MCDM and Fuzzy Logic!

Multi-Criteria Decision Making technique: A potential technique indeed!

Multi-Criteria Decision Making (MCDM) technique is a mathematical approach used to make decisions in complex and uncertain environments where multiple criteria need to be considered. It is a process of selecting the best option among multiple alternatives, each having different strengths and weaknesses across a set of criteria.

MCDM techniques involve the use of mathematical models, algorithms, and decision-making tools to analyze and compare different options against a set of criteria. There are a large number of Multi-Criteria Decision Making (MCDM) techniques that can be integrated for selecting an entity. Here are 30 commonly used MCDM techniques:

1. Analytic Hierarchy Process (AHP): AHP is a widely used MCDM technique that allows decision-makers to evaluate alternatives by breaking down complex decision problems into simpler, hierarchical structures. The AHP method uses pairwise comparisons of criteria and alternatives to determine the relative importance of each criterion and alternative.
2. Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS): TOPSIS is another popular MCDM technique that helps decision-makers to identify the best alternative by comparing each alternative to an ideal solution and a worst solution. The ideal solution represents the best possible values for each criterion, while the worst solution represents the worst possible values.
3. Elimination and Choice Expressing Reality (ELECTRE): ELECTRE is a family of MCDM techniques that evaluates alternatives based on a set of criteria by constructing outranking relations between alternatives. It compares each alternative to a set of decision rules and identifies those that are the best compromise between criteria.
4. Simple Additive Weighting (SAW): SAW is a basic MCDM technique that assigns weights to criteria based on their relative importance and calculates a score for each alternative based on the weighted sum of its performance on each criterion.
5. Technique for Order Preference by Similarity to Reference Solution (TOPSIS-R): TOPSIS-R is a variant of TOPSIS that uses reference solutions instead of ideal and anti-ideal solutions to determine the relative distance and ranking of the alternatives.
6. Multi-Attribute Utility Theory (MAUT): MAUT is a method that models the preferences of decision-makers as a utility function and then evaluates the alternatives based on their expected utility.
7. Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE): PROMETHEE is a method that evaluates the alternatives based on their relative performance and assigns them to different preference classes using a pair-wise comparison approach.
8. Grey Relational Analysis (GRA): GRA is a method that compares the alternatives based on their proximity to a reference alternative and assigns them a relative ranking.
9. Complex Proportional Assessment (COPRAS): COPRAS is a method that evaluates the alternatives based on their relative performance and assigns them to different preference classes using a weighted sum approach.
10. Analytic Network Process (ANP): ANP is a method that models the interdependencies among the criteria and evaluates the alternatives based on their performance in the network.
11. Fuzzy Analytic Hierarchy Process (FAHP): FAHP is a variant of the Analytical Hierarchy Process (AHP) that uses fuzzy sets to represent the subjective judgments of decision-makers. It allows decision-makers to express their preferences in linguistic terms and provides a flexible and intuitive way to model complex decision problems.
12. Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS): FTOPSIS is a variant of the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) that uses fuzzy sets to handle uncertainty and imprecision in the decision-making process. It allows decision-makers to express their preferences in linguistic terms and provides a more realistic and practical approach to decision-making.
13. Fuzzy Preference Ranking Organization Method for Enrichment Evaluations (FPROMETHEE): FPROMETHEE is a variant of the Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) that uses fuzzy sets to handle imprecision and uncertainty in the decision-making process. It allows decision-makers to express their preferences in linguistic terms and provides a more natural and intuitive way to model complex decision problems.
14. Fuzzy Simple Additive Weighting (FSAW): FSAW is a variant of the Simple Additive Weighting (SAW) method that uses fuzzy sets to represent the criteria weights and the performance values of the alternatives. It allows decision-makers to handle uncertainty and imprecision in the decision-making process and provides a more realistic and practical approach to decision-making.
15. Fuzzy Elimination and Choice Expressing Reality (FE ELECTRE): FE ELECTRE is a variant of the Elimination and Choice Expressing Reality (ELECTRE) method that uses fuzzy sets to handle imprecision and uncertainty in the decision-making process. It allows decision-makers to express their preferences in linguistic terms and provides a more natural and intuitive way to model complex decision problems.
16. Technique for Order of Preference by Similarity to Ideal Solution based on Interval Type-2 Fuzzy Sets (IT2TS-TOPSIS): This is a Multi-Criteria Decision Making (MCDM) technique that combines the concepts of interval type-2 fuzzy sets and TOPSIS method. This technique is used to evaluate the alternatives based on a set of criteria.?The IT2TS-TOPSIS method deals with uncertainty in the decision-making process by using interval type-2 fuzzy sets to represent the criteria weights and the performance scores of alternatives. In contrast to the traditional fuzzy sets, interval type-2 fuzzy sets have two levels of uncertainty, which provide more flexibility and better represent the real-world decision-making situations.
17. VIKOR (Vise Kriterijumska Optimizacija I Kompromisno Resenje) Method: It is used to evaluate the alternatives based on multiple criteria. The VIKOR method was developed by Yugoslav researchers, Brans and Mareschal in the early 1980s. VIKOR method is used to determine the ranking of the alternatives based on the compromise solution. It considers two conflicting criteria of maximizing the best and minimizing the worst performance measures. It is a compromise ranking method that takes into account the compromise between the ideal and the worst solutions, and it aims to identify the solution that is closest to the ideal solution and farthest from the worst solution.
18. Technique for Order Preference by Similarity to Ideal Solution based on Atanassov's Intuitionistic Fuzzy Sets (IF-TOPSIS): Used to evaluate the alternatives based on multiple criteria. The IF-TOPSIS method uses Atanassov's intuitionistic fuzzy sets to deal with the uncertainty and vagueness in the decision-making process. The IF-TOPSIS method is an extension of the traditional TOPSIS method, which is used to determine the best alternative based on the distance from the ideal solution and the distance from the negative ideal solution. The IF-TOPSIS method also considers the degree of hesitation in the decision-making process by introducing the concept of intuitionistic fuzzy sets.
