A new multi attribute decision making method hierarchical fuzzy axiomatic design

A very specific and technical topic!

Hierarchical Fuzzy Axiomatic Design (HFAD) is a multi-attribute decision making (MADM) method that combines the principles of fuzzy set theory and axiomatic design to evaluate and prioritize alternatives based on multiple attributes.

Here's a breakdown of the components:

  1. Hierarchical: The method involves a hierarchical structure, where the decision-making problem is decomposed into smaller sub-problems, and each sub-problem is evaluated separately.
  2. Fuzzy: Fuzzy set theory is used to handle uncertainty and imprecision in the decision-making process. Fuzzy numbers and fuzzy sets are used to represent the attributes and their weights.
  3. Axiomatic Design: Axiomatic design is a design methodology that emphasizes the importance of functional requirements and the decomposition of complex systems into simpler components. In HFAD, the axiomatic design principles are applied to the decision-making process to ensure that the decision is based on a clear understanding of the functional requirements.

The HFAD method involves the following steps:

  1. Problem definition: Define the decision-making problem and identify the attributes that are relevant to the decision.
  2. Hierarchical decomposition: Decompose the decision-making problem into smaller sub-problems, and identify the attributes and their weights for each sub-problem.
  3. Fuzzy attribute evaluation: Evaluate each attribute using fuzzy numbers and fuzzy sets to represent the uncertainty and imprecision in the evaluation process.
  4. Fuzzy weight calculation: Calculate the weights of each attribute using fuzzy numbers and fuzzy sets to represent the uncertainty and imprecision in the weight calculation process.
  5. Hierarchical evaluation: Evaluate each sub-problem using the fuzzy attribute evaluations and fuzzy weights, and aggregate the results to obtain the overall evaluation of each alternative.
  6. Ranking and selection: Rank the alternatives based on their overall evaluations, and select the best alternative.

The advantages of HFAD include:

  1. Handling uncertainty and imprecision: HFAD can handle uncertainty and imprecision in the decision-making process by using fuzzy numbers and fuzzy sets.
  2. Hierarchical decomposition: HFAD allows for hierarchical decomposition of the decision-making problem, which can help to simplify complex decision-making problems.
  3. Axiomatic design principles: HFAD incorporates the axiomatic design principles, which can help to ensure that the decision is based on a clear understanding of the functional requirements.

However, HFAD also has some limitations, including:

  1. Complexity: HFAD is a complex method that requires a good understanding of fuzzy set theory and axiomatic design.
  2. Subjectivity: The evaluation of attributes and weights is subjective and may be influenced by personal biases and preferences.
  3. Computational complexity: HFAD can be computationally intensive, especially for large-scale decision-making problems.

Overall, HFAD is a powerful MADM method that can be used to evaluate and prioritize alternatives based on multiple attributes in complex decision-making problems. However, it requires a good understanding of the underlying principles and techniques, and may not be suitable for all decision-making contexts.