The New Fuzzy Analytical Hierarchy Process with Interval Type-2 Trapezoidal Fuzzy Sets and Its Application

Abstract

The degree of type-1 fuzzy sets membership function cannot express the linguistic variable of a complex problem. The type-2 fuzzy sets as a problem solver such that more fuzziness for constructing membership functions can be handled. Recently, many multi-criteria decision making (MCDM) methods have been expanded using type-2 fuzzy sets. Analytical Hierarchy Process (AHP) is one of the well-known MCDM that can take into account multiple and conflicting criteria at the same time. Our goal is to develop an interval type-2 trapezoidal fuzzy AHP through the new proposed ranking i.e. the modified total integral value. Based on the illustrative examples for trapezoidal type-2 fuzzy sets, the new proposed ranking has a well-performance in ranking. Furthermore, we apply the new trapezoidal type-2 fuzzy AHP to a supplier selection problem. Based on the results of the application, the new fuzzy AHP has the same ranking results as the existing fuzzy AHP.

Keywords:

• Type-2 fuzzy sets
• fuzzy AHP
• ranking interval type-2 fuzzy sets
• fuzzy multi-criteria decision making

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Universiti Tun Hussein Onn Malaysia [research grant TIER 1 (H777)].

Notes on contributors

Muhammad Sam'an

Muhammad Sam'an received Bachelor Degree from Universitas Negeri Semarang and Master Degree from Universitas Diponegoro in Mathematics 2010 and 2016 respectively and now, he is studying in the postgraduate student, Faculty of Technology Management and Business, Universiti Tun Hussein Onn Malaysia (UTHM). His research interests are in Optimization, Fuzzy Mathematics and Computational Mathematics.

Yosza Dasril

Yosza Dasril received PhD and Master degree in Applied Mathematics from Universiti Putra Malaysia in 2003 and 1999 respectively and Bachelor Degree in Mathematics from Universitas Riau, Indonesia in 1994. From 1999 to 2006, he was a lecturer in the Universiti Malaysia Terengganu (UMT). In the middle of 2006 into Nov 2019, he serve as a Senior Lecturer at the Faculty of Electronic and Computer Engineering, Universiti Teknikal Malaysia Melaka (UTeM). Currently, he is a Senior Lecturer at Faculty of Technology Management and Business, Universiti Tun Hussein Onn Malaysia (UTHM). His research interests are in Optimization, Engineering Mathematics and Computational Mathematics.

Much Aziz Muslim

Much Aziz Muslim received Bachelor Degree from Universitas Stiekubank, Semarang and Master Degree from Universitas Gadjah Mada in computer science and now, he is studying in the postgraduate Student, Faculty of Technology Management and Business, Universiti Tun Hussein Onn Malaysia (UTHM) and a lecturer in the Universitas Negeri Semarang. His research interests are in Optimization and Data mining.