A new approach to qualitative cross impact analysis considering the interaction effects and uncertainty

Decision making is a future oriented process to a great extent, since every decision involves some assumptions about the future. In other words, without anticipating the future, it is rather unlikely to make effective decisions. The effectiveness, usefulness, and applicability of decisions and plans can only be achieved thorough enhancing the ability to anticipate possible opportunities and threats, instead of the accuracy of forecasts. Therefore, in order to improve decision making, futures research aims to systematically explore, examine, and evaluate a range of possible and preferable alternative futures. In order to shape and move towards desired futures, organizations have to quickly respond and adapt to rapid and unprecedented changes in the environment. The lack of control and predictability caused by uncertainty forces organizations to continuously improve their ability to foresee. Especially in the long run, since the uncertain future of an organization is shaped by many different interdependent factors and their possible developments, it is unrealistic to predict a single best future. Thus, it becomes inevitable to apply scenario planning which allows considering consistent combinations of these alternative developments and thereby examining all possible future scenarios. Scenarios are useful when numerous factors need to be considered, and the degree of uncertainty about the future is high. A scenario is not a forecast, it is rather an internally consistent view of what the future might turn out to be. They are stories that anticipate the future, they are not intended to exactly predict the future. The main purpose of scenarios is to help managers recognize the uncertainties they are likely to face and make better decisions. In other words, they should be used to think about the future. A scenario planning approach generally comprises the following steps: i) Scenario Preparation, ii) Scenario Field Analysis, iii) Future Projection, iv) Scenario Creation, and finally v) Scenario Transfer. This approach applies the principles of "multiple futures" and "systems thinking" to determine the critical factors and their possible combinations forming the alternative scenarios. This thesis primarily focuses on the Scenario Field Analysis step of the scenario planning process. This step explores the characteristic behavior of a factor in relation to all other factors within a scenario field and reveals those ones that play a central role in the development of the field in the future. The most common approach used for this purpose is Cross Impact Analysis (CIA). The main concern of the very first version of CIA, introduced in the late 1960s, was to explore how factors are likely to interact with each other. Considering the relationships through the effects of single factors on others may provide a relatively useful tool to analyze the structure of the scenario field. However, a significant information loss is inevitable here, because the role of interaction in the system is extremely important that cannot be assumed as negligible. Note that, although, in the Cross Impact literature, the term "interaction" is used to represent the interrelationship (i.e. the "cross impact" itself), the term "interaction" used in this thesis refers to the multidimensional aspect where a number of variables has a joint impact on others. Over the years, researchers have introduced various approaches to overcome some certain drawbacks of the CIA and several of them have discussed the importance of integrating "interaction effects" into (qualitative) CIA. Nevertheless, none of them has proposed an effective approach to overcome this shortcoming. In order to address this issue, this thesis aims to introduce a new approach that considers not only the direct and indirect relationships between factors in a pairwise manner but also the multidimensional aspects where two factors may jointly affect another one. Directly integrating the interactions into the CIA will create a cognitive and computational burden and the simple structure of (Qualitative) Cross Impact Analysis that consists of matrix multiplication becomes a mathematically more complex problem. Instead, in this study, the aggregation of the expert assessments and determination the key variables that have a central role in the future by considering the interaction effects are handled by utilizing the properties of the fuzzy measure theory and the Choquet integral. In the proposed approach, a 2-additive Choquet integral based on fuzzy measures is integrated into the stages of the Qualitative CIA. Measure is one of the most fundamental concepts in mathematics and the classical measure can be defined as a nonnegative additive set function. The additivity property may be very effective and preferable for some applications, but in most real world problems, it becomes insufficient and not applicable. For this reason, it is replaced by monotonicity in non-additive measures, in other words "fuzzy measures", which are used to explicitly represent the interaction between the factors. However, because fuzzy measures are defined on power sets, the problem becomes more complex and for large number of factors in the set its complexity increases exponentially. To overcome this complexity issue, Michel Grabisch introduced 2-additive measures where only the interaction between factor pairs is taken into consideration and higher order interactions are omitted. The Choquet integral defined on fuzzy measures, is a common aggregation function used in decision problems with multiple criteria especially when such interactions occur. One other drawback that the researchers in the area argued is the ill-equipped human mind with its limited cognitive capacity. Especially in the probabilistic CIA, experts are asked for assessing at least one of the conditional probabilities, joint probabilities, or marginal probabilities of events, but to make these assessments they have to know both the existing interrelations in the system and the possible outcomes which the provided assessments will lead to. Due to the limited cognitive capacity of human being, this way of assessment will be cumbersome. To address this issue a new approach is proposed to consider the uncertainty inherent in the expert judgment process. In this proposed approach, Hesitant Fuzzy Sets is integrated into the stages of the Qualitative CIA. One of the most common approaches suggested in the literature for dealing with uncertainty is fuzzy set theory. However, it has been realized for some time that this theory has its limitations in modeling certain types of uncertainty and, in turn, several improvements and extensions of fuzzy sets have been suggested. One of those extensions, Hesitant Fuzzy Sets, is developed to model uncertainty caused by hesitation that might arise in the assignment of membership degrees of the elements to a fuzzy set. Finally, a third approach is introduced that is able to consider both the multidimensional interaction effects and uncertainty caused by hesitation of the experts in cross impact analysis, which allows a more effective and applicable analysis of real world problems. That means, instead of simply aggregating expert assessments, the assessments of each expert in terms of hesitant fuzzy direct, indirect and multidimensional interaction effects are incorporated into the calculations and, thereby, information loss is avoided as far as possible. This will be achieved by integrating the Hesitant Fuzzy Set approach with the 2-additive Choquet integral. In order to examine the effectiveness and applicability of the proposed approaches, variables defined for a problem of automotive industry are utilized. The main reason to choose this illustrative example is that it is compact involving only 10 variables and assessing the relationships is relatively easy. The illustrative example is also analyzed by the classical Qualitative CIA and the results are finally compared. Finally, since the future is unknown, it is unreasonable to expect any suggested new method in scenario planning to yield accurate and precise outcomes. Instead, these methods should provide organizations a framework to systematically examine the scenario field. By using the proposed approach, organizations will be able to determine the critical factors in the scenario development process more realistically by considering both multidimensional interaction effects and uncertainty. This suggests a more effective and consistent approach to scenario development.