Himpunan Kabur Hesitant Ganda yang Diperluas (Expanded Dual Hesitant Fuzzy Sets)

Konsep Expanded Dual Hesitant Fuzzy Sets merupakan suatu pengembangan dari konsep Hesitant Fuzzy Sets. Berdasarkan konsep Hesitant Fuzzy Sets telah diperoleh beberapa konsep seperti Dual Hesitant Fuzzy Sets, Expanded Hesitant Fuzzy Sets, dan Extended Hesitant Fuzzy Sets yang menjadi konsep dasar pengembangan Expanded Dual Hesitant Fuzzy Sets. Kemudian akan dikaji beberapa operasi-operasi terkait Expanded Dual Hesitant Fuzzy Sets, skor pada Expanded Dual Hesitant Fuzzy Sets, hukum perbandingan, dan penerapan konsep Expanded Dual Hesitant Fuzzy Sets dalam masalah pengambilan keputusan

Dual Hesitant Fuzzy Set

Konsep dual hesitant fuzzy set merupakan suatu pengembangan dari konsep fuzzy set. Berdasarkan konsep fuzzy sets telah diperoleh beberapa konsep seperti Intuitionistic fuzzy sets dan Hesitant Fuzzy Sets yang menjadi konsep dasar pengembangan dual hesitant fuzzy set. Kemudian akan dikaji beberapa operasi-operasi terkait dual hesitant fuzzy set, pembuktian teorema-teorema yang ada dan dikaji juga tentang penerapan konsep dual hesitant fuzzy set dalam masalah pengambilan keputusan

Dual hesitant fuzzy aggregation operators

Dual hesitant fuzzy sets (DHFSs) is a generalization of fuzzy sets (FSs) and it is typical of membership and non-membership degrees described by some discrete numerical. In this article we chiefly concerned with introducing the aggregation operators for aggregating dual hesitant fuzzy elements (DHFEs), including the dual hesitant fuzzy arithmetic mean and geometric mean. We laid emphasis on discussion of properties of newly introduced operators, and give a numerical example to describe the function of them. Finally, we used the proposed operators to select human resources outsourcing suppliers in a dual hesitant fuzzy environment. First published online: 11 Sep 201

KOEFISIEN KORELASI BEBERAPA HIMPUNAN KABUR

Koe�sien korelasi yaitu bertujuan untuk mengukur tingkat keeratan hubungan antara dua variabel atau parameter. Teori himpunan kabur (fuzzy set) telah diperkenalkan oleh Zadeh pada tahun 1965, dimana teori ini dapat menjadi alternatif yang lebih baik dalam mencari solusi permasalahan yang mengandung ketidakpastian. Kemudian semakin berkembang ilmu pengetahuan, maka semakin banyak bentuk umum dari himpunan kabur (fuzzy set/FS ) yang diusulkan dan dikembangkan, diantaranya ada himpunan kabur intuisionistik (Intuitionistic FuzzySets/IFS), himpunan kabur hesitant (Hesitant Fuzzy Sets (HFS)), dan himpunan kabur dual hesitant (Dual Hesitant Fuzzy Sets (DHFS)). Oleh karena itu, Pada penelitian ini yang dikaji yaitu Koe�sien korelasi himpunan kabur intuisionistik, koe�sien korelasi himpunan kabur hesitant dan koe�sien korelasi himpunan kabur dual hesitant. Kemudian koe�sien yang diperoleh di antara dua DHFS dengan menggunakan konsep dari statistik, formulanya dikembangkan untuk koe�sien korelasi r1 untuk keanggotaan dan r2 untuk bukan keanggotaan. Selanjutnya rata-rata dari r1 dan r2 menentukan koe�sien korelasi r di antara data yang diwakili oleh dua DHFS. Kata Kunci: Koe�sien korelasi, himpunan kabur, himpunan kabur intusionistik, himpunan kabur hesitant, himpunan kabur dual hesitant, koe�sien korelasi himpunan kabur intuisionistik, koe�sien korelasi himpunan kabur hesitant, koefeisien korelasi himpunan kabur dual hesitant

