💻 computer science

A data-driven classifier integrating symmetric intuitionistic fuzzy TOPSIS with self-interactive sequential three-way decision

This paper proposes a data-driven, loss-function-free binary classifier that integrates symmetric intuitionistic fuzzy TOPSIS with self-interactive sequential three-way decision to overcome existing limitations by utilizing objective attribute weights, balanced distance measurements, and an internal feedback loop for adaptive thresholding, thereby enhancing classification performance and robustness.

Original authors: Yangyang Guo, Wenyan Xu, Qiang Chen

Published 2026-07-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yangyang Guo, Wenyan Xu, Qiang Chen

Original paper licensed under CC BY 4.0 (https://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 a hiring manager trying to decide who to hire from a pile of resumes. You have a list of candidates (the data) and a list of skills to check (the attributes). Your goal is to sort them into three piles: Hire, Don't Hire, and "I'm not sure, let's look closer."

This paper introduces a new, smarter way to do this sorting, called SIF-TOPSIS-S3WD. It combines three powerful ideas to make the decision process more fair, balanced, and resistant to messy data. Here is how it works, broken down into simple steps:

1. The Problem with Old Methods

Traditional methods often have three big flaws:

Subjective Weights: The person doing the hiring might guess which skills are most important (e.g., "I think coding is 50% more important than teamwork"). This is biased.
One-Sided Scoring: They might focus too much on "good" traits and ignore "bad" traits, or vice versa, leading to an unbalanced view.
The "Snowball" Effect: Some methods try to solve the "unsure" candidates by adding more questions one by one. If you get the first few answers wrong, those mistakes pile up, making the final decision worse.

2. The New Solution: A Three-Stage Process

The authors propose a system that fixes these issues using three main stages:

Stage 1: Let the Data Decide the Importance (Objective Weights)

Instead of a human guessing which skills matter most, the system uses a mathematical tool called Shannon Entropy (think of it as a "chaos meter").

The Analogy: Imagine you are judging a cooking contest. If every contestant uses salt exactly the same way, salt isn't a good way to tell them apart. But if some use a lot and some use none, salt becomes a very important factor.
How it works: The system looks at the data. If a skill varies wildly between candidates, the system gives it a high weight (it matters a lot). If everyone is the same on a skill, the system gives it a low weight (it doesn't help distinguish them). This removes human bias.

Stage 2: The Perfect Balance (Symmetric Intuitionistic Fuzzy TOPSIS)

Once the weights are set, the system needs to score the candidates. It uses a method called TOPSIS, which is like finding the "Perfect Candidate" and the "Worst Candidate" in the room.

The Analogy: Imagine a scale. On one side is the "Ideal Hero" (perfect skills, no flaws). On the other is the "Ideal Villain" (worst skills, maximum flaws).
The Innovation: Most old methods only look at how close you are to the Hero. This new method looks at both sides equally. It asks: "How close are you to the Hero, AND how far are you from the Villain?"
The Result: It calculates a "Relative Closeness" score. This ensures that being slightly flawed doesn't get you penalized unfairly, and being slightly good doesn't get you an unearned pass. It treats "good" and "bad" evidence symmetrically.

Stage 3: The Self-Correcting Loop (Self-Interactive Sequential Three-Way Decision)

Now, the system has a score for everyone. But what do you do with the people in the middle?

The Old Way: Traditional methods might add more questions (attributes) to the "unsure" group. If you ask a bad question, you might misclassify someone, and that mistake gets carried forward to the next round.
The New Way: This system uses a Self-Interactive Loop.
- It takes the "unsure" group and asks: "What is the best way to split this specific group right now?"
- It doesn't add new questions. Instead, it adjusts the thresholds (the passing grade) dynamically based on the current group's scores.
- It creates a feedback loop: It tries different passing grades, sees which one creates the fairest split, and locks that in.
- The Benefit: Because it doesn't keep adding new questions (which can introduce errors), it avoids the "snowball effect" of misclassifications. It refines the decision using the same information, just looking at it through a smarter lens each time.

3. Did It Work? (The Results)

The authors tested this new "Hiring Manager" on nine real-world datasets (like medical data for breast cancer or diabetes).

Performance: It performed very well, often beating standard methods like Random Forests or basic TOPSIS. It was particularly good at finding the "positive" cases (high Recall), meaning it rarely missed a candidate who should have been hired.
Robustness: They tested what happens if the data is "dirty" (noisy, missing values, or outliers). Even when the data was corrupted, this new method stayed stable and didn't crash, whereas older methods struggled more.

Summary

In short, this paper builds a classifier that:

Doesn't guess which features are important (it calculates it).
Balances good and bad evidence equally (no bias).
Refines decisions by adjusting the rules for the "unsure" group, rather than adding more potentially confusing questions.

The result is a decision-making tool that is fairer, more accurate, and tougher against messy data.

Technical Summary: A Data-Driven Classifier Integrating Symmetric Intuitionistic Fuzzy TOPSIS with Self-Interactive Sequential Three-Way Decision

Problem Statement
Binary classification tasks often face challenges related to uncertainty, hesitation, and overlapping class boundaries. While existing methods like logistic regression and support vector machines are effective, they may struggle with complex forms of uncertainty. Fuzzy sets and sequential three-way decisions (S3WD) offer theoretical extensions to handle these issues. However, current approaches suffer from specific limitations:

Subjectivity and Bias: Intuitionistic Fuzzy TOPSIS (IF-TOPSIS) methods often rely on subjective attribute weights or asymmetric closeness formulas that introduce directional bias.
Misclassification Accumulation: Traditional S3WD models typically resolve ambiguous instances by progressively increasing the attribute set. This can lead to low decision accuracy at early stages and the accumulation of misclassifications as attributes are added.
Threshold Dependence: Existing S3WD models heavily rely on loss functions to determine thresholds, which are either manually set or computationally expensive to derive.
Lack of Integration: There is insufficient exploration of integrating objective attribute weighting with the trisecting process in TOPSIS-based classification settings.

