Fuzzy Choquet Integral based MAGDM. Application in water resources emergency management.

Author: Irakly Parshutkini
Keywords: Fuzzy numbers, Fuzzy sets, Choquet aggregation, Multiple attribute group decision making System, Emergency management system, Water resource management
Annotation:

The master's thesis discusses a multi-criteria group decision-making system based on fuzzy Choquet integral aggregation, which helps to make a unified decision considering the mutual influence of different criteria. Fuzzy set theory differs from standard sets in many ways. Humans, by their nature, think more in terms of fuzzy definitions than clarity. A person has the ability to evaluate an object or event in degrees, therefore, he is not limited by the range of evaluations. The spread of fuzzy numbers has led to their development, both in theoretical studies and in practical applications. Fuzzy numbers based computing techniques and information work correctly based on human experience. A person creates a knowledge base where he explains fuzzy numbers and fuzzy logic rules. A good example of this is the use of fuzzy terms, where a human-understandable verbal meaning is translated into fuzzy numbers and processed in a fuzzy environment. Fuzzy environment is applicable in decision-making systems. As we mentioned, it is more natural for a person to evaluate by degrees. From the decision evaluated according to the individual criteria, it is necessary to obtain a single value, the rank, in order to compare this decision with the others. For this we need to aggregate the fuzzy numbers. It is quite easy to aggregate independent numbers, such as the arithmetic mean, where we assume that the number weights are equal, or by weighted arithmetic with individual weights. The situation changes when two or more criteria affect each other. In such a case, it is difficult to obtain a uniform result with the averaging operator. We will have a similar difficulty in group decisions making, when one event or object is evaluated by several people, they can influence each other's decision. Aggregation of fuzzy numbers based on the Choquet integral discussed in the paper takes into account both the mutual influence of the criteria and the observers. By introducing the λ-fuzzy measure and using Choquet aggregation, the information system is even closer to human logic. In a practical example, created information system is considered is used in the management of water resources, in particular, in emergency cases, when the most optimal decision should be made, taking into account many factors. The web application in question is built on the ASP.NET Core framework. With its help, it is possible to create a task from anywhere in the world, view it, fix the assessment and make a decision based on the experts' assessments. The system works with Interval-Valued q-Rung Orthopair Fuzzy Numbers, which is an advantage compared to Zadeh fuzzy numbers - the evaluation of the criterion is done by two independent functions, the evaluation itself is not bounded by a range of degrees, and the value of the function itself is an interval, not a single specific value.