ABSTRACT
Intuitionistic fuzzy set (IFS) theory can be applied for multi-aspect systems due to its capability to address uncertainty and incomplete information in terms of membership and non-membership degrees. Unfortunately, classical Γ -structures cannot handle fuzzy and imprecise information in real problems. In fact, there is no rigorous base to practically express the effectiveness of multi-attribute systems in IFS environment. Here, we develop a generalized IFS with the notion of Γ -module called intuitionistic fuzzy Γ -submodule (IF Γ M) to establish a novel " Global electronic (e)-Commerce (GeC) Theory ". To simplify the analysis of parameters, (α , β) -cut representation is proposed in terms of comprehensive distribution of fuzzy number for the classification of components. On the other hand, Cartesian product is implemented to correspond the elements. Substantial properties of IF Γ M including (α , β) -cut, Cartesian product and t -intuitionistic fuzzy Γ -submodule (t -IF Γ M) are characterized with illustrative examples to extend the framework of IF Γ M, where (α , β) -cut and support t -IF Γ M are verified to be Γ -submodules based on the properties of IF Γ M. Through Γ -module homomorphism, image and inverse image, the parametric connections between (α , β) -cuts are systematically investigated. In addition, a mathematical relationship between the Cartesian product and (α , β) -cut is determined. The overlapping intersection of a collection of t -IF Γ M is proved to be t -IF Γ M, and the image and inverse image are preserved under Γ -module homomorphism. As global e -trades are increasingly expanding after the recent coronavirus disease 2019 (COVID-19) hit, with the growth of 26.7-trillion dollars, businesses are required to transform their traditional functional natures to online (or blended) strategies for cost efficiency and self-survival in the present competitive environment. Therefore, compared to recent studies on IFS in the context of Γ -structures, the main contribution of this study is to provide a theoretical basis for the establishment of a new GeC Theory through the developed IF Γ M method and Γ -module M which targets the purchasing rate of customers through e -commerce companies. In the end, the performance of the proposed method in terms of upper and lower cut, t -intuitionistic fuzzy set, support and IF Γ M model, is analyzed in the developed GeC Theory. The proposed GeC Theory is validated using real datasets of e -commerce mega companies, i.e., Amazon, Alibaba, eBay, Shopify. They are characterized based on the amount of online shopping by samples (individuals). Compared to the existing methods, the GeC approach is an effective IFS-based method for complex systems with uncertainty. [ FROM AUTHOR] Copyright of Engineering Applications of Artificial Intelligence is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)
ABSTRACT
Graph theoretic techniques have been widely applied to model many types of links in social systems. Also, algebraic hypercompositional structure theory has demonstrated its systematic application in some problems. Influenced by these mathematical notions, a novel semihypergroup-based graph (SBG) of G=H,E is constructed through the fundamental relation γn on H, where semihypergroup H is appointed as the set of vertices and E is addressed as the set of edges on SBG. Indeed, two arbitrary vertices x and y are adjacent if xγny. The connectivity of graph G is characterized by xγ*y, whereby the connected components SBG of G would be exactly the elements of the fundamental group H/γ*. Based on SBG, some fundamental characteristics of the graph such as complete, regular, Eulerian, isomorphism, and Cartesian products are discussed along with illustrative examples to clarify the relevance between semihypergroup H and its corresponding graph. Furthermore, the notions of geometric space, block, polygonal, and connected components are introduced in terms of the developed SBG. To formulate the links among individuals/countries in the wake of the COVID (coronavirus disease) pandemic, a theoretical SBG methodology is presented to analyze and simplify such social systems. Finally, the developed SBG is used to model the trend diffusion of the viral disease COVID-n in social systems (i.e., countries and individuals).
ABSTRACT
In this study, we generalize fuzzy Γ -module, as intuitionistic fuzzy Γ -submodule of Γ -module (IF Γ M), and utilize it for modeling the spread of coronavirus in air travels. Certain fundamental features of intuitionistic fuzzy Γ -submodule are provided, and it is proved that IF Γ M can be considered as a complete lattice. Some elucidatory examples are demonstrated to explain the properties of IF Γ M. The relevance between the upper and lower α -level cut and intuitionistic fuzzy Γ -submodules are presented and the characteristics of upper and lower under image and inverse image of IF Γ M are acquired. It is verified that the image and inverse image of intuitionistic fuzzy Γ -submodule are preserved under the module homomorphism. The obtained IF Γ M is used to model the aerial transition of viral diseases, that is, COVID-n, via flights.
ABSTRACT
In this study, we generalize fuzzy Γ‐module, as intuitionistic fuzzy Γ‐submodule of Γ‐module (IFΓM), and utilize it for modeling the spread of coronavirus in air travels. Certain fundamental features of intuitionistic fuzzy Γ‐submodule are provided, and it is proved that IFΓM can be considered as a complete lattice. Some elucidatory examples are demonstrated to explain the properties of IFΓM. The relevance between the upper and lower α‐level cut and intuitionistic fuzzy Γ‐submodules are presented and the characteristics of upper and lower under image and inverse image of IFΓM are acquired. It is verified that the image and inverse image of intuitionistic fuzzy Γ‐submodule are preserved under the module homomorphism. The obtained IFΓM is used to model the aerial transition of viral diseases, that is, COVID‐n, via flights.