Extended hesitant fuzzy sets

Hesitant fuzzy sets (HFSs) are a useful tool to manage situations in which the decision makers (DMs) hesitate about several possible values for the membership to assess a variable, alternative, etc. However, HFSs have the information loss problem and cannot identify different DMs, which interferes with the application of HFSs in decision making. To overcome these limitations, we develop the extended hesitant fuzzy sets (EHFSs) in this paper. As an extension of HFSs, EHFSs have close relationships with existing fuzzy sets including intuitionistic fuzzy sets (IFSs), fuzzy multisets (FMSs), type-2 fuzzy sets (T2FSs), dual hesitant fuzzy sets (DHFSs), and especially HFSs. We propose a concept of extended hesitant fuzzy elements (EHFEs), then study the basic operations and the desirable properties of EHFEs in detail. Some extended hesitant distance measures are developed to illustrate their advantages comparing with the existing hesitant distance measures. To extend EHFSs to decision making, we combine the proposed distance measures with the Dempster-Shafer belief structure. First published online: 15 Jun 201

An Extended VIKOR Method for Multiple Attribute Decision Analysis with Bidimensional Dual Hesitant Fuzzy Information

Bidimensional dual hesitant fuzzy (BDHF) set is developed to present preferences of a decision maker or an expert, which is more objective than existing fuzzy sets such as Atanassov’s intuitionistic fuzzy set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, after investigating some distance measures, we define a new generalized distance measure between two BDHF elements with parameter λ for the sake of overcoming some drawbacks in existing distance measures. Covering all possible values of parameter λ, a new approach is designed to calculate the generalized distance measure between two BDHF elements. In order to address complex multiple attribute decision analysis (MADA) problems, an extension of fuzzy VIKOR method in BDHF context is proposed in this paper. In VIKOR method for MADA problems, weight of each attribute indicates its relative importance. To obtain weights of attributes objectively, a new entropy measure with BDHF information is developed to create weight of each attribute. Finally, an evaluation problem of performance of people’s livelihood project in several regions is analyzed by the proposed VIKOR method to demonstrate its applicability and validity

The Selection of Investment Priorities using Expanded Dual Hesitant Fuzzy Sets

The concept of expanded dual hesitant fuzzy set is a concept that can be applied in decision-making problems. In decision-making problems, expanded dual hesitant fuzzy set can be applied to represent the opinions of multiple experts or stakeholders in a more elaborate manner. It enables decision-makers to provide more detailed information about their preferences and hesitancy

Decision making with both diversity supporting and opposing membership information

Online big data provides large amounts of decision information to decision makers, but supporting and opposing information are present simultaneously. Dual hesitant fuzzy sets (DHFSs) are useful models for exactly expressing the membership degree of both supporting and opposing information in decision making. However, the application of DHFSs requires an improved distance measure. This paper aims to improve distance measure models for DHFSs and apply the new distance models to generate a technique for order preference by similarity to an ideal solution (TOPSIS) method for multiple attribute decision making (MADM)

Novel Parameterized Utility Function on Dual Hesitant Fuzzy Rough Sets and Its Application in Pattern Recognition

Based on comparative studies on correlation coefficient theory and utility theory, a series of rules that utility functions on dual hesitant fuzzy rough sets (DHFRSs) should satisfy, and a kind of novel utility function on DHFRSs are proposed. The characteristic of the introduced utility function is a parameter, which is determined by decision-makers according to their experiences. By using the proposed utility function on DHFRSs, a novel dual hesitant fuzzy rough pattern recognition method is also proposed. Furthermore, this study also points out that the classical dual tool is suitable to cope with dynamic data in exploratory data analysis situations, while the newly proposed one is suitable to cope with static data in confirmatory data analysis situations. Finally, a medical diagnosis and a traffic engineering example are introduced to reveal the effectiveness of the newly proposed utility functions on DHFRSs. Document type: Articl