An approach to decision-making via picture fuzzy soft graphs

Abstract

Fuzzy soft graphs are effective mathematical tools that are used to model the vagueness of the real world. A fuzzy soft graph is a fusion of the fuzzy soft set and the graph model and is widely used across different fields. In this current research, the concept of picture fuzzy soft graphs is presented by combining the theory of picture soft sets with graphs. The introduction of this new picture fuzzy soft graphs is an emerging concept that can be rather developed into various graph theoretical concepts. Since soft sets are most usable in real-life applications, the newly combined concepts of the picture and fuzzy soft sets will lead to many possible applications in the fuzzy set theoretical area by adding extra fuzziness in analyzing. The notions of picture soft graphs, strong and complete picture soft fuzzy graphs, a few types of product picture fuzzy soft graphs, and regular, totally regular picture fuzzy soft graphs are discussed and validated using real-world scenarios. In addition, an application of decision-making for medical diagnosis in the current COVID scenario using the picture fuzzy soft graph has been illustrated.

Graphical Exploration of Generalized Picture Fuzzy Hypersoft Information with Application in Human Resource Management Multiattribute Decision-Making

“…Definition 4 (see [19]). A hs-set H over U is a pair (W, D), where D is the Cartesian product of In 2021, Chellamani et al [32] explored the graphical notations of pfs-sets to handle pfs-information efficiently.…”

“…Definition 5 (see [32]). Let M ⋆ � (B, E) be a simple graph with B as set of vertices and E as set of edges and E be a nonvoid set of parameters.…”

“…In order to manage s-set information in graphs, umbakara and George [29] characterized soft graphs in 2014. As its extension, fuzzy soft graph (fs-graph) [30], intuitionistic fuzzy soft graph (ifs-graph) [31], and picture fuzzy soft graph (pfs-graph) [32] are conceptualized. In order to evaluate uncertain nature of approximate elements as a whole in fs-set and ifs-set, Alkhazaleh et al [33] and Bashir et al [34] characterized possibility fuzzy soft set (pofs-set) and possibility intuitionistic fuzzy soft set (poifs-set), respectively, by assigning possibility degree to each approximate element collectively in these structures.…”

An Algorithm for Coloring of Picture Fuzzy Graphs Based on Strong and Weak Adjacencies, and Its Application

“…Researchers recently expanded PFGs in numerous types, such as q-rung PFGs [10], balanced PFGs [11], the application of PFGs for selecting best routes in an airlines network [12], picture fuzzy soft graphs [13], complex PFGs [14], regular PFGs [15], and so on. Numerous studies had also been conducted on the use of PFGs in practical issues such as the application of balanced PFGs [11], decision making under picture fuzzy soft graphs [13], the implementation of regular PFGs in communication networks [15], road map design using picture fuzzy multigraphs [16], the application of PFGs in social networks [17], the shortest path algorithm in picture fuzzy digraphs [18], the site selection problem using laplacian energy of PFGs [19], the application of picture fuzzy tolerance graphs [20], the genus of PFGs [21], and multiple attribute decision-making via PFGs [22].…”

Preferred hospitalization of COVID-19 patients using intuitionistic fuzzy set-based matching approach

“…A number of researchers are contributing consistently towards the development of fuzzy set-based research works. Presently application of fuzzy set theory is found in many areas such as artificial intelligence (Hung and Yang 2004 ), decision-making (Xu and Yager 2008 ; De et al 2019 , 2020 ; Chellamani et al 2021 ; Sun et al 2021 ), optimization (Kumar and Kaur 2012 ), Pattern Recognition (Hung and Yang 2004 ; Gupta and Kumar 2021 ), weather forecasting (Tham et al 2002 ), marketing (Patra 2022 ), medical science (Liu and Wang 2007 ; Sun et al 2021 ; Verma and Rohtagi 2022 ), transportation (Kumar and Kaur 2012 ), social network analysis (Poulik and Ghorai 2021 ), etc. Fuzzy sets are considered as precise mathematical tools for processing data which is derived from vague information.…”