Fuzzy AHP (Triangular and Spherical)

[Neeraj Kaushik]

Dear Friends,

Are you a user of MCDM techniques? If so, then at some stage of your learning, you must have encountered the Fuzzy variants of MCDM techniques.

Fuzzy set theory provides a framework to represent and process imprecise information. By allowing elements to have partial membership in sets, fuzzy logic enables a more nuanced and realistic modeling of human thought and linguistic expressions, such as "slightly important" or "moderately preferred." This approach becomes crucial when decision-makers face situations where clear-cut data is unavailable or when the criteria themselves are subjective and difficult to quantify precisely. Employing fuzzy numbers allows for the capture of this inherent vagueness, leading to more robust and reflective decision outcomes.

In the realm of Multi-Criteria Decision Making (MCDM) techniques, the integration of fuzzy logic significantly enhances their capability to handle complex problems. MCDM methods are designed to evaluate multiple conflicting criteria to arrive at an optimal decision. When these criteria involve qualitative assessments or human perceptions, traditional MCDM techniques can fall short. Fuzzy MCDM methods, such as Fuzzy AHP, address this by incorporating fuzzy numbers into the evaluation process.

I've explained the concept and working of Fuzzy Numbers (in the context of Fuzzy AHP). I've demonstrated the application of Triangular Fuzzy Numbers (TFNs) and Spherical Fuzzy Numbers (SFNs) within the AHP framework. TFNs are a common choice for representing fuzzy values due to their simplicity and ease of computation, effectively capturing the lower, most probable, and upper bounds of an uncertain value. 

SFNs, a more recent development, offer an even greater degree of flexibility by allowing decision-makers to express their opinions not only on membership but also on non-membership and hesitancy. This additional dimension makes SFNs particularly powerful in situations with high uncertainty or divided opinions. It provides a richer representation of decision-makers' preferences and their confidence levels. 

Read about SFN from the base paper A novel spherical fuzzy analytic hierarchy process and its renewable energy application

Fuzzy Set Introduction: https://youtu.be/WJA4YxeGElo

Happy Learning

Neeraj

[Neeraj Kaushik]

Dear Friends,

Building on our previous discussion about Fuzzy AHP, I've created a new video specifically detailing the practical application and calculation of Triangular Fuzzy Numbers (TFNs). 

TFNs are fundamental to fuzzy MCDM techniques, providing a straightforward yet powerful way to quantify imprecise linguistic assessments. In this video, I walk through the step-by-step process of how TFNs are constructed and utilized within the AHP framework, demonstrating their role in converting subjective human judgments into a measurable format. This approach is invaluable for tackling decision-making scenarios where exact numerical data is scarce, and expert opinions need to be accurately integrated.

AHP Triangular Fuzzy Weight Calculations: https://youtu.be/6SmHi0CHZgc

Happy Learning

Neeraj

[Neeraj Kaushik]

Dear Friends,

Building on our discussions about Fuzzy AHP, let's continue our discussion on the practical application and calculation of Spherical Fuzzy Numbers (SFNs) within the AHP framework. SFNs offer enhanced flexibility by allowing decision-makers to express not only membership but also non-membership and hesitancy, making them particularly powerful in situations with high uncertainty. 

I've explained all this in a video that provides a step-by-step guide on constructing and utilizing SFNs, converting subjective judgments into a measurable format for more robust decision outcomes.

AHP Spherical  Fuzzy Weight Calculations: https://youtu.be/SV2e90x0YpA

Happy learning

Neeraj

[John Kevin Padro]

Hi Dr. Neeraj,

Can you elaborate in calculating consistency ratio (CR), refer to this picture the value for CR is  0.057. I try to solve on my own, however I didn't get it.

Hoping for your positive response

[Neeraj Kaushik]

Dear John

Thanks for reminding me the missing link in the previous email regarding the consistency ratio calculation.

I've explained the same in this video:

Consistency Ratio (CR) in AHP: https://youtu.be/tWu3CCUQxHk 

Happy Learning 

Neeraj

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[John Kevin Padro]

Hello I have some questions with this one

Do you have a reference that the given score index are 8, 6, 4, and 2, then the spherical fuzzy set are (0.85, 0.15, 0.05), (0.75, 0.25, 0.15), (0.65, 0.35, 0.25), and (0.55, 0.45, 0.35), respectively?