Introduction

Flocking or swarm behavior is observed in many species in nature. A prominent Recent advances in modeling have led to the widespread application of agent-based simulation in complex systems across a wide range of academic fields, including organizational behavior, decision-making, and problem-solving. Emergence behavior is a result of the complexity of agent behaviors and their interactions; it can be found in a wide range of systems, from the simplest to the most complex, and can take many different forms (positive or negative). From [1] divided emergent behaviors into four categories according to the kinds of input that vary and the causal connections between a system's micro and macro levels. In complex systems, a weak emergence [2] can be identified and comprehended. Emergence validation techniques in the field of complex systems can be divided into three primary groups: grammar-based, variable-based, and event-based. Variable-based approaches use a particular variable to characterize emergence. Variations in this variable's values are considered to indicate the existence of emergence properties [3]. One may use the center of mass of a flock of birds, as demonstrated in [4], as an illustration of how emergence in bird flocking behavior occurs. A sequence of events that alter the state of a system or a subsystem is referred to as behavior in event-based approaches [5].

This paper is organized as follows. Section two defines the fundamental concepts, section three introduces the related works, section four presents the proposed approach, the first results are shown in section 5 and finally, section six makes a conclusion.

Proceedings of the 7th International Conference on Informatics and Applied Mathematics IAM'24 , December 4-5, 2024, GUELMA,ALGERIA. ⋆ You can use this document as the template for preparing your publication. We recommend using the latest version of the ceurart style.

al.boukehila@lagh-univ.dz (A. Boukehila); fatimazohrabouakrif@gmail.com (F. Z. Bouakrif); Talebnr@hotmail.fr (N. Taleb)

Fundamental Concepts

Fuzzy Expert System

One basic method that arises immediately from the nature of fuzzy logic is the merging of fuzzy logic and expert systems. Right present, fuzzy expert systems are the most widely used application of fuzzy logic, with numerous implementations running in a wide range of fields [6]. A professor at the University of California, Berkeley named Lotfi Zadeh first proposed the idea of fuzzy in 1970 [7].Numerous industries employ fuzzy expert systems. A few instances are software quality assessment [8], agricultural [9], [10], security systems [11], [12], and medical [13], [14]. In a fuzzy expert system, the rules often take the following form:

If A is low and B is high then X = medium.

Where A and B are input variables, X is an output variable. Here low, high, and medium are fuzzy sets de fined on A, B, and X respectively.

Emergence in complex systems

There have been enormous efforts to define the meaning of emergence. Originating in philosophy [5], emergence has gained popularity within the study of complex systems and Multi-agent systems. The study of emergence has several potential for understanding the interactions of agents and their environments [15]. We use fromm's [1] categorization in this study. He presents a taxonomy that categories four forms of emergence based on distinct sorts of feedback and causation.Addressing security vulnerabilities is crucial to ensure trust and reliability in IoV systems, which also impacts overall efficiency, as discussed next.

The Boids model

Reynolds [9] showed that algorithmically implementing the three rules of alignment, cohesion and separation leads to flocking behavior while an individual only needs local knowledge about its surrounding neighbors (called Boids). These rules are :

• Cohesion : this is the force which makes boids move close to the other boids in their neighbourhoods. • Alignment: this is the force which makes boids move in the same direction as the otheir boids in their neighbourhoods. • Separation: This is the force which makes boids avoid collision with the other boids in their neighbourhoods. The emergence behavior in the Boid model is the presence of an unexpected grouping packing behaviour , this behaviour is often observed in this model, This is the reason why the boid model is one of the most used ABS model to study weak emergence.

Related Work

Agent-based simulation (ABS) specifically used compared to other simulation techniques. Emergence as a result from simulation, is normally investigated with (ABS) tools. Structures with massive wide variety of parts frequently display emergence, and through ABS simulating platforms, it is common to visualize and to control the rise of unexpected behaviour. Variety of emergence definitions exists, however to facilitate the study, we simulated the technique primarily based on bedau's [2] week emergence definition, a weak emergence can be verified via simulation, it is expected and may be controlled in certain systems. For Example, in boids model, the simulation of the flocking is controlled by three rules : separation, cohesion, and alignment. Applying those regulations will result in a grouping behaviour (emergent). Professionals can with a few parameters modifications, accelerate the rise of the flocking or, eliminate it. Many techniques have been used to track emergence. [16] defined emergent behavior as a time-series changing point and proposed the use of changing point detection techniques for the discovery of emergent behavior. [13] employed interaction statistics as a metric to examine the emergence of emergent behavior from agent-based simulation(abs). [14] introduced a method for semantically validating emergence using an ontology-based framework. The method measured the semantic differences between element attribute values using a semantic state distance metric. A summary of metric-based approaches for analyzing vision-based car behavior is provided by [17], [18], [4], [19] which employ interaction metrics to identify and categorize emergence in real-time simulations, and [3] which employed age metrics to identify and categorize emergence through swarms of unmanned aerial vehicles (UAVs). We discuss our work in the next part to address the constraints stated by [20], who presented a statistical metric to find emergence and demonstrated how data loss affects communication in contested situations.