Methodology
The paper proposes a unified, data-driven framework called SIF-TOPSIS-S3WD, which integrates symmetric intuitionistic fuzzy TOPSIS with a self-interactive sequential three-way decision mechanism. The methodology proceeds in three distinct stages:

Objective Weight Determination:
Instead of manual weighting, the authors employ an improved Shannon entropy-based method within an intuitionistic fuzzy environment. This approach calculates elementary information measures ( $E_{ij}$ ) based on membership, non-membership, and hesitation degrees. These measures are normalized to compute entropy values, which are then used to derive objective attribute weights. The weights are embedded into the decision matrix using an Atanassov-type power operation, which strengthens high-weight attributes and suppresses low-weight ones while preserving the intuitionistic fuzzy structure.
Symmetric Intuitionistic Fuzzy TOPSIS:
The framework computes a symmetric relative closeness degree for each object. Unlike traditional TOPSIS, this method:
- Identifies Positive Ideal Solutions (PIS) and Negative Ideal Solutions (NIS) dynamically based on net effectiveness scores ( $\mu' - \nu'$ ) rather than predefined attribute types.
- Uses a max-type symmetric metric to calculate distances to PIS and NIS. This metric treats deviations in membership and non-membership degrees equally, eliminating directional bias.
- Calculates a relative closeness degree ( $T_i$ ) that reflects both attraction to the positive ideal and repulsion from the negative ideal.
Self-Interactive Sequential Three-Way Decision (S3WD):
Rather than expanding the attribute set, the classifier operates on a fixed set of attributes. It transforms the continuous relative closeness degrees into hierarchical classification decisions (Positive, Negative, and Boundary regions) through an internal feedback loop:
- Threshold Traversal: A finite grid of candidate threshold pairs $(\alpha, \beta)$ is generated based on the number of objects in the current boundary region.
- Probability Assessment: For each object, probability assessment functions ( $h_1, h_2, h_3$ ) are derived from the relative closeness degree to estimate the likelihood of belonging to the positive, negative, or boundary regions.
- Optimal Trisection: A trisection-evaluation measure ( $H$ ) quantifies the quality of different threshold combinations. The algorithm iteratively selects the threshold pair that maximizes $H$ , creating an adaptive, loss-function-free decision process.
- Termination: The process repeats on the remaining boundary objects until convergence or until no unique optimal trisection can be determined, inherently avoiding misclassification accumulation associated with progressive attribute expansion.

Key Contributions
The paper identifies three primary contributions:

Objective Weighting: An enhanced intuitionistic fuzzy Shannon entropy approach is introduced to determine attribute weights objectively by incorporating hesitation information, reducing the subjective bias common in conventional IF-TOPSIS models.
Symmetric Evaluation: A symmetric relative closeness degree based on a max-type distance is proposed. This imposes balanced penalization on deviations in membership and non-membership information, improving geometric consistency.
Loss-Function-Free S3WD: A new sequential three-way decision framework is constructed that relies on relative closeness degrees and an internal self-interactive mechanism. It generates hierarchical decisions with adaptive dynamic thresholds on a fixed attribute set, naturally avoiding the risk of misclassification accumulation found in traditional S3WD settings.

Experimental Results
The proposed classifier was evaluated on nine binary classification datasets from the UCI Machine Learning Repository (e.g., Wdbc, Breast, Glioma, German).

Performance: The method achieved competitive results, particularly in terms of Recall and F1-score. It obtained the best or tied-best results on several datasets (Breast, Glioma, German, Statlog) and demonstrated the highest average recall among compared methods. While Naive Bayes showed higher average accuracy in some metrics, SIF-TOPSIS-S3WD provided a favorable balance between precision and recall.
Robustness: Under mixed feature perturbations (Gaussian noise, missing values, and outliers) at levels up to 30%, the proposed method maintained stable performance. It consistently ranked among the top three methods across perturbation levels, outperforming traditional TOPSIS variants which were found to be more sensitive to data corruption.
Sensitivity: Sensitivity analysis regarding the hesitation parameter ( $\pi$ ) indicated that the optimal value is dataset-dependent, suggesting the need for data-driven tuning rather than a universal constant.

Significance and Claims
The authors claim that the synergy between symmetric intuitionistic fuzzy representation and sequential three-way decisions provides a robust and interpretable framework for binary classification. The significance of the work lies in:

Shifting from ranking-oriented IF-TOPSIS to a hierarchical classification mechanism.
Providing a loss-function-free alternative to traditional S3WD models that eliminates the need for manual loss function specification.
Mitigating the problem of misclassification accumulation by operating on a fixed attribute set with adaptive thresholds rather than progressive attribute expansion.
Demonstrating that the classifier offers a data-driven, weight-aware approach that is competitive in performance and robustness against data contamination.

The paper concludes modestly, noting that while the method is competitive, it is not uniformly dominant across all datasets and metrics. Future work is suggested to extend the framework to multi-class settings and explore learning-based mechanisms for determining the hesitation degree.