19. DEMATEL (Decision-Making Trial and Evaluation Laboratory): A technique used to analyze the cause-and-effect relationships among the criteria and to identify the key factors that influence the decision-making process. The DEMATEL method was developed in the 1970s by the Japanese researcher, Prof. K. Y. Yoon. The DEMATEL method is used to model the complex decision-making problems that involve multiple criteria and interdependent relationships among them. It involves constructing a directed graph that represents the cause-and-effect relationships among the criteria and identifying the critical factors that have a significant impact on the decision-making process.
20. Fuzzy Analytic Hierarchy Process with Grey Relational Analysis (GAFAHP): The GAFAHP method is used to deal with the imprecise and uncertain information in the decision-making process by combining the fuzzy logic and AHP method. The method uses fuzzy set theory to handle the imprecise judgments and uncertainties of decision-makers in the AHP process. Moreover, it employs the GRA method to overcome the inconsistency of pairwise comparison matrices in the AHP process.
21. Grey Decision Making Trial and Evaluation Laboratory (GDEMATEL): Used to analyze the cause-and-effect relationships among the criteria and to identify the key factors that influence the decision-making process. It is an extension of the traditional DEMATEL method, which was developed in the 1970s by the Japanese researcher, Prof. K. Y. Yoon. The GDEMATEL method is used to model the complex decision-making problems that involve multiple criteria and interdependent relationships among them. It involves constructing a directed graph that represents the cause-and-effect relationships among the criteria and identifying the critical factors that have a significant impact on the decision-making process. The GDEMATEL method uses grey numbers to represent the imprecise and uncertain information in the decision-making process. The method integrates the grey incidence analysis and the DEMATEL method to evaluate the criteria and identify the key factors that influence the decision-making process.
22. Grey Relational Analysis based on Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS-GRA): The FTOPSIS-GRA method is used to handle the imprecise and uncertain information in the decision-making process by combining the fuzzy logic and TOPSIS method. The method uses fuzzy set theory to handle the imprecise judgments and uncertainties of decision-makers in the TOPSIS process. Moreover, it employs the GRA method to overcome the inconsistency of pairwise comparison matrices in the TOPSIS process.
23. Multiple Criteria Decision Making based on Aggregated Weight (MCDAW): The MCDAW method involves assigning weights to each criterion and aggregating the weighted criteria scores for each alternative. The method uses a simple additive weighting method to calculate the overall score of each alternative.
24. Multiple Objective Decision Making based on Best Worst Method (MOWO-BWM): The MOWO-BWM method is used to determine the best and worst alternatives for each objective and then rank the alternatives based on their overall performance. The MOWO-BWM method involves assigning scores to each alternative for each objective based on their best and worst performance. The method uses the BWM technique to determine the best and worst alternatives for each objective and then aggregates the scores to rank the alternatives.
25. Multi-Criteria Decision Making based on Probabilistic Linguistic Term Sets (P-LTS): The P-LTS method is used to handle the uncertainty and imprecision in the decision-making process by using probabilistic linguistic information. The P-LTS method involves assigning probabilistic linguistic terms to each criterion and then calculating the probability distribution function for each alternative. The method uses the expected utility theory to calculate the expected value of each alternative and then ranks the alternatives based on their expected values.
26. Grey Relational Analysis based on Multiple Criteria Decision Making (GRAMCDM): The GRAMCDM method is used to handle the uncertainty and imprecision in the decision-making process by using GRA to compare the alternatives. The GRAMCDM method involves determining the performance of each alternative for each criterion, constructing the decision matrix, and then using GRA to compare the alternatives. The method uses the grey relational coefficient to calculate the similarity between the alternatives and the ideal alternative for each criterion.
27. Interactive Decision Maps (IDM): Used to evaluate alternatives based on multiple criteria using graphical representations. The IDM method is used to facilitate communication and understanding between decision-makers by using visual aids. The IDM method involves constructing a graphical representation of the decision problem by mapping the criteria and alternatives onto a two-dimensional plane. The method uses interactive software to allow decision-makers to manipulate the graphical representation and explore the trade-offs between the criteria and alternatives.
28. Rough Set Theory (RST): It is a mathematical framework used for data analysis and decision-making under uncertainty. The RST method is used to identify patterns in data and make decisions based on these patterns. The RST method is used in Multi-Criteria Decision Making (MCDM) to handle uncertainty and imprecision in the decision-making process. The RST method involves defining the decision problem as a set of objects and a set of criteria. The RST method uses mathematical operations to determine the rough set approximation of the objects and criteria. The rough set approximation is a set of lower and upper approximations that represent the set of objects and criteria that satisfy a given condition.
29. Multi-Objective Optimization on the Basis of Ratio Analysis (MOORA): Used to evaluate alternatives based on multiple criteria. The MOORA method is used to select the best alternative from a set of alternatives by using ratio analysis. The MOORA method involves calculating the ratios of the performance of each alternative for each criterion to the corresponding best or worst performance. The ratios are then aggregated using weighted sums or weighted products to obtain the overall ranking of the alternatives.
30. Multi-Criteria Decision Making based on Fuzzy TOPSIS and Fuzzy VIKOR: This is a hybrid approach that combines two popular MCDM techniques, namely, Fuzzy TOPSIS and Fuzzy VIKOR. The method is used to evaluate alternatives based on multiple criteria, where the criteria are expressed in linguistic terms or fuzzy numbers.

