Pythagorean Bulanık Bi-ideallerin Bazı Cebirsel Özellikleri

Year 2025, Volume: 10 Issue: 1, 42 - 59, 29.06.2025

Filiz Çıtak

https://doi.org/10.33484/sinopfbd.1524118

Abstract

Bulanık kümeler, belirsizlik içeren problemlerin çözümünde çok önemli bir yere sahiptir. Karar verme, mühendislik, cebir vb. alanlarda bulanık kümeler üzerine çok sayıda çalışma vardır. Bu çalışmada, bulanık kümelerin bir tür genelleştirilmesi olan Pythagorean bulanık kümelerin cebir de ki davranışlarını tartışıyoruz. İlk olarak, Pythagorean bulanık çarpımı tanımlıyoruz ve bazı özelliklerini inceliyoruz. Ardından, Pythagorean bulanık ideali ile Pythagorean bulanık çarpımı arasındaki ilişkiyi araştırıyoruz. Sonra, Pythagorean bulanık bi-ideali tanımlıyoruz. Bi-idealleri bulanık bi-idealler açısından karakterize eden teoremi veriyoruz. Pythagorean bulanık bi-ideallerin Pythagorean bulanık çarpım altındaki davranışlarını inceliyoruz. Pythagorean bulanık bi-ideallerin arakesitinin, kartezyen çarpımının ve Pythagorean bulanık çarpımının da Pythagorean bulanık bi-ideal olduğunu ispatlıyoruz. Dahası, Pythagorean bulanık bi-idealinin görüntüsünü ve ters görüntüsünü araştırıyoruz.

Keywords

Pythagorean bulanık küme , Pythagorean bulanık ideal , Pythagorean bulanık bi-ideal

Some Algebraic Properties of Pythagorean Fuzzy Bi-ideals

Abstract

Fuzzy sets have a significant place in solving problems involving uncertainty. There are many studies on fuzzy sets in decision-making, engineering, algebra, etc. In this study, we discuss the behavior of Pythagorean fuzzy sets, which are a kind of generalization of fuzzy sets in algebra. First, we define the Pythagorean fuzzy product and examine some of its properties. Then, we investigate the relationship between the Pythagorean fuzzy ideal and the Pythagorean fuzzy product. Then, we define Pythagorean fuzzy bi-ideal. We give the theorem that characterizes bi-ideals in terms of fuzzy bi-ideals. We examine the behavior of Pythagorean fuzzy bi-ideals under Pythagorean fuzzy product. We prove that the intersection, Cartesian product, and Pythagorean fuzzy product of Pythagorean fuzzy bi-ideals are also Pythagorean fuzzy bi-ideals. Furthermore, we investigate the image and the inverse image of the Pythagorean fuzzy bi-ideal.

Keywords

Pythagorean fuzzy sets , Pythagorean fuzzy ideals , Pythagorean fuzzy bi-ideals

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