Multi Criteria Decision Making menggunakan Operator Group Generalized Interval Value Pythagorean Fuzzy

Multi Criteria Decision Making (MCDM) adalah proses penentuan solusi terbaik dalam suatu masalah berdasarkan kriteria yang telah ditentukan. Dalam berbagai kasus, pengambil keputusan sulit untuk menyatakan pendapatnya dalam angka yang tegas. Oleh karena itu, penggunaan bilangan fuzzy dianggap lebih efisien. Salah satu bilangan fuzzy yang digunakan dalam kasus MCDM adalah Interval Value Pythagorean Fuzzy Number (IVPFN). Informasi fuzzy pada kasus MCDM dinyatakan dalam IVPFN. Akurasi informasi fuzzy dinilai oleh Group Generalized Parameter (GGP) yang dinyatakan dengan cara yang sama seperti informasi fuzzy, yaitu dengan IVPFN. Informasi fuzzy dan GGP selanjutnya diagregasi menggunakan operator Group Generalized Interval Value Pythagorean Fuzzy Weighted Average (GGIVPFWA) dan Group Generalized Interval Value Pythagorean Fuzzy Weighted Geometric (GGIVPFWG). Kedua operator tersebut bertujuan untuk menemukan alternatif terbaik yang dapat dipilih. Hasil keputusan dari operator GGIVPFWA dan GGIVPFWG selanjutnya diverifikasi menggunakan weighted similarity measure dan menunjukkan bahwa kedua operator tersebut dapat menyelesaikan masalah MCDM secara efektif dan akura

R- Fuzzy sets in factor space

Interval-valued fuzzy sets, both-branch fuzzy sets and R-Fuzzy sets are three extended forms of ordinary fuzzy sets. Compared to traditional fuzzy sets, interval-valued fuzzy sets have a stronger ability to express uncertainty because they provide more choices for the descriptions of attributes. Using both-branch fuzzy sets has solved some problems in engineering decision and engineering control. For R-Fuzzy sets, a new fuzzy system is constructed, with both-branch fuzzy sets as a special case. The resulting theorems improve the flexibility of uncertainty system models and expand the range of fuzzy system applications as well

An Extended VIKOR Method for Multiple Criteria Group Decision Making with Triangular Fuzzy Neutrosophic Numbers

In this article, we combine the original VIKOR model with a triangular fuzzy neutrosophic set to propose the triangular fuzzy neutrosophic VIKOR method. In the extended method, we use the triangular fuzzy neutrosophic numbers (TFNNs) to present the criteria values in multiple criteria group decision making (MCGDM) problems. Firstly, we summarily introduce the fundamental concepts, operation formulas and distance calculating method of TFNNs. Then we review some aggregation operators of TFNNs. Thereafter, we extend the original VIKOR model to the triangular fuzzy neutrosophic environment and introduce the calculating steps of the TFNNs VIKOR method, our proposed method which is more reasonable and scientific for considering the conflicting criteria. Furthermore, a numerical example for potential evaluation of emerging technology commercialization is presented to illustrate the new method, and some comparisons are also conducted to further illustrate advantages of the new method

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value