A New Soft Set Operation: Complementary Soft Binary Piecewise Lamda (λ) Operation

Abstract

In 1999, Molodtsov introduced Soft Set Theory as a mathematical tool to deal with uncertainty. It has been applied to many fields both as theoretical and application aspects. Since 1999, different kinds of soft set operations have been defined and used in various types. In this paper, we define a new kind of soft set operation called, “complementary soft binary piecewise lambda operation” and we handle its basic algebraic properties. Also, it is intended to contribute to the literature of soft set by gaining the relationships between this new soft set operation and some other types of soft set operations via examining the distribution of complementary soft binary piecewise lambda operation over extended soft set operations, complementary extended soft set operations, soft binary piecewise operations, complementary soft binary piecewise operations and restricted soft set operations in order to inspire to obtain the algebaric structures of soft sets and some new decision making methods.

Keywords

• Soft sets
• soft set operations
• conditional complements

Yeni Bir Esnek Küme İşlemi: Tümleyenli Esnek İkili Parçalı Lambda (λ) İşlemi

Abstract

Molodtsov, 1999 yılında Esnek Küme Teoriyi belirsizlikle başa çıkmak için bir matematiksel araç olarak ortaya koymuştur. Teori, hem teorik hem de uygulama yönüyle birçok alana uygulanmıştır. 1999 yılından bu yana, farklı çeşitlerde esnek küme işlemleri tanımlanmış ve çeşitli türlerde kullanılmıştır. Bu çalışmada, “tümleyenli esnek ikili parçalı lambda işlemi” adı verilen yeni bir esnek küme işlemi tanımlanmış ve temel cebirsel özellikleri araştırılmıştır. Ayrıca tümleyenli esnek ikili parçalı lambda işleminin genişletilmiş esnek küme işlemleri, tümleyenli genişletilmiş esnek küme işlemleri, esnek ikili parçalı işlemler, tümleyenli esnek ikili parçalı işlemler ve kısıtlanmış esnek küme işlemleri üzerine dağılması incelenerek bu yeni esnek küme işlemi ile diğer esnek küme işlemleri arasındaki ilişkiler elde edilerek esnek kümelerin cebirsel yapılarını ve bazı yeni karar verme yöntemlerini elde etmek için okuyuculara ilham vermek adına esnek küme literatürüne katkı sağlanması amaçlanmaktadır.

Keywords

• Esnek kümeler
• esnek küme işlemleri
• koşullu tümleyenler

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