New Operations of Picture Fuzzy Relations and Fuzzy Comprehensive Evaluation

Analysis of Cybersecurities within Industrial Control Systems Using Interval-Valued Complex Spherical Fuzzy Information

Technology affects almost every aspect of life and is constantly changing. Digital communication technology has made it easier and faster to connect people all over the world. Digital technology is used in varies fields, including business, industries, companies, and educational institutions. There are various benefits of technology; it is also associated with a number of risks and dangerous threats known as cybercrimes. Cybercrime is a criminal activity that targets digital technology, like a computer, a computer network, or a mobile device. Cybersecurity is the way we reduce the risk of becoming a victim of cybercrime. Cybersecurity is the process of defending against cyberattacks. By using these concepts, we investigated the interval-valued complex T-spherical fuzzy relations (IVCT-spherical-FRs) introduced in this paper. We studied the relationships between different types of cybersecurity and the sources of cyberattacks. Furthermore, the Hasse diagram for the interval-valued complex T-spherical partial order set and relation is developed. The concepts of Hasse diagram are being used to examine various cybersecurity techniques and practices. The most effective method is identified using the features of Hasse diagrams. Finally, comparison tests are used to demonstrate the benefits of the proposed methods.

Bipolar Picture Fuzzy Graphs with Application

In this manuscript, we introduce and discuss the term bipolar picture fuzzy graphs along with some of its fundamental characteristics and applications. We also initiate the concepts of complete bipolar picture fuzzy graphs and strong bipolar picture fuzzy graphs. Firstly, we apply different types of operations to bipolar picture fuzzy graphs and then we introduce various products of bipolar picture fuzzy graphs. Several other terms such as order and size, path, neighbourhood degrees, busy values of vertices and edges of bipolar picture fuzzy graphs are also discussed. These terminologies also lay the foundations for the discussion about the regular bipolar picture fuzzy graphs. Moreover, we also discuss isomorphisms, weak and co-weak isomorphisms and automorphisms of bipolar picture fuzzy graphs. Finally, at the base of bipolar picture fuzzy graph we present the construction of a bipolar picture fuzzy acquaintanceship graph, which would be an important tool to measure the symmetry or asymmetry of acquaintanceship levels of social networks, computer networks etc.

CPT-TODIM method for picture fuzzy multiple attribute group decision making and its application to food enterprise quality credit evaluation

With the development of society, people’s living standard is constantly improving. Meanwhile, people need various food to satisfy their needs in daily life. Under this situation, more and more food enterprises are appearing in the market. However, some issues about food safety come out. Because of the huge number of food company, managers are difficult in achieving profitability. Therefore, some of the managers try to use some unhealthy materials to produce food in the society. So, it is important for people to distinguish healthy and unhealthy food enterprises in their daily life. In order to help government discern and control the quality of healthy food enterprises in the market, we need to propose an effective evaluation system in estimating food enterprises. In this paper, we introduce a method of evaluating the quality degree of food enterprises which can help us to distinguish enterprises effectively. As we all know, the method of TODIM is widely used in multiple attribute decision making (MADM). In this article, we describe the extended TODIM which based on the cumulative prospect theory (CPT) with picture fuzzy numbers (PF-CPT-TODIM) and use it to evaluate food companies. What’s more, we use entropy method to decide the weights of various attributes. Finally, we select optimal enterprise by using the PF-CPT-TODIM method. Furthermore, we use the comparison of the results of classical PF-TODIM method and PFWA operators to test the availability of PF-CPT-TODIM. It not only can enrich decision-making methods but also make up for the traditional PF-TODIM method in considering the psychological aspects of decision makers.

Linguistic Picture Fuzzy Dombi Aggregation Operators and Their Application in Multiple Attribute Group Decision Making Problem

The aims of this study are to propose the linguistic picture fuzzy Dombi (LPFD) aggregation operators and decision-making approach to deal with uncertainties in the form of linguistic picture fuzzy sets. LPFD operators have more flexibility due to the general fuzzy set. Utilizing the Dombi operational rule, the series of Dombi aggregation operators were proposed, namely linguistic picture fuzzy Dombi arithmetic/geometric, ordered arithmetic/ordered geometric and Hybrid arithmetic/Hybrid geometric aggregation operators. The distinguished feature of these proposed operators is studied. At that point, we have used these Dombi operators to design a model to deal with multiple attribute decision-making (MADM) issues under linguistic picture fuzzy information. Finally, an illustrative example to evaluate the emerging technology enterprises is provided to demonstrate the effectiveness of the proposed approach, together with a sensitivity analysis and comparison analysis, proving that its results are feasible and credible.

