Certain Operations on Complex Picture Fuzzy Graphs

2023

IJITRA is an Open Access publication. It may be read, copied, and distributed free of charge according to the conditions of the Creative Commons Attribution 4.0 International license. International Journal of Information Technology, Research and Applications (IJITRA) is a journal that publishes articles which contribute new theoretical results in all the areas of Computer Science,

Advances in Mathematics: Scientific Journal

In this manuscript, we present complex cubic intuitionistic fuzzy set (CCIFS) which is a combination of complex cubic membership values and complex cubic non-membership values and define some related operations on these sets. Also, an algorithm and a realistic example are given to show its usefulness.

Computational and Applied Mathematics

The paper aims are to propose a new concept called as complex picture fuzzy set (CPFS), as an extension of complex intuitionistic fuzzy set (CIFS). The addition of a neutral membership degree to the definition of CIFS makes CPFS a generalized form of CIFS. The uniqueness of this new theory lies in the capability to attain the wider range with the help of degree of neutral membership, non-membership, and membership. The range of values of membership degrees is broaden to the unit disk in a complex plane. We define elementary operations and properties of CPFSs and explore the MCDM issues with the help of CPFSs, based on Hamacher operations and some aggregation methods. Then, we introduce some operators to aggregate the CPF data, namely complex picture fuzzy Hamacher weighted averaging, ordered weighted averaging, hybrid averaging and complex picture fuzzy Hamacher weighted geometric, ordered weighted geometric and hybrid geometric operators, benefited from the basic Hamacher operations, and averaging, geometric aggregation techniques. We also construct MCDM problem using these operators and perform a calculation for the selection of best ERP system, to demonstrate the authenticity and efficiency of this manuscript. Moreover, we study a comparison to validate the consistency and superiority of our techniques.

The objective of this paper is to investigate and extends the innovative concept of complex fuzzy set. The novelty of the complex fuzzy set lies in the range of values its membership function may attain. In contrast to a traditional fuzzy membership function, this range is not limited to [0,1], but extended to the unit circle in the complex plane. Consequently, a major part of this work is dedicated to a discussion of the intuitive interpretation of soft complex fuzzy sets, parameterized soft complex sets, complex fuzzy soft hypergroup, complex fuzzy soft hyperring and complex fuzzy soft hyperideal. We also developing the innovative concepts of soft complex intuitionistic fuzzy sets with example.

Symmetry

A complex fuzzy set (CFS) is described by a complex-valued truth membership function, which is a combination of a standard true membership function plus a phase term. In this paper, we extend the idea of a fuzzy graph (FG) to a complex fuzzy graph (CFG). The CFS complexity arises from the variety of values that its membership function can attain. In contrast to a standard fuzzy membership function, its range is expanded to the complex plane’s unit circle rather than [0,1]. As a result, the CFS provides a mathematical structure for representing membership in a set in terms of complex numbers. In recent times, a mathematical technique has been a popular way to combine several features. Using the preceding mathematical technique, we introduce strong approaches that are properties of CFG. We define the order and size of CFG. We discuss the degree of vertex and the total degree of vertex of CFG. We describe basic operations, including union, join, and the complement of CFG. We show new m...

2020

In this paper picture fuzzy graph has shown more advantage in handling vagueness and uncertainty than fuzzy set. We have applied concept of picture fuzzy set to fuzzy set. Picture fuzzy graph is generalization of fuzzy graph. The concept of picture fuzzy graph has discussed here. In this paper complement and Ring sum operation of picture fuzzy graphs has discussed isomorphic property of picture fuzzy graphs. We have used picture Fuzzy graph play important role in representation of many uncertain decision making problem in daily life since Picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, e.g. number theory, coding theory, cryptography, computer science, operation research, also we are using certain concepts of bipolar fuzzy directed hypergraphs Finally we have proved the Ring sum of two picture fuzzy graphs is also a picture fuzzy graph.

IEEE Access

Fuzzy graph models are found everywhere in natural and human made structures, including process dynamics in biological, physical and social systems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A complex vague model is useful in the field of mathematics which gives more precision, comparability and flexibility to the system as compared to the vague model. In these years, a mathematical approach is a generalized approach of blending different aspects. According to the above mathematical approach, we investigate strong techniques which are based on complex vague graphs. The purpose of this research study is to present and explore the key properties including: Cartesian products, composition, strong product, semi-strong product and direct product of complex vague graphs with examples. Finally, we present application of complex vague graphs in decision-making problems. INDEX TERMS Complex vague graph, Cartesian products, composition, strong product, semi strong product, direct product.

Correctly determining a company's market worth during an entire year or a certain period presents a difficulty to decision-makers. In the case of the merger of companies, the need performs heavier when both the companies' owners are attracted to establishing a fair price at the optimal time to merge. The effectiveness of representing, connecting and manipulating both uncertainty and periodicity information becomes highly required. Hence, study and nhance some properties and conditions of the algebraic structure of complex hesitant fuzzy graphs. Therefore, the degree of composition between two complex hesitant fuzzy graphs is proposed. Also, the formal definitions of union, joint and complement are presented to be covered in the realm of complex hesitant fuzzy graphs. A real-life application is illustrated to show the relation between vertices and edges in the form of complex hesitant fuzzy graphs.

Romanian Journal of Information Science and Technology, 2018

The Fuzzy Set Theory has been applied in various problems in numerous fields. In particular, the concepts of t-norms and t-conorms serve a significant role in shaping the theory and its applications. The notion of Complex Fuzzy Sets extends the Fuzzy Set Theory and provides several advantages over the classical theory, especially in terms of the capability to concisely, efficiently, and accurately represent complex relations between fuzzy set components. Some of the areas where complex fuzzy sets have been successfully applied are the areas of time series analysis and multi-criteria decision making problems. The notions of complex t-norms and t-conorms have not been fully developed so far. In this paper, we present the complex fuzzy set forms of t-norms and t-conorms and detail their properties. Additionally, we provide two numerical examples of applying the complex t-norm and tconorm to multi-criteria decision making in the context of medicine- related problems using medical datasets.

2016

In this paper, we propose the notion of complex intuitionistic fuzzy sets defined by complex-valued membership and non-membership functions in order to make extension the result presented in [6]. We first give a Cartesian representation, and then we discuss the polar representation.