[Paper Review] Feasible strategies for conflict resolution within intuitionistic fuzzy preference-based conflict situations

Guangming Lang, Mingchuan Shang+3 more|arXiv (Cornell University)|Feb 3, 2026

Game Theory and Applications0 citations

TL;DR

The paper develops an intuitionistic fuzzy preference-based framework for three-way conflict analysis, defining new conflict measures, trisections, and adjustment-based feasible strategies, and demonstrates them with an illustrative example.

ABSTRACT

In three-way conflict analysis, preference-based conflict situations characterize agents' attitudes towards issues by formally modeling their preferences over pairs of issues. However, existing preference-based conflict models rely exclusively on three qualitative relations, namely, preference, converse, and indifference, to describe agents' attitudes towards issue pairs, which significantly limits their capacity in capturing the essence of conflict. To overcome this limitation, we introduce the concept of an intuitionistic fuzzy preference-based conflict situation that captures agents' attitudes towards issue pairs with finer granularity than that afforded by classical preference-based models. Afterwards, we develop intuitionistic fuzzy preference-based conflict measures within this framework, and construct three-way conflict analysis models for trisecting the set of agent pairs, the agent set, and the issue set. Additionally, relative loss functions built on the proposed conflict functions are employed to calculate thresholds for three-way conflict analysis. Finally, we present adjustment mechanism-based feasible strategies that simultaneously account for both adjustment magnitudes and conflict degrees, together with an algorithm for constructing such feasible strategies, and provide an illustrative example to demonstrate the validity and effectiveness of the proposed model.

Motivation & Objective

• Motivate the need to capture uncertainty and nuance in agents’ attitudes toward issue pairs beyond qualitative relations.
• Introduce intuitionistic fuzzy Preference-Based Conflict Situations (IFPS) to model issue-pair attitudes.
• Define intuitionistic fuzzy conflict measures and trisections for agents, issues, and issue bundles.
• Propose adjustment mechanism-based feasible strategies for conflict resolution and provide an algorithm.
• Demonstrate validity via an illustrative example and discuss threshold-based decisions.

Proposed method

• Define intuitionistic fuzzy preferences for issue pairs with mu and nu components and hesitation pi=1-mu-nu.
• Introduce CF_ij as a distance-based conflict function across agents for an issue pair and prove its properties.
• Aggregate CF_ij to CF_J over issue bundles and define trisections IR_J^{=}, IR_J^{≈}, IR_J^{≺} for agents.
• Define CM measures for an agent with respect to a bundle or the full issue set and partition agents into SA, WA, NA via thresholds.
• Use Bayesian minimum risk theory to determine thresholds for decisions on conflict coalitions.
• Provide an algorithm for constructing feasible strategies that adjust attitudes while considering conflict.

Figure 1 : Changes of strong, weak, and non- conflict agents in each iteration.

Experimental results

Research questions

• RQ1 How can intuitionistic fuzzy preferences better capture nuanced agent attitudes toward issue pairs than classical models?
• RQ2 How to define and interpret conflict measures CF_ij, CF_J, and CM in an intuitionistic fuzzy setting?
• RQ3 How can three-way trisections be formed for agent pairs, agents, and issues under IFPS?
• RQ4 What adjustment strategies balance adjustment magnitudes and conflict degrees to achieve feasible conflict resolution?
• RQ5 Can the proposed framework be validated through illustrative examples (e.g., geopolitical scenarios)?

Key findings

• Introduces intuitionistic fuzzy preference-based conflict settings and corresponding conflict functions with proven properties (non-negativity, symmetry, triangle inequality).
• Defines multi-issue conflict measures CF_J and CM leading to agent and issue tri-sections under specified thresholds.
• Proposes strong/weak/non-conflict coalitions and trisections for both agents and issues, with an algorithmic path to feasible strategies.
• Demonstrates calculations and tables for example scenarios, illustrating how the framework yields nuanced conflict analysis beyond qualitative relations.
• Connects Bayesian minimum risk theory to threshold determination for assigning agents to conflict coalitions within the IFPS framework.

Figure 2 : Changes of strong, weak, and non- conflict issues in each iteration.