💻 computer science

A method of Risk Analysis and threat management using analytic hierarchy process

This paper proposes a real-time risk analysis and threat management framework for modern air defense command and control systems that integrates fuzzy set theory, the Analytic Hierarchy Process (AHP), and TOPSIS to quantify expert opinions and prioritize hostile targets in a simulated, autonomous environment.

Original authors: Manvi Sahni, Sumanta Kumar Das

Published 2026-07-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Manvi Sahni, Sumanta Kumar Das

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are the captain of a spaceship, but instead of steering through calm space, you are flying through a chaotic storm of incoming asteroids, alien drones, and rogue satellites. Your job isn't just to see them; it's to decide which one to blast first before they smash your ship. This is the daily nightmare of modern air defense. In the real world, these "asteroids" are enemy missiles, fighter jets, and drones, and the "ship" is a country's protected airspace. The problem is that there are too many threats moving too fast for a human brain to sort out perfectly. If you shoot at the wrong one, you waste your ammo and leave the real danger free to strike. To solve this, scientists use a branch of math called "decision-making," which is basically a fancy way of organizing a messy list of options to find the best one. Two of the most popular tools for this are the Analytic Hierarchy Process (AHP), which is like a structured game of "this is more important than that," and TOPSIS, which is a method for finding the option that is closest to being perfect and furthest from being terrible. When you mix these with "fuzzy logic"—a way of handling vague ideas like "very fast" or "highly dangerous" instead of just strict numbers—you get a super-smart computer brain that can help commanders make split-second life-or-death choices.

This paper by Manvi Sahni and Sumanta Kumar Das is about building that super-smart brain for air defense. The authors wanted to create a system that could automatically look at a bunch of incoming enemies, figure out which one is the scariest, and tell the defense system to focus on that one first. They didn't just guess; they built a mathematical model that acts like a digital referee. Imagine a referee who has to rank ten different players in a game. Instead of just looking at who is running the fastest, the referee looks at speed, how close they are to the goal, how big they are, and whether they look like they are trying to score or just distract. The authors used a method called AHP to decide which of these factors matters most. For example, they asked experts to compare "Range" (how far away the enemy is) against "Speed" (how fast they are coming). The experts decided that "Lethality" (how deadly the weapon is) and "Intent" (what the enemy is trying to do) were the heavy hitters, while things like "Angle of Attack" were also important but slightly less so.

Once the referee decided what to look for, the authors needed a way to actually rank the enemies. This is where the "fuzzy" part comes in. Real life isn't black and white; a missile isn't just "fast" or "slow," it's somewhere in between. The system uses fuzzy logic to translate these squishy, human-like descriptions into hard numbers. Then, they used a technique called TOPSIS to do the final sorting. Think of TOPSIS as a game of "closest to the ideal." The system creates a "Perfect Enemy" (the one you absolutely must stop right now) and a "Worst Enemy" (the one you can ignore). It then measures every single incoming target to see which one is closest to the "Perfect Enemy" and furthest from the "Worst Enemy." The one that wins this race gets the highest priority.

The authors tested this idea in a computer simulation, not on a real battlefield. They created a fake war zone, 200 km by 200 km wide, filled with different types of bad guys: fast fighter jets, slow bombers, groups of missiles, and even electronic jamming planes. They let their new computer system run the show without any humans touching the controls. The results were interesting. The system correctly figured out that a group of fast fighters coming from very close range was a bigger emergency than a slow missile that was still far away. It also realized that a bomber trying to drop bombs was more dangerous than a spy plane just looking around, even if the spy plane was closer. In one specific test, a tactical ballistic missile was ranked as the number one threat, beating out everything else because it was fast, lethal, and had a dangerous trajectory.

However, the authors are careful to say that this is a simulation, not a magic shield that has been tested in a real war. They admit that their current model only looks at "hard" threats like missiles and bombs. They didn't include "soft" tricks like decoys, chaff (those little strips of foil planes drop to confuse radar), or jamming that tries to blind the sensors. They also didn't test what happens if two different defense systems try to talk to each other to share the workload. So, while the paper suggests that this mix of AHP, fuzzy logic, and TOPSIS is a very promising and easy-to-use way to manage threats in real-time, it remains a "half-way" step between theory and the messy reality of a battlefield. It's a strong proof-of-concept that shows computers can be taught to prioritize danger better than a human might when things get chaotic, but there is still more work to be done before it can handle every trick an enemy might pull.

Technical Summary: A Method of Risk Analysis and Threat Management Using Analytic Hierarchy Process: An Application to Air Defense

Problem Statement
Modern air combat operations have been revolutionized by sophisticated offensive capabilities, including electronic attacking (EA) devices, high-speed fighters, unmanned air vehicles (UAVs), and precision missiles. In response, defensive air defense (AD) systems must rely on robust Command and Control (C2) architectures capable of rapid risk analysis and threat management. The core challenge lies in the efficient classification of targets, intent recognition, threat assessment (TA), and weapon allocation (WA) amidst complex, multidisciplinary data. Traditional decision-making loops, such as OODA (Observe-Orient-Decide-Act), require enhancement to handle the speed and complexity of modern threats. This paper addresses the need for a structured, automated method to prioritize hostile targets for AD C2 systems to ensure effective resource allocation and survival against technological advancements.

