Feasible strategies for conflict resolution within intuitionistic fuzzy preference-based conflict situations

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.

💡 Research Summary

The paper addresses a fundamental limitation of existing three‑way conflict analysis models that rely solely on three qualitative relations—preference, converse, and indifference—to represent agents’ attitudes toward issue pairs. Such binary or ternary representations cannot capture the nuanced uncertainty and hesitation often present in real‑world preferences. To overcome this, the authors introduce an intuitionistic fuzzy preference‑based conflict situation (IFP‑S). In this framework each agent’s attitude toward a pair of issues (i, j) is expressed by an intuitionistic fuzzy number (µₐ(i,j), νₐ(i,j)), where µ denotes the degree of preference, ν the degree of non‑preference, and the residual πₐ(i,j)=1‑µ‑ν represents hesitation. The symmetry condition µₐ(i,j)=νₐ(j,i) and zero diagonal entries ensure logical consistency.

Two conflict measurement functions are defined. The first, C_{ij}(a,b), evaluates conflict on a specific issue pair by assigning three numeric values (δ₌, δ≈, δ≍) to the cases of agreement, partial agreement, and disagreement, respectively, based on the interaction of the µ and ν values of the two agents. The second, C_I(a,b), aggregates these pairwise conflicts across the entire issue set, weighting the cardinalities of the intersections of preference, non‑preference, and indifference relations by the corresponding δ values. A max‑min normalization maps C_I into the unit interval, with analytically derived minimum and maximum bounds.

Threshold determination is handled via a decision‑theoretic loss function. By minimizing expected loss, two thresholds ζ* (separating alliance from neutrality) and ζ** (separating neutrality from conflict) are computed automatically. These thresholds partition the agent‑pair space into three crisp relations: alliance (R=), neutrality (R≈), and conflict (R≍).

The core contribution lies in the construction of feasible adjustment strategies that simultaneously consider (1) the magnitude of adjustment required for an agent’s intuitionistic fuzzy preference (Δₐ(i,j)), measured as a distance (e.g., L₁ or L₂) between current and target preference values, and (2) the current conflict degree (C_{ij} or C_I). The problem is cast as a multi‑objective optimization: minimize adjustment cost while reducing conflict. The authors propose a Pareto‑front based algorithm that (i) computes Δ and conflict for all agent‑issue pairs, (ii) extracts Pareto‑optimal candidates, (iii) applies adjustments sequentially, and (iv) iteratively updates conflict measures until a satisfactory configuration is reached.

An illustrative case study models the Middle‑East conflict with six agents (Israel, Egypt, Palestine, Jordan, Syria, Saudi Arabia) and five political‑military issues. Intuitionistic fuzzy preference matrices are constructed from expert judgments. Applying the proposed conflict functions yields a finer trisection of agent pairs compared with traditional three‑valued models. The adjustment algorithm identifies minimal changes (e.g., increasing µ by 0.03 for a specific issue pair) that shift a pair from the conflict region to the alliance region, thereby demonstrating the practical utility of the approach.

Overall, the paper makes three major contributions: (1) a high‑resolution intuitionistic fuzzy representation of preferences, (2) a rigorous conflict quantification and thresholding mechanism grounded in decision theory, and (3) a concrete, algorithmic framework for feasible conflict resolution that balances adjustment effort against conflict reduction. The methodology is both theoretically sound and practically applicable, offering a valuable tool for multi‑stakeholder, multi‑issue decision environments. Future work is suggested on dynamic preference evolution and scalable algorithms for large‑scale networks.