Choquet Integral and Multi-Criteria Decision Making

Decision problems involve the simultaneous consideration of achieving several different goals that are often in conflict. People struggle in finding efficient methods to solve such decision problems. These are mostly ill-posed problems. In decision problems goals and constraints constitute the classes of alternatives whose boundaries are not sharply defined. Fuzzy goals and fuzzy constraints can be defined precisely as fuzzy sets in the space of alternatives. Aggregation operators are used to get a single collective decision value. In this thesis, a geometric aggregation operator is proposed for generalized trapezoidalvalued intuitionistic fuzzy numbers and for generalized interval valued trapezoidal fuzzy numbers to aggregate the opinions in the process of decision making by a group of experts. A technique for order preference by similarity to ideal solution is given for group decision making, where inter-dependent characteristics of different criteria and preferences of the decision makers is under consideration. Furthermore, Choquet integral based distances between any two trapezoidal valued intuitionistic fuzzy numbers and generalized interval valued trapezoidal fuzzy numbers are defined. Combining the trapezoidal-valued intuitionistic fuzzy geometric aggregation operator with Choquet integral based distance, an extension of TOPSIS method is developed to deal with a multi-criteria trapezoidal-valued intuitionistic fuzzy group decision making problems. Another notion of distance between hesitant fuzzy data has been used to formulate the technique for order preference by similarity to ideal solution for hesitant fuzzy sets. A method has been developed to aggregate the opinion of decision makers on all the alternatives on different criteria, where experts' opinions are represented either by hesitant fuzzy sets or hesitant fuzzy linguistic term sets. The group decision making problem is formalized by interval-valued 2-tuple linguistic information. Some operational laws on interval-valued 2-tuples are presented. Based on these laws, new aggregation operators are introduced by using Choquet integral. A multi-criteria decision making method based on these aggregation operators is proposed. \ud Examples are given to illustrate the efficiency, practicality and feasibility of all our proposed methods. This thesis ends with the conclusion and some directions for future research in this area