Using generalized fuzzy sets in multiple criteria decision-making methods

Multiple criteria decision-making problems can be defined by limited criteria and choosing the most appropriate alternative among alternatives. In multiple criteria decision-making problems, due to the creation of decision matrices based on the opinions of the individuals (experts), a decision mechanism is formed by ignoring both bias and the relationships between the criteria. In particular, data obtained from individuals may contain incomplete and unclear data. Therefore, using fuzzy sets in this case gives more reliable results in decision mechanism. On the other hand, by generalizing fuzzy sets, a larger fuzzy set can be formed for decision makers to express unclear data. In the scope of the thesis, the methods proposed in multiple criteria decision making methods are combined with generalized fuzzy sets, traditional methods and combining methods.Within the scope of the thesis, firstly, Fermatean fuzzy sets were combined with Dombi T-norm operator. Then, TOPSIS method, which is one of the traditional methods, was applied. Thanks to the flexible parameter of the Dombi T-norm structure, the aggregation method changes as the parameter value changes. Thus, the aggregation operator covers a wide range. The second issue of the thesis involves the Dombi operator primarily in the q-rung fuzzy sets environment. The priority operator has a effective role in the evaluation of different priority criteria and decision makers in the decision mechanism. Some desirable properties of the proposed operator such as limitation, monotonicity and idempotency are also shown. In addition, the proposed method is hybridized with the MULTIMOORA structure. On the other hand, validity tests and numerical examples are given for the proposed method. The third issue of the thesis involves the application of the neutral operator with the force operator. The neutrality operator handles the biased decision-making situation among decision makers in probabilistic sum. Also, a score function used for heuristic fuzzy sets is generalized for q-rung fuzzy numbers. As the fourth issue of the thesis, a priority dual Muirhead mean operator is proposed for spaced q-rung fuzzy numbers. Thus, the dual Muirhead operator is combined with the priority operator. The last issue of the thesis is the application of the power Dombi operator in T-spherical fuzzy sets. All proposed methods have been tested with numerical problems. In addition, the ranking results obtained are compared with other methods prposed in the literature.