Circular intuitionistic fuzzy TOPSIS method with vague membership functions: Supplier selection application context

Abstract

The membership function of a general type-2 fuzzy set is three-dimensional in order to incorporate its vagueness through the third dimension. Similarly, Circular intuitionistic fuzzy sets (CIFSs) have been recently introduced by Atanassov (2020) as a new extension of intuitionistic fuzzy sets, which are represented by a circle representing the vagueness of the membership function. CIFSs allow decision-makers to express their judgments including this vagueness. In this study, the TOPSIS method, which is one of the most used multi-criteria decision-making methods is extended to its CIF version. The proposed CIF-TOPSIS methodology is applied to the supplier selection problem. Then, a sensitivity analysis based on criteria weights is conducted to check the robustness of the proposed approach. A comparative analysis with single-valued intuitionistic fuzzy TOPSIS method is also performed to verify the developed approach and to demonstrate its effectiveness

A New Circular Intuitionistic Fuzzy MCDM: A Case of Covid-19 Medical Waste Landfill Site Evaluation

“…The circular intuitionistic fuzzy numbers (C-IFS) are introduced to the literature by Atanassov in 2020 [10]. This new fuzzy set is an extension of the IFS and has a difference from IFS by including a circle of the number consisting of membership degree and non-membership degree [11]. The preliminaries of circular intuitionistic fuzzy numbers (C-IFS) are introduced by definitions as follows:…”

“…Like all previous fuzzy extentions, C-IFS can be used in a combination with MCDM approaches. So far in the literature, C-IFS TOPSIS method was implemented in a supplier selection problem [11] and pandemic hospital site selection [12]. As another method, C-IFS VIKOR methodology was used in waste disposal site evaluation problem [13].…”

Dairesel Sezgisel Bulanık Çok Kriterli Karar Verme Metodolojisi

“…Bu yeni bulanık küme, SBK'nin uzantısıdır. Üye olma ve üye olmama derecelerinden oluşan bir sayı çemberi içermesiyle SBK'den farklıdır (Kahraman & Alkan, 2021).…”

“…Denklem 5'teki r, her bir x ∈ E elemanının etrafındaki dairenin yarıçapıdır (Kahraman & Alkan, 2021). Belirsizlik fonksiyonu ise şu şekilde tanımlanır: 𝜋 C (𝑥) = 1 − 𝑢 C (𝑥) − 𝑣 C (𝑥).…”

“…Devamında yine Atanassov, bu konsepti geliştirerek 2020'de dairesel sezgisel bulanık kümeler (D-SBK) olarak adlandırılan yeni bir SBK uzantısı önermiştir (Atanassov, 2020). Bu yeni kümenin geliştirildiği SBK'den merkezi üye olma ve üye olmama derecelerinden oluşan bir yarıçap notasyonu içermesi ile farklılaşır (Kahraman & Alkan, 2021).…”