Limited Rationality and Its Quantification Through the Interval Number Judgments With Permutations.

Area of Science:

• Operations Research
• Decision Science
• Fuzzy Mathematics

Background:

• Traditional Analytic Hierarchy Process (AHP) assumes full rationality, which is often unrealistic.
• Decision-makers (DMs) experience uncertainty when comparing alternatives, leading to limited rationality.
• Fuzzy AHP uses fuzzy numbers, but interval numbers better capture subjective uncertainty in comparisons.

Purpose of the Study:

• To investigate limited rationality in decision-making using interval numbers within the AHP framework.
• To propose new consistency concepts and methods for interval multiplicative reciprocal comparison matrices.
• To develop a novel algorithm for solving decision-making problems with interval preference relations.

Main Methods:

• Introduction of interval multiplicative reciprocal comparison matrices to model DM uncertainty.
• Analysis of matrix consistency and proposal of approximation-consistency and acceptable approximation-consistency.
• Development of a novel method for determining interval weight vectors and a new decision-making algorithm.

Main Results:

• Interval number judgments in multiplicative matrices are inherently inconsistent.
• Proposed approximation-consistency concepts provide a framework for handling inconsistent interval judgments.
• A new algorithm effectively determines interval weights and solves decision problems with interval preferences.

Conclusions:

• The proposed methods successfully address the uncertainty and limited rationality in decision-making.
• The novel approach provides a more realistic way to handle subjective comparisons in AHP.
• The developed algorithm offers a practical tool for complex decision problems involving interval data.