Methodology
The proposed approach integrates Fuzzy Set Theory, the Analytic Hierarchy Process (AHP), and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) into a two-step decision-making framework. The system is modeled as a single-participant Multiple Attribute Decision Making (MADM) problem.

Hierarchy Construction (AHP): The decision-making process is structured into a hierarchy with the goal of "Risk Analysis and Threat Management" at the top.
- Criteria: Six specific target attributes are defined as criteria: Range (C1), Speed (C2), Altitude (C3), Lethality (C4), Intent (C5), and Angle of Attack (AoA) (C6).
- Alternatives: Nine distinct target types serve as alternatives, including fighters, bombers, groups of fighters/bombers, electronic attack aircraft, AWACS, tactical ballistic missiles, cruise missiles, and "other" targets.
- Weighting: Pair-wise comparisons are conducted among the six criteria (15 judgments) and among the nine alternatives for each criterion. Weights are derived using the geometric mean technique. Consistency is verified via the Consistency Index (CI), with values reported around 0.07–0.09.
Fuzzy Inference System (FIS): To handle the subjectivity of expert opinions and the imprecision of real-world data, a Mamdani-type Fuzzy Inference System is employed.
- Inputs/Outputs: Input variables (Range, Velocity, Altitude, AoA, Lethality, Intent) and the output (Threat) are defined using trapezoidal and semi-trapezoidal membership functions.
- Rules: A rule base is established based on intuitive and expert considerations (e.g., a "Close" range with "Fast" velocity and "High" lethality results in a "High" threat).
- Defuzzification: The weighted average method is used to generate a crisp decision matrix.
Prioritization (TOPSIS): The decision matrix generated by the FIS is processed through TOPSIS to rank the threats.
- The method calculates the distance of each alternative from the Positive Ideal Solution (PIS) and the Negative Ideal Solution (NIS).
- A relative closeness coefficient ( $G_i$ ) is computed for each target.
- Targets are prioritized based on this coefficient, where a higher value indicates a higher threat level requiring immediate engagement.

Key Contributions

Hybrid Modeling: The paper presents a novel integration of AHP for structuring the decision hierarchy and weighting criteria, Fuzzy Set Theory for quantifying subjective expert knowledge and handling uncertainty, and TOPSIS for the final ranking and prioritization of threats.
Automated C2 Simulation: The model is implemented in a simulated environment that operates without human intervention, representing a state-of-the-art approach for automated C2 systems.
Comprehensive Attribute Analysis: The study explicitly models six critical threat attributes simultaneously, moving beyond simple kinematic data to include intent and lethality.

Results
The system was tested in a simulated air combat scenario (200 km × 200 km) involving a mixed offensive force (fighters, bombers, missiles, UAVs, AWACS) and a defensive force equipped with various Surface-to-Air Missiles (SAMs) and an AHP-based C2 system.

Prioritization Logic: The simulation results demonstrate that the system correctly prioritizes threats based on a combination of factors. For instance:
- Fast-moving, highly lethal targets (e.g., a group of A-10 Thunderbolts at 2.5 Mach) within close range (100 km) received the highest priority.
- Slower, distant targets (e.g., Tomahawk missiles beyond 200 km) received lower priority.
- Targets with "Strike" intent were prioritized over those with "Surveillance" or "Electronic Attack" intent, even if the latter were lethal.
- Low-altitude, high-angle-of-attack targets were deemed more dangerous than high-altitude, low-angle targets.
Validation: The results obtained from the TOPSIS-FIS model were compared against a separate set of testing data and found to perform satisfactorily. The system successfully ranked Tactical Ballistic Missiles as the highest priority (Rank 1) and AWACS as the lowest (Rank 9) in the specific test case, reflecting the immediate physical threat posed by ballistic trajectories.

Significance and Claims
The authors claim that this method is particularly useful for futuristic risk and threat management in battlefield environments. The significance of the work lies in its practical applicability:

Real-Time Capability: The method is described as easy to implement and suitable for real-time applications, addressing the speed requirements of modern air defense.
Decision Support: It provides a structured, mathematical basis for C2 decision-making, reducing reliance on purely intuitive human judgment in high-stress environments.
Scalability: The model serves as a foundational step for developing intelligent systems that can handle complex, multidisciplinary threat assessments.

Limitations
The paper acknowledges that the current model does not include "soft kill" or non-lethal options such as decoys, chaffs, relocation of forces, or jamming strategies. Furthermore, the study is limited to a single C2 system; future work is proposed to investigate how multiple C2 systems might negotiate resource utilization.

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