This research attempts to seek for multi criteria decision making through the PROMETHEE method. This paper aims to propose an application of multi criteria decision making in intuitionistic fuzzy sets. The main goal of the paper; to establish a smart evaluation system in education with a multi criteria decision making approach using intuitionistic fuzzy logic and PROMETHEE method. The success ranking of schools was analyzed through the use of the PROMETHEE method. Besides, the most successful school was identified among these ranked schools. In this research, the intuitionistic fuzzy PROMETHEE method was employed during ranking of schools' success. The main reason for using intuitionistic fuzzy PROMETHEE is that it takes into account both intuitionistic fuzzy weights and intuitionistic fuzzy preferences at the same time. This paper applies to many fields; however, we proposed an application in the field of education in this study. The primary purpose of this paper is expected to create an algorithm of intuitionistic fuzzy PROMETHEE and offer an application example that will shed light on many application areas. Using multi-criteria decision-making methods together with intuitionistic fuzzy logic will help us obtain more rational and more objective results.
The education system has 4 basic elements. These; education system, educator, student (education student) and physical facility. In this study, the physical condition is researched. The aim of this study is to evaluate and interpret the suitability of the physical structures of schools in terms of education and training according to teachers by the multi-criteria decision making method in fuzzy logic. One of the factors affecting success is the physical structure. This study has been conducted with the help of teachers' ideas to determine whether physical structure has an impact on student achievement. This study is an application of a multi-criteria decision-making method, as there are many factors affecting physical structure. In this study 'individual interview' technique has been applied to interpret physical conditions of schools. Scores obtained as a result of individual interviews have been interpreted using multi-criteria decision making method. Teachers' ideas affecting success have been taken into consideration. The results have been compared with the official data.
Intuitionistic fuzzy set theory was introduced by Atanassov as an extension of fuzzy sets [1]. The algebraic structures like groups, rings, modules, etc. were generalized to intuitionistic fuzzy sets by different authors. Some properties of them were studied [4, 9, 11, 14, 15]. In this study, we generalized the action of a group on a set to intuitionistic fuzzy action. We obtained some basic results.
In this paper, the intuitionistic fuzzy PROMETHEE method is explained in detail and an original application has been made. The aim of the paper is to bring innovation to the evaluation system in the field of education by using the intuitionistic fuzzy PROMETHEE method. The advantages of using the PROMETHEE method, which is one of the many methods used in multi-criteria decision-making problems, in the intuitionistic fuzzy sense are explained in detail. Intuitionistic fuzzy PROMETHEE is a method that attracts our attention thanks to its benefits such as allowing the researcher to observe the positive and negative rankings simultaneously, expressing the degree of hesitation, changing the significance weights of the criteria, and using different methods when identifying the significance levels for each criterion, putting the degree of hesitation of significance weights into action, and enabling decision-makers, who are given the opportunity to use different criteria types and different criteria types for alternatives and criteria, to establish a unique system; moreover, the method also provides us numerous advantages while using it in our application area. It is of great importance for decision-makers to determine the specific importance level for each criterion. In this paper, controlled sets are used to express the importance of the criteria in the form of intuitionistic fuzzy values. The intuitionistic fuzzy-based PROMETHEE algorithm, aiming to contribute to the education system by examining the factors affecting the students' achievement, is a unique algorithm, and it is the first to shed light on various researchers.
In this study, ?-interval valued set is defined whose elements are closed sub-intervals including ? of unit interval that is I = [0, 1]. With different order relation on this set, the properties of ?-interval valued set are examined. By the help of this order relation, it is shown that ?-interval valued set is complete lattice. Negation function on ?-interval valued set is given in order to study the theoretical properties of this set. By means of discussions on ?-interval valued set, the fundamental features of ?-interval valued set are studied. By the help of ?-interval valued set, ?-interval valued fuzzy sets are defined. The fundamental algebraic properties of these sets are examined. The level subsets of ?-interval valued fuzzy sets are defined to give the relations between ?-interval valued sets and crisp sets. With the help of this definition, some propositions and examples are given.
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