Linguistic Spherical Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

The key objective of the proposed work in this paper is to introduce a generalized form of linguistic picture fuzzy set, so-called linguistic spherical fuzzy set (LSFS), combining the notion of linguistic fuzzy set and spherical fuzzy set. In LSFS we deal with the vague and defective information in decision making. LSFS is characterized by linguistic positive, linguistic neutral and linguistic negative membership degree which satisfies the conditions that the square sum of its linguistic membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of linguistic spherical fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose linguistic spherical fuzzy weighted averaging and geometric operators based on spherical fuzzy numbers. Further, the proposed aggregation operators of linguistic spherical fuzzy number are applied to multi-attribute group decision-making problems. To implement the proposed models, we provide some numerical applications of group decision-making problems. In addition, compared with the previous model, we conclude that the proposed technique is more effective and reliable.

Fuzzy Attribute Expansion Method for Multiple Attribute Decision-Making with Partial Attribute Values and Weights Unknown and Its Applications

In the real world, there commonly exists types of multiple attribute decision-making (MADM) problems with partial attribute values and weights totally unknown. Symmetry among some attribute information that is already known and unknown, and symmetry between the pure attribute set and fuzzy attribute membership set can be a considerable way to solve this type of MADM problem. In this paper, a fuzzy attribute expansion method is proposed to solve this type of problem based on two key techniques: the spline interpolation technique and the attribute weight reconfiguration technique, which are respectively used for the determination of attribute values and the reconfiguration of attribute weights. The spline interpolation technique to expand attribute values can enhance the performance of some regression methods and clustering methods by the comparisons between the results of these methods dealing with practical cases with and without the application of the technique, which further illustrates the effectiveness of this technique. For MADM problems with partial attribute values and weights totally unknown, compared with traditional fuzzy comprehensive evaluation (FCE), FCE with the application of fuzzy attribute expansion method can obtain results more similar with the ones when all attribute values and weights are known, which is proved by the practical power quality evaluation example.

Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making

As an extension of the intuitionistic fuzzy set (IFS), the recently proposed picture fuzzy set (PFS) is more suitable to describe decision-makers’ evaluation information in decision-making problems. Picture fuzzy aggregation operators are of high importance in multi-attribute decision-making (MADM) within a picture fuzzy decision-making environment. Hence, in this paper our main work is to introduce novel picture fuzzy aggregation operators. Firstly, we propose new picture fuzzy operational rules based on Dombi t-conorm and t-norm (DTT). Secondly, considering the existence of a broad and widespread correlation between attributes, we use Heronian mean (HM) information aggregation technology to fuse picture fuzzy numbers (PFNs) and propose new picture fuzzy aggregation operators. The proposed operators not only fuse individual attribute values, but also have a good ability to model the widespread correlation among attributes, making them more suitable for effectively solving increasingly complicated MADM problems. Hence, we introduce a new algorithm to handle MADM based on the proposed operators. Finally, we apply the newly developed method and algorithm in a supplier selection issue. The main novelties of this work are three-fold. Firstly, new operational laws for PFSs are proposed. Secondly, novel picture fuzzy aggregation operators are developed. Thirdly, a new approach for picture fuzzy MADM is proposed.

L-Fuzzy Sets and Isomorphic Lattices: Are All the “New” Results Really New? †

We review several generalizations of the concept of fuzzy sets with two- or three-dimensional lattices of truth values and study their relationship. It turns out that, in the two-dimensional case, several of the lattices of truth values considered here are pairwise isomorphic, and so are the corresponding families of fuzzy sets. Therefore, each result for one of these types of fuzzy sets can be directly rewritten for each (isomorphic) type of fuzzy set. Finally we also discuss some questionable notations, in particular, those of “intuitionistic” and “Pythagorean” fuzzy sets.