Sifat-Sifat Operasi pada Himpunan Lunak Fuzzy Berparameter Fuzzy
Operating Properties on Fuzzy Parameterized Fuzzy Soft Set
Molodtsov memperkenalkan himpunan lunak yang menggabungkan antara himpunan semesta dengan suatu himpunan parameter melalui suatu fungsi dari himpunan parameter ke himpunan kuasa atas himpunan semestanya. L. A Zadeh memperkenalkan teori baru yaitu himpunan fuzzy. Seiring berjalannya waktu konsep himpunan fuzzy berkembang menghasilkan himpunan lunak fuzzy. Pengembangan konsep himpunan lunak memberikan teori baru yang dinamakan himpunan lunak berparameter fuzzy. Penggabungan konsep himpunan lunak fuzzy dengan himpunan lunak berparameter fuzzy diperoleh himpunan lunak fuzzy berparameter fuzzy. Pada artikel ini akan dibahas mengenai himpunan lunak fuzzy berparameter fuzzy khususnya sifat-sifat operasi himpunan, sehingga dapat dikaji apakah sifat-sifat operasi pada himpunan biasa juga berlaku pada himpunan lunak fuzzy berparameter fuzzy. Berdasarkan pembahasan disimpulkan bahwa, sifat-sifat operasi yang berlaku pada himpunan lunak fuzzy berparameter fuzzy meliputi sifat transitif, sifat komutatif terhadap operasi gabungan, irisan, sifat asosiatif terhadap operasi gabungan, irisan, sifat De Morgan’s, serta sifat distributif terhadap operasi gabungan dan irisan.
Molodtsov introduced a soft set that combines the universal set with a parameter set through a function from the parameter set to the power set over the universal set. L. A Zadeh introduced a new theory, namely the fuzzy set. Over time, the concept of fuzzy sets develops to produce fuzzy soft sets. The development of the soft set concept provides a new theory called the fuzzy parameterized soft set. Combining the concept of fuzzy soft set with fuzzy parameterized soft set is obtained fuzzy parameterized fuzzy soft set. In this article, we will discuss about fuzzy parameterized fuzzy soft set, especially the characteristics of the set operation, so that it can be studied whether the operating properties of ordinary sets also apply to fuzzy parameterized fuzzy soft set. Based on the discussion, it can be concluded that the operating properties that apply to fuzzy parameterized fuzzy soft set include transitive properties, commutative properties of union operations, intersection, associative properties of union operations, intersection, De Morgan's properties, and distributive properties of union and intersection operations.