Extensions of Z-fuzzy numbers and novel multi criteria decision making models

Abstract

The ordinary fuzzy sets are based on the fact that the belonging of an element to a set can take values between 0 and 1, and they emerged due to the incapability of classical sets to describe uncertainty in human thought. After fuzzy sets were introduced to the literature, it began to propose more than one parameter to define uncertainty. For example, while ordinary fuzzy sets use only membership functions, intuitionistic and Pythagorean fuzzy sets use membership and non-membership functions; neutrosophic, picture, and spherical fuzzy sets use membership, non-membership and indeterminacy functions. Although all these fuzzy sets have different properties and conditions for defining uncertainty, they are unable to define the reliability degrees of judgments. Z-fuzzy numbers allow judgments to be defined not only with a restriction function but also with their reliability degrees. In this thesis, extensions of Z-numbers have been proposed to the literature by integrating fuzzy set extensions with Z-numbers. Thus, novel Z-numbers have been presented to the literature for defining uncertainty, and fuzzy sets have been given the ability to represent reliability under their own properties and conditions. In addition, multi-criteria decision-making (MCDM) methods have been expanded by using ordinary fuzzy Z-numbers and these new fuzzy Z-numbers. Thus, new Z-fuzzy MCDM methods have been introduced to the literature. For this purpose, in the first three chapters, new Z-fuzzy MCDM methods are presented such as Z-CODAS, Z-AHP and Z-EDAS methods. In other three chapters, decomposed fuzzy Z-numbers, picture fuzzy Z-numbers, and interval-valued spherical fuzzy Z-numbers have been developed and integrated with different MCDM methods. Each chapter is summarized below: In Chapter 2, the COmbinative Distance-based ASsessment (CODAS) method, which is a method based on Euclidean and Taxicab distances, is expanded with Z-numbers and introduced to the literature. The proposed Z-CODAS method has been applied to the supplier selection problem. For this purpose, firstly, decision criteria are weighed based on Z-pairwise comparison matrices. Then, the obtained criteria weights are integrated into the Z-CODAS method and used to rank alternative suppliers. The obtained results are compared with the ordinary fuzzy simple additive weighting (SAW) method. Chapter 3 presents a multi-experts MCDM method for evaluating social sustainable development factors. The proposed approach integrates Z-numbers and AHP method and may guide many sustainable development researches. In this study, Z-numbers have been used for the first time to evaluate social sustainable development factors. In addition, the other contribution of the study is presenting the Z-AHP method with multi-experts which can be useful for the solution of many MCDM problems containing uncertainty. The proposed Z-AHP method allows pairwise evaluations to be represented with their reliability degrees and integrated into the calculations. Chapter 4 extends the Evaluation based on Distance from Average Solution (EDAS) method to the Z-EDAS method. In this chapter, a decision making methodology is proposed by the integration of Z-AHP method and Z-EDAS method. The practicality of the proposed methodology is presented with an application on wind turbine selection problem. The comparative analysis conducted with Z-TOPSIS method demonstrates that the usefulness and competitiveness of the proposed methodology are provided. The results show that proposed methodology can both represent decision makers' judgments extensively, and reveal a logical ranking results related to alternatives by the usage of reliability information. In Chapter 5, decomposed fuzzy Z-numbers, which are the integration of decomposed fuzzy sets (DFSs) and Z-numbers, are introduced to model functional and dysfunctional judgments in a reliable decision environment. Collecting judgments under the circumtances of Z-numbers from experts using functional and dysfunctional questions can provide more consistent and reliable decision environment. In this chapter, a new decomposed fuzzy Z-linguistic scale and defuzzification formula are introduced. Then, decomposed fuzzy Z-TOPSIS method is developed for the solutions of MCDM problems under uncertainty. An application on transfer center location selection for a private cargo company in Marmara Region of Turkey is presented. The effect of the reliability parameter on the results is analyzed. Chapter 6 presents a decision methodology that integrates the picture fuzzy Z-AHP (PF Z-AHP) method for weighting criteria and a novel PF Z-TOPSIS method for ranking the alternatives. Although the picture fuzzy TOPSIS methods are used to model decision makers' hesitancy in their evaluations, adding reliability degrees to these evaluations can provide better solutions and reliable decision environments for real-life applications. In order to analyze the utility of the proposed PF Z-AHP&TOPSIS methodology, it is applied for solar energy panel selection problem. The sensitivity and comparative analyses are also performed to analyze given decisions and the effects of Z-numbers on the results. In Chapter 7, a new interval-valued spherical fuzzy (IVSF) Z-number is developed combining the ability of SFSs to allow the assignment of membership degrees in a wider domain with the ability of Z-numbers to represent reliability. In addition, a novel Interval-valued Spherical Fuzzy Z-Analytic Hierarchy Process (IVSF Z-AHP) is proposed by integrating the IVSF Z-numbers and AHP method. Then, a new IVSF Z linguistic scale and a new defuzzification formula are proposed. The proposed IVSF Z-AHP method is applied for green supplier selection problem to show the practicality and applicability of the method. Comparative analysis and sensitivity analysis show the necessity of reliability information in decision making. In summary, in this thesis, new extensions of Z-numbers and new fuzzy MCDM methods integrated with these extensions are proposed to the literature. Then, the proposed method and methodologies have been applied to various decision-making problems to demonstrate their practicality. In order to show the importance of reliability information, this information has been ignored and the problems have been resolved with the same data and it has been investigated whether the rankings of the alternatives changed. The results and the analyzes provide evidence that reliability information has the potential to change the rankings of alternatives. Especially when the reliability degrees of experts' judgments are wanted to be considered in the decisions, managers or practitioners can use the proposed approaches in this thesis to produce more reliable and meaningful solutions to their problems. In further researches, many different extensions of Z-numbers can be developed and compared with the results of the methods proposed in this thesis.