# Artificial Empathy and Imprecise Communication in a Multi-Agent System
## 1 Introduction  
Empathy is a multifaceted concept that plays a critical role in human collaboration, extending beyond verbal messages to include a variety of nonverbal signals and observational cues [1]. It significantly enhances the learning process, acting as a bridge in understanding and relating to others. Empathy is broadly categorized into two types: cognitive and emotional. Cognitive empathy involves a \"crisp\" approach, utilizing facts, logic, and prediction. It is about understanding others' perspectives and thoughts logically. On the other hand, emotional empathy is somewhat more \"chaotic\". It relates to experiencing and sharing the feelings of others, thereby assisting in assigning significance or \"weights\" to the cognitive aspects. This form of empathy is internal and highly subjective [2, 3]. Artificial empathy, as a concept in the realm of intelligent systems, seeks to replicate these empathetic processes in machines or software agents. It involves designing algorithms and models that enable these systems to understand and respond to the emotional and cognitive states of humans or other agents [4, 5, 6]. This capability is particularly crucial in settings where understanding and reacting to complex, dynamic human behaviors and interactions are essential. Communication disturbances, often resulting in discrepancies between the intended and received message, can blur the representation of another agent's knowledge. Thesedisturbances can be seen as layers of uncertainty accumulating at each stage of communication. This uncertainty becomes particularly significant in scenarios characterized by rapidly changing situations and actions. However, uncertainty is not merely a challenge, it is also an asset, particularly in learning and adapting to unknown situations or environments. In an effective swarm, or a group of cooperating agents, learning new behaviors is a continuous process [7,8]. By implementing a form of artificial empathy, cooperating agents can operate without the need for external supervision or predefined communication rules. They learn these rules organically by comparing incoming signals to their existing knowledge states. This approach minimizes the need for extensive initial knowledge. Communication in such a system may not be ideal, but it allows agents to learn and adapt more rapidly and effectively, fostering a more resilient and responsive collaborative environment. The swarming agent has to decide what action to take, in order to get itself in the preferred state in the future. In order to state this preference, the agent has to make a prediction about the uncertain future. It has to decide, based on present, imprecise knowledge, what will be its future state if it continues an egoistic action, or helps an agent (empathetic action) and what state will the agent be in the future. All those future states are not only uncertain but also prone to imprecision. The criteria for the agent are not crisply stated--they differ depending on the states. The criterion for decision making is based on the similarity to known states, with the similarity being \"significantly high\" (0.9 out of 1 in the conducted research). The very idea is not to state strict decision criteria explicitly. The chosen criteria define the state. They are dependent on a particular platform and environment (e.g., for a UAV, this will include wind, humidity, visibility, etc.). The particular values can be modeled as fuzzy numbers in order to extend the possible means of state description into a more descriptive and subjective form of natural language (e.g., the UAV is high above the ground). A more detailed, mathematical description is given further in this work. The mathematical aspects of this study play a pivotal role in quantifying and modeling the dynamics of artificial empathy and uncertainty within collaborative systems. We have developed a new decision model that represents the states of agents, their decision-making processes, and the nuances of their communication.