Proposed Approach

we analyse the boids model, which captures the motion of bird flocking and is a seminal example for studying emergence. We model this system as a multi-agent system in which each bird is an agent. In this section, we present the multi-agent simulation framework (Figure 1) that consists of two components, agent-based simulation engine and expert system engine. These two components communicate with each other to implement their functionality. The main functionality of the simulation engine during the simulation is to retrieve data which will be passed to the expert system to detect new system state which can be unknown (Emergent behaviour).

The simulation engine

We use Reynolds's Boids model [21] with multi-agent system for the simulation, Netlogo [20]simulation plat-form is used. The purpose of this simulation engine is:

1.

Step 1: Running the system in several ''normal"situations when interaction=separation.

2.

Step 2: In every situation ,gathering and formalizing the simulation data.

3. Rerun step1 and step2 but with emergent situations.

The fuzzy expert system

The designed fuzzy expert system for identifying emergent behavior consists of four parts.The parts have been defuzzed.The information derived from the fuzzy rules generated was inferred using the Mamdani fuzzy inference approach, which was utilized in this work. Numerous computer languages can be used to create a fuzzy expert system. This system is implemented using MATLAB as a tool.

The Knowledge-Base

The fuzzy knowledge base contains fuzzy facts and rules so that the knowledge base systems will allow approximate reasoning. For easily performing knowledge representation and reasoning, all rules in the knowledge base are presented as a set of if <antecedent clauses> then <consequent clauses> rules.

Fuzzification

Convert values to fuzzy inputs by using membership functions [22]. In this research, there are three linguistic variables (input variables) used, namely:Alignment(A), separation(S),cohesion(C) and one output variable : Emergent behavior (EB). Fuzzy linguistic values of input/output variables are set as [Low, medium, high]. we use the triangular shape has been selected due to its simplcity. Triangular Membership Function:

Triangular(𝑥, 𝑎, 𝑏, 𝑐) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ 0, 𝑥 < 𝑎 𝑥−𝑎 𝑏−𝑎 , 𝑎 ≤ 𝑥 ≤ 𝑏 𝑐−𝑥 𝑐−𝑏 , 𝑏 ≤ 𝑥 ≤ 𝑐 0, 𝑥 > 𝑐

The next step in the fuzzification process is the development of fuzzy rules.

Inference engine

The inference process is the mathematical operation used to determine the certainty degree of the emergent behaviour being in each of the three levels considered .Mamdani [23] is a well-known fuzzy logic method,fuzzy Mamdani is frequently used to create systems with reasoning that resembles human intuition.

Defuzzification

After the inference process, the overall result is a fuzzy certainty value measuring the emergent behaviour in each of the three levels (Low,Medium,High). This result must be defuzzied to obtain a final crisp output.the commonly used defuzzification method is known as centroid.it finds a point representing the center of gravity(COG)of the aggregated fuzzy set.

First Result

Our initial experiments for emergence identification are presented in this section. This is the Boids model, or ABS model. As stated in section 4, we intend to take the following three actions. Initially, the simulation should be run using only the "Separation" interaction. The intention is to stop a packing behavior from developing. This is referred to as "normal behavior." In every iteration, we retrieve interaction data from the simulation. In Figure 3 we have several grouping behaviours, in this case, we run the simulation with all Boids rules. We retrieve the simulation data into an excel file using a Netlogo Spreadsheet extension. In order to combine these fuzzy sets, which reflect the outputs of rules into a single fuzzy set for decision-making, the Mamdani method is implemented after each If-Then rule generates a changed fuzzy set as output. Defuzzification is the final stage of the fuzzy expert system, whereby the merged fuzzy set produces a single scalar number for emergent behavior detection.

Conclusion

In recent years, the significance of emerging has increased.Emergence can happen in a range of systems and be either positive or negative. As a result, we need a system that offers a consistent technique for evaluating and controlling such actions. In this paper, the usage of expert systems in conjunction with ABS data was examined. We suggest a technique to identify flocking behavior in multi-agent systems using a fuzzy expert system in order to solve this problem. The rules database is currently being tested and expanded. We hope to evaluate our method with more sophisticated models on more ABS systems, as the initial results are promising.