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

Partial orderings for hesitant fuzzy sets

New partial orderings =o=o, =p=p and =H=H are defined, studied and compared on the set HH of finite subsets of the unit interval with special emphasis on the last one. Since comparing two sets of the same cardinality is a simple issue, the idea for comparing two sets A and B of different cardinalities n and m respectively using =H=H is repeating their elements in order to obtain two series with the same length. If lcm(n,m)lcm(n,m) is the least common multiple of n and m we can repeat every element of A lcm(n,m)/mlcm(n,m)/m times and every element of B lcm(n,m)/nlcm(n,m)/n times to obtain such series and compare them (Definition 2.2). (H,=H)(H,=H) is a bounded partially ordered set but not a lattice. Nevertheless, it will be shown that some interesting subsets of (H,=H)(H,=H) have a lattice structure. Moreover in the set BB of finite bags or multisets (i.e. allowing repetition of objects) of the unit interval a preorder =B=B can be defined in a similar way as =H=H in HH and considering the quotient set View the MathML sourceB¿=B/~ of BB by the equivalence relation ~ defined by A~BA~B when A=BBA=BB and B=BAB=BA, View the MathML source(B¿,=B) is a lattice and (H,=H)(H,=H) can be naturally embedded into it.Peer ReviewedPostprint (author's final draft

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

Intuitionistic Hesitant Fuzzy UP (BCC)-Filters of UP (BCC)-Algebras

The concepts of intuitionistic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and UP (BCC)-filters of UP (BCC)-algebras are presented, some of their features are explained, and their extensions are demonstrated using the theory of hesitant fuzzy sets as a foundation. The necessary conditions for those intuitionistic hesitant fuzzy sets are provided and include their relation to their complement. The concept of prime and weakly prime of intuitionistic hesitant fuzzy sets was also introduced and studied. We also talk about the connections between intuitionistic hesitant fuzzy UP (BCC)-subalgebras (UP (BCC)-ideals, UP (BCC)-filters) and their level subsets. The homomorphic pre-images of intuitionistic hesitant fuzzy UP (BCC)-filters in UP (BCC)-algebras are also studied and some related properties are investigated

Órdenes parciales para hesitant fuzzy sets

Se define un nuevo orden parcial H en el conjunto H de subconjuntos finitos del intervalo unidad. Con este preorden H no es un retículo, pero sí lo son algunos subconjuntos de H interesantes. H se puede inyectar de forma natural en un retículo B. En H y B se pueden definir t-normas.Peer ReviewedPostprint (author's final draft

Analisis Kelayakan Rencana Investasi Travel Baru Menggunakan Metode Hesitant Fuzzy Sets

Transportation is a tool that supports the construction and economic development of a country. Because in this modern era, transportation provides easy access to the movement of goods and people from one place to another. This research was conducted at a company engaged in public transportation services. The main services provided are inter-city buses in the province, inter-city inter-provincial buses, tour buses and travel transportation. In 2018, the company has plans to add six travel vehicles and the capital owned is 500.000.000 Rupiah. While the remaining capital needed will be borrowed from Bank Antardaerah, so a business feasibility study is needed that can determine whether or not the investment plan is feasible. In addition, the Hesitant Fuzzy Sets method is used to model all forms of uncertainty that can cause losses. Hesitant Fuzzy Sets are an extension of the fuzzy set to handle inaccuracies where there are two or more sources of obscurity that appear simultaneously. Some basic methods used to determine the feasibility of investment plans are Payback Period (PP), Minimum Acceptable Rate of Return (MARR) and Internal Rate of Return (IRR). In addition, the Hesitant Fuzzy Sets method is used to model all forms of uncertainty that can cause losses. One example of such uncertainty is income uncertainty and expenditure uncertainty which are received by the company every year. The reason for using Hesitant Fuzzy Sets, because the method is an extension of the fuzzy set that can handle inaccuracies where there are two or more sources of obscurity that appear simultaneously

Expanded hesitant fuzzy sets and group decision making: slides for FUZZ-IEEE 2017

[EN]We define expanded hesitant fuzzy sets, which incorporate all available information of the decision makers that provide the membership degrees that define a hesitant fuzzy set. We show how this notion relates to hesitant fuzzy set and extended hesitant fuzzy set. We define various scores for this setting, which generalize popular scores for hesitant fuzzy elements. Finally, a group decision making procedure is presented and illustrated with an example