Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem

In modern mathematics, many concepts and ideas are described in terms of category theory. From this viewpoint, it is desirable to analyze what can be determined if, instead of the basic category of sets, we consider a similar category of fuzzy sets. In this paper, we describe a natural fuzzy analog of the category of sets and functions, and we show that, in this category, fuzzy relations (a natural fuzzy analogue of functions) can be determined in category terms -- of course, modulo 1-1 mapping of the corresponding universe of discourse and 1-1 re-scaling of fuzzy degrees.

Aplikasi analisis kelas laten untuk mendeteksi karakteristik unik pada konstruk efikasi guru dalam mengajar

Penelitian ini bertujuan untuk mengidentifikasi adanya kelompok-kelompok unik berdasarkan atribut yang terukur pada efikasi mengajar guru untuk memunculkan tipe-tipe unik efikasi guru. Penelitian ini melibatkan 142 guru yang diminta mengisi Skala Efikasi Mengajar. Analisis kelas laten yang dilakukan memunculkan empat tipe guru berdasarkan responsnya. Dua kelas menunjukkan tipe kategori yang berjenjang (efikasi tinggi dan rendah) dan dua kelas menunjukkan kategori unik (efikasi terkait dengan interaksi dengan siswa dan terkait dengan persiapan mengajar). Adanya dua kelas unik tersebut menunjukkan bahwa dimensi-dimensi efikasi guru dalam mengajar tidak bersifat homogen. Ada guru yang dominan pada satu dimensi akan tetapi tidak dominan pada dimensi lainnya. Adanya guru dengan karakteristik unik ini memberikan konsekuensi agar penyusunan alat ukur efikasi diri dan program-program peningkatan efikasi guru dalam mengajar dapat mengakomodasinya.Kata kunci: efikasi guru dalam mengajar, analisis kelas laten, kategori unik THE APPLICATION OF LATENT CLASS ANALYSIS TO DETECT THE UNIQUE CHARACTERISTICS ON TEACHERS EFFICACY CONSTRUCTS IN TEACHINGAbstractThis study aims to identify the unique groups based on attributes measured on the efficacy of teachers to bring unique types of teacher efficacy.The research involved a total of 142 teachers who were asked to complete Teaching Efficacy Scale. The results of latent class analysis exhibit four types of teacher’s efficacy based on their similarity responses to given measure. Two classes show an ordered category (high efficacy and low teaching category) whereas two classes show a unique category (efficacy related to interaction with students and efficacy related to teaching preparation). The presence of these two unique classes suggests that teacher perceptions of his/her ability in teaching can be viewed as a type of attribute. There are teachers swho have high levels of efficacy in one dimension but tend to be low on other dimensions. The presence of this type has several consequences for the development of teaching efficacy measure, and programs to improve teachers should accommodate this unique type.Keywords: teaching efficacy, latent class analysis, unique categories