeguards evaluation, by comparing multiple attribute decision making methods, energy policy evaluation, prioritization of energy sources, evaluation of credit rating and measuring sustainable development. It also has application in the quantification of causal relations. The basic advantage of CBD approach is that it can deal with heterogeneous information in multiple criteria decision making and MAGDM context. It can cope with information given in different scales by transforming the input data to belief degrees. Belief degrees are then converted to CBDs, to facilitate mathematical operations and any missing data originating from lack of expertise or lack of evidence can be handled. Since it gives a final score as a distribution to linguistic levels, it provides more information related to the performance of an alternative, which enriches the interpretation of the results. Therefore, we find CBD approach suitable for MAGDM problems with heterogeneous information. The proposed CBD based approach aims to aggregate objective factors and subjective opinions of decision makers provided in different formats and scales. The methodology to achieve this employs transformation formulas. Using these transformation formulas many preference representation formats such as fuzzy linguistic sets, 2-tuple linguistic representation models, hesitant fuzzy sets, intuitionistic fuzzy sets and classical fuzzy sets and both direct value and interval value assignments, are transformed into the belief structure without any loss of information. In addition, aggregation formulas are proposed to combine evaluations of decision makers and find a collective preference. The proposed approach also calculates consensus degree to measure the degree of agreement between the decision makers. The proposed approach is analyzed using an illustrative example and its validity is ensured through comparative analysis with existing methods in the literature. When compared to the existing methods, we show that the proposed approach presents a general methodology that can be applied to both homogeneous and heterogeneous MAGDM problems. Therefore, it is fair to say that that it can be applied to most MAGDM problems defined in the literature and faced in real life. A restriction to this claim is the use of expert evaluation formats that are different from the preference representation structures described in study. For instance, if expert judgements are collected in interval intuitionistic fuzzy sets or interval hesitant fuzzy sets, transformation formulae for converting these formats to belief degrees should be defined. We mention this issue as a new research direction. According to the results, the proposed approach achieves similar rankings with the original methods in the literature. Furthermore, it provides more information to the decision makers related to the general characteristic of the alternatives that enables to see the ranking of alternatives for different satisfaction levels. Therefore, we can conclude that the proposed approach presents a general methodology that can deal with different types of information in both homogeneous and heterogeneous MAGDM problems. Another advantage of the proposed approach is the easiness of the mathematical operations. For instance, when dealing with hesitant information, if the number of possible membership degrees (of the expert evaluations) increases, the number of operations and problem size also increases dramatically in the further steps of the methodologies. However, in the proposed approach, the transformation formulae depend on simple fuzzy set operations in most cases and the complexity of the further steps does not increase with growth in the size of the problem. The proposed approach has been applied to energy export policy of a country at the strategic level. Energy exports have been an inseparable and major instrument of national policy to support economic income, which also provides insights into opportunities for advancements in other areas. Energy-exporting countries are working intensively on the development of a sustainable energy export policy that is unaffected by fluctuating economic structure, fluctuations in energy prices and other unpredictable events. Energy decision problems are complex and multi-aspect problem situations due to some critical uncertainties and fluctuations. Many legal restrictions, political and geopolitical instability, dynamic market are some of these problems. The capability of CBD to deal with these difficulties makes it a suitable approach for the problem of this thesis. Energy export alternatives are evaluated and prioritized by the CBD approach. Five energy items (petroleum products, crude oil, electricity, gasoline, and natural gas) are considered as alternatives and a total of seven criteria and twenty-four sub-criteria are considered. The expert panel made evaluations using the preferred scale to prioritize items with respect to the sub-criteria. To collect expert evaluations, a questionnaire was designed, in which experts may prefer different evaluation formats to present their evaluations effectively. Besides, experts may not prefer to make an evaluation on a criterion given the lack of information or lack of expertise. After applying the steps of the CBD approach, energy export alternatives are ranked according to the aggregated score to interpret the results of the scenarios. MAGDM with heterogeneous information is a complex task because of involvement of multiple experts, multiple criteria, multiple stages, etc. Similarly, the methods used for MAGDM under heterogeneous information are also complicated with multiple stages, feedbacks, complex calculations, etc. Therefore, a universal software model is needed for a group decision support systems (GDSS) in which could be applied to different methods in different problems. Developed web-based GDSS enables experts to gather their assessments via the web application and analyze quickly when decision makers are unable to come together. With the developed web-based GDSS framework, it is aimed to increase the effectiveness of the negotiation and consensus process.