These techniques can be combined and integrated to provide a more comprehensive and robust decision-making process. The choice of techniques depends on the specific decision problem, the number of criteria, and the availability of data. MCDM techniques are used in various fields such as business, engineering, healthcare, environmental studies, and social sciences. They can be applied to a wide range of decision-making problems, such as selecting the best location for a new facility, choosing the most cost-effective solution for a project, or identifying the best investment opportunities.

Overall, MCDM techniques provide a structured and systematic approach for decision-making, helping decision-makers to consider multiple criteria and trade-offs when choosing between different options.

Fuzzy Logic and its usage in MCDM techniquesBottom of Form

Fuzzy logic is a mathematical approach used in MCDM (Multi-Criteria Decision Making) technique to handle uncertainty and imprecision in decision-making. Fuzzy logic allows decision-makers to express judgments or preferences in linguistic terms rather than precise numerical values, which is often more realistic and practical.

In fuzzy logic, membership functions are used to represent the degree of membership of an element in a fuzzy set, which is a set of values that are not precisely defined but have some degree of membership. The membership function assigns a degree of membership between 0 and 1 to each element based on how well it satisfies the conditions for membership.

Fuzzy logic is important in MCDM technique because it allows decision-makers to handle the vagueness and uncertainty that often arise when evaluating alternatives based on multiple criteria. It provides a flexible and intuitive approach to modeling complex decision problems, allowing decision-makers to express their preferences in a more natural way. For example, in a decision problem involving the selection of a supplier, the decision-makers may have imprecise or uncertain information about the quality, price, and delivery time of the different suppliers. Fuzzy logic can be used to represent these criteria as fuzzy sets and evaluate the alternatives based on their degree of membership in each set.

Overall, fuzzy logic is an important tool in MCDM technique for handling uncertainty and imprecision, providing a more realistic and practical approach to decision-making.

