On homomorphism of fuzzy multigroups

In this paper, the homomorphism of fuzzy multigroups is briefly delineated following [2] and their corresponding isomorphism theorems are considered

Aplikasi Intuitionistic Fuzzy Multisets Dalam Pemilihan E-commerce Terbaik

Negara Indonesia saat ini sedang mengalami perkembangan teknologi yang sangat pesat. Perkembangan teknologi yang sangat pesat mempengaruhi aktivitas masyarakat dalam menjalankan kehidupan sehari-hari, khususnya pada masa pandemi Covid-19. Salah satu bentuk aktivitas masyarakat khususnya dalam bidang ekonomi yang mengalami perubahan cukup signifikan akibat pandemi Covid-19 yaitu dalam hal transaksi jual-beli. Untuk menanggulangi hal tersebut, masyarakat mayoritas beralih dengan menggunakan e-commerce. Perkembangan e-commerce di Indonesia semakin meningkat dengan banyaknya perusahaan e-commerce yang berdiri hingga saat ini seperti Shopee, Lazada, Tokopedia, dan masih banyak lagi. Dari berbagai macam pilihan e-commerce yang terdapat di Indonesia terkadang membuat masyarakat sebagai konsumen menjadi bingung dalam memilih e-commerce terbaik. Oleh sebab itu, penelitian ini bertujuan untuk merekomendasikan sistem pendukung keputusan dalam pemilihan e-commerce terbaik berdasarkan beberapa kriteria dengan menggunakan metode Jarak Euclidean dalam Intuitionistic Fuzzy Multisets (IFMS). Penelitian ini menggunakan lima alternatif e-commerce yaitu Shopee, Lazada, Tokopedia, Bukalapak, dan Blibli. Penilaian terhadap e-commerce didasarkan pada enam kriteria yaitu harga, variasi produk, variasi metode pembayaran, variasi metode pengiriman, kesesuaian produk dengan gambar, dan voucher yang diberikan. Data yang digunakan dalam penelitian ini merupakan hasil studi kasus terhadap 20 responden yang pernah menggunakan e-commerce dan data diperoleh melalui pembagian kuisioner berupa google form. Hasil penelitian diperoleh e-commerce terbaik berdasarkan banyaknya responden yang direkomendasikan yaitu Lazada, dengan jumlah responden yang direkomendasikan sebanyak 9 responden

Hesitant fuzzy network topsis methods with the incorporation of z-numbers and social network analysis for small and large scale group decision making

It is critical to arrive at an acceptable level of consensus in a group for an agreeable and implementable decision. The evaluation of alternatives in conventional TOPSIS decision making does not take into account the inherent vagueness of information as it requires a systematic decision-making process in which relies on numerous conditions and unpredictable situations. It is common in deciding the best choice with the highest satisfaction degree that are evaluated based on attributes. However, two or more alternatives with the same or nearest satisfaction degree would lead to hesitancy in the decision. Thus, fuzzy network TOPSIS is incorporated with the hesitant fuzzy set is developed namely hesitant fuzzy network TOPSIS. Nevertheless, the reliability of decisions by experts and the complexity in large scale are less highlighted in hesitant fuzzy network TOPSIS. Therefore, this study aims in formulating hesitant fuzzy network TOPSIS with the incorporation of Z-numbers. The formulation also implies social network analysis for large-scale group decision making. In this study, four new fuzzy network TOPSIS are developed in small scale and large-scale group decision making. The proposed methods enhance the transparency and reliability by incorporating fuzzy network and Z numbers respectively. In addition, social network analysis is suitable for dealing with the complexity involved in large scale group decision making. For the practicality and the effectiveness of the proposed methods in a realistic scenario, a case study of stock selection and the analysis of results comparing proposed methods to the established methods has been considered. The ranking of the proposed methods are validated comparatively using performance indicators namely Spearman rho correlation, Root Means Squared Error, and Absolute Distance by assuming ranking based on Return on Investment as a benchmarking. Based on the case study, the proposed methods outperform the established methods in terms of average rank position. In conclusion, the proposed methods contribute significantly toward the implementation of small scale and large scale group decision making using hesitant fuzzy set, fuzzy network and Z numbers

On the Knowledge-based Dynamic Fuzzy Sets

In 1965, L.A. Zadeh [1] introduced fuzzy set as a generalization of crisp set by considering membership degrees of elements. That membership degree is represented gradually as a real number in an interval [0,1]. Wang et al. [2] generalized the concept of fuzzy set, called Dynamic Fuzzy Sets (DFS). In the DFS each membership degree of an element is given by a membership function dealing with time variable. Thus, the membership degree of an element in a given dynamic fuzzy set might dynamically change according to the time�s variable. In 2002, Intan and Mukaidono [3] proposed an extended concept of fuzzy set, called Knowledge-based Fuzzy Sets (KFS). In the KFS, the membership degree of an element given a fuzzy set is subjectively determined by a single knowledge. The membership degree of an element with respect to a given fuzzy set may be different provided by different knowledge of persons. This paper combines both concepts, DFS and KFS, called Knowledge-based Dynamic Fuzzy Sets (KDFS), by realizing that membership function of a given fuzzy set provided by a certain knowledge may be dynamically changed over time. Three kinds of summary fuzzy sets are proposed and discussed. Some basic operations of KDFS are defined. Their properties are verified and examined

Neutrosophic Algebraic Structures and Their Applications

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more

Neutrosophic SuperHyperAlgebra and New Types of Topologies

In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P2(S) } and so on. That’s why the n-th PowerSet of a Set S { defined recursively and denoted by Pn(S) = P(Pn-1(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real world. The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology