An algorithm to compute the strength of competing interactions in the Bering Sea based on pythagorean fuzzy hypergraphs

The networks of various problems have competing constituents, and there is a concern to compute the strength of competition among these entities. Competition hypergraphs capture all groups of predators that are competing in a community through their hyperedges. This paper reintroduces competition hypergraphs in the context of Pythagorean fuzzy set theory, thereby producing Pythagorean fuzzy competition hypergraphs. The data of real-world ecological systems posses uncertainty, and the proposed hypergraphs can efficiently deal with such information to model wide range of competing interactions. We suggest several extensions of Pythagorean fuzzy competition hypergraphs, including Pythagorean fuzzy economic competition hypergraphs, Pythagorean fuzzy row as well as column hypergraphs, Pythagorean fuzzy k-competition hypergraphs, m-step Pythagorean fuzzy competition hypergraphs and Pythagorean fuzzy neighborhood hypergraphs. The proposed graphical structures are good tools to measure the strength of direct and indirect competing and non-competing interactions. Their aptness is illustrated through examples, and results support their intrinsic interest. We propose algorithms that help to compose some of the presented graphical structures. We consider predator-prey interactions among organisms of the Bering Sea as an application: Pythagorean fuzzy competition hypergraphs encapsulate the competing relationships among its inhabitants. Specifically, the algorithm which constructs the Pythagorean fuzzy competition hypergraphs can also compute the strength of competing and non-competing relations of this scenario.

Digital Color Image Processing Using Intuitionistic Fuzzy Hypergraphs

Hypergraphs are considered a useful mathematical tool for digital image processing and analysis since they can represent digital images as complex relationships between pixels or block of pixels. The notion of hypergraphs has been extended in fuzzy theory leading to the concept of fuzzy hypergraphs, then in intuitionistic fuzzy theory conducting to the concept of intuitionistic fuzzy hypergraphs or IFHG. The latter is very suitable to model digital images with uncertain or imprecise knowledge. This paper deals with color image denoising, segmentation, and edge detection in a color image initially represented in RGB space using intuitionistic fuzzy hypergraphs. First, the RGB image is transformed to HLS space resulting in three separated components. Then each component is intuitionistically fuzzified based on entropy measure from which an intuitionistic fuzzy hypergraph is generated automatically. The generated hypergraphs will be used for denoising, segmentation, and edge detection.

Color Image Processing Under Uncertainty

Most digital images have uncertainties associated with the intensity levels of pixels and/or edges. These uncertainties can be traced back to the acquisition chain, to uneven lighting conditions used during imaging or to the noisy environment. On the other hand, intuitionistic fuzzy hypergraphs are considered a useful mathematical tool for digital image processing since they can represent digital images as complex relationships between pixels and model uncertain or imprecise knowledge explicitly. This paper presents the approach for noisy color image segmentation and edge detection based on intuitionistic fuzzy hypergraphs. First, the RGB image is transformed to the HLS space resulting in three separated components. Then each component is intuitionistically fuzzified based on entropy measure from which an intuitionistic fuzzy hypergraph is generated automatically. The generated hypergraphs will be used for denoising, segmentation, and edges detection. The first experimentations showed that the proposed approach gave good results especially in the case of dynamic threshold.

Hesitant fuzzy graphs, hesitant fuzzy hypergraphs and fuzzy graph decisions1

Up to now, there have been a lot of research results about multi-attribute decision making problems by fuzzy graph theory. However, there are few investigations about multi-attribute decision making problems under the background of indecisiveness. The main reason is that the difference of cognition and the complexity of thinking by decision makers, for the same question have different opinions. In this paper, we proposed a hesitant fuzzy hypergraph model based on hesitant fuzzy sets and fuzzy hypergraphs. At the same time, some basic graph operations of hesitant fuzzy hypergraphs are investigated and several equivalence relationship between hesitant fuzzy hypergraphs, hesitant fuzzy formal concept analysis and hesitant fuzzy information systems are discussed. Since granular computing can deal with multi-attribute decision-making problems well, we considered the hesitant fuzzy hypergraph model of granular computing, and established an algorithm of multi-attribute decision-making problem based on hesitant fuzzy hypergraph model. Finally an example is given to illustrate the effectiveness of the algorithm.

A method of using fuzzy hypergraphs to evaluate structural and technological survivability of attitude control systems for unmanned spacecraft

Successful completion of a mission by an unmanned spacecraft (USC), both under nominal operational conditions both under examined contingencies and unexamined off-nominal situations is possible through designing survivability into the USC onboard system (OS). An analysis of current methods for evaluating USC OS survivability during their configuration management and reconfiguration under conditions of examined in-flight contingencies widely used in the design and development of the said USC has shown that these methods are not acceptable for evaluating the USC OS survivability in case of unexamined off-nominal situations in flight. This calls for development of conceptually novel methodological and procedural framework for evaluating structural survivability of USC OS configurations that take into account the level of participation of functional elements (FE) and OS subsystems in the USC control operations under various scenarios of the mission plan implementation. The paper proposes an original approach to evaluating the structural and technological survivability of the USC OS based on a fuzzy hypergraph formal representation of the operations to control the USC attitude, where the edges of the hypergraph connect the FE and OS subsystems that support the implementation of this or that specific control process. The paper also shows how one could use for the quantitative evaluation of the structural and technological survivability of a specific USC OS configuration the results of differentiation of a fuzzy hypergraph that could be visualized as a fuzzy hypergraph of technological independence of OS FE. Such an approach makes it possible to analyze the effects of FE on OS, identify the most critical elements, which have the lowest technological independence under mission plan implementation conditions, which could be used for providing a rationale for the required level of structural and functional redundancy of USC elements and subsystems introduced during various phases in its life cycle. Keywords: unmanned spacecraft, onboard systems survivability, fuzzy hypergraph derivative.

Fuzzy Graphs and Fuzzy Hypergraphs

Relationship is the core building block of a network, and today's world advances through the complex networks. Graph theory deals with such problems more efficiently. But whenever vagueness or imprecision arises in such relationships, fuzzy graph theory helps. However, fuzzy hypergraphs are more advanced generalization of fuzzy graphs. Whenever there is a need to define multiary relationship rather than binary relationship, one can use fuzzy hypergraphs. In this chapter, interval-valued fuzzy hypergraph is discussed which is a generalization of fuzzy hypergraph. Several approaches to find shortest path between two given nodes in an interval-valued fuzzy graphs is described here. Many researchers have focused on fuzzy shortest path problem in a network due to its importance to many applications such as communications, routing, transportation, etc.