Fuzzy operators and its functions

In fuzzy logic, there are several basic operators that are used to perform fuzzy computations. These operators include:

1. Fuzzy set membership function: This is the most fundamental operator in fuzzy logic. It determines the degree to which an element belongs to a fuzzy set. The membership function maps each element of the universe of discourse to a membership value between 0 and 1.
2. Fuzzy negation: The fuzzy negation operator is used to determine the degree to which an element does not belong to a fuzzy set. It is represented by the word "not" and is often denoted by a "~" symbol.
3. Fuzzy conjunction: Fuzzy conjunction is used to combine two or more fuzzy sets to produce a single fuzzy set. The most commonly used fuzzy conjunction operators are "and", "min", and "product".
4. Fuzzy disjunction: Fuzzy disjunction is used to combine two or more fuzzy sets to produce a single fuzzy set. The most commonly used fuzzy disjunction operators are "or", "max", and "probabilistic sum".
5. Fuzzy implication: Fuzzy implication is used to determine the degree to which one fuzzy set implies another. The most commonly used fuzzy implication operators are "if-then", "Mamdani", and "Sugeno".
6. Fuzzy aggregation: Fuzzy aggregation is used to combine the results of multiple fuzzy rules into a single output. The most commonly used fuzzy aggregation operators are "weighted average", "centroid", and "height".
7. Fuzzy defuzzification: Fuzzy defuzzification is used to convert a fuzzy output into a crisp output. The most commonly used fuzzy defuzzification operators are "centroid", "bisector", and "mean of maxima".

Complex forms of Fuzzy logic

Fuzzy logic is a mathematical framework that deals with uncertainty and imprecision. Some of the complex forms of fuzzy logic include:

1. Type-2 fuzzy logic: Type-2 fuzzy logic is an extension of type-1 fuzzy logic that allows for higher levels of uncertainty and imprecision. In type-2 fuzzy logic, the membership function is also uncertain, and is represented as a fuzzy set of fuzzy sets.
2. Fuzzy decision trees: Fuzzy decision trees are decision-making tools that use fuzzy logic to handle uncertainty and imprecision in decision-making. Fuzzy decision trees allow for multiple paths to be taken based on the degree of uncertainty or imprecision associated with a decision.
3. Fuzzy neural networks: Fuzzy neural networks are a combination of fuzzy logic and artificial neural networks. They are used to model complex systems that exhibit uncertainty and imprecision.
4. Fuzzy clustering: Fuzzy clustering is a technique that uses fuzzy logic to group data points into clusters based on their degree of similarity. Unlike traditional clustering techniques, which assign each data point to a single cluster, fuzzy clustering allows data points to belong to multiple clusters simultaneously.
5. Fuzzy rule-based systems: Fuzzy rule-based systems are decision-making systems that use fuzzy logic to handle uncertainty and imprecision. They consist of a set of fuzzy rules that are used to make decisions based on input variables. Fuzzy rule-based systems can be used in a wide range of applications, such as control systems, expert systems, and decision support systems.

An Example for understanding the concepts

Suppose you are an investment manager and you want to select a stock portfolio based on four criteria: return on investment (ROI), risk, liquidity, and volatility. You have collected data on each stock in your universe of options and assigned fuzzy membership functions to each of the criteria. You have also assigned each stock a score from 0 to 1 based on how well it performs in each of the criteria. For example, a stock with a high ROI score would have a score close to 1, while a stock with a low ROI score would have a score close to 0.

To select the best stock portfolio, you can use a fuzzy MCDM method called Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS). The FTOPSIS method involves the following steps:

1. Normalize the scores for each stock by dividing each score by the sum of all scores for that criterion. This ensures that each criterion is equally weighted.
2. Determine the ideal and anti-ideal solutions for each criterion. The ideal solution is the maximum score for each criterion, while the anti-ideal solution is the minimum score for each criterion.
3. Calculate the distance of each stock to the ideal and anti-ideal solutions using the Euclidean distance formula.
4. Calculate the similarity of each stock to the ideal and anti-ideal solutions using the fuzzy membership functions.
5. Calculate the relative closeness of each stock to the ideal solution using the weighted average of the similarities.
6. Rank the stocks based on their relative closeness to the ideal solution.

Using the above steps, you can calculate the relative closeness of each stock to the ideal solution and rank them accordingly. The one with the highest rank/position is the best/suitable stock for investment.