I am trying to use Fuzzy Shannon Entropy and Fuzzy COPRAS for selection of alternative in multi criteria group decision making problem.
(i) There are many variant of fuzzy Extant Fuzzy set, Intuitionistic Fuzzy set IFS), Trapezoid Fuzzy set (IT2FS) etc.
(ii) Very complicated mathematical formulation given in few papers for Fuzzy Entropy calculation.
Can some one suggest me simplest Fuzzy Entropy method similar to deterministic Shannon Entropy method. along with sample calculation with data in excel sheet for my understanding.
An early help will be appreciated !
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Entropy is the compressive procedure of information which results in higher rate of compression and high speed of transmission which compresses the required number of bits depending on the observation of repetitive information/message. Further, the concept of fuzzy entropy is a non-probabilistic measure which replaces the bits in a new framework of fuzzy information theory. An appropriate measure of entropy or fuzziness of messages is shown to be a simple ratio of distances i.e., the distance between the fuzzy message and its nearest and farthest non fuzzy neighbors. Besides, the conditioning of fuzzy is examined as the degree of subset-hood of one fuzzy set or the message in another. This quantity is shown to behave as a conditional probability in many contexts. The procedure of fuzzy Shannon entropy involves the steps:
Step 1: The decision matrix which shows the performance of different alternatives with respect to various criteria is formed.
Step 2: The decision matrix, Beneficial (maximization), and non-beneficial (minimization) criteria are normalized. To have the comparable and dimensionless performance measures, all the entries of the decision matrix are linearly normalized.
Step 3: Entropy values are determined for each criterion.
Step 4: Entropy weights are calculated.
Further, to analyze and enhance the fuzzy Shannon Entropy method for criteria weight determination in MCDM, the range of value (ROV) method can be adapted. The ROV method determines the ranking of the alternatives based on the ordinal specification of criteria importance from a decision maker. Thus, in situations where decision makers are facing problems in supplying quantitative weights, the application of the ROV method calculates the best and worst utility for each alternative.
@ Malek. I am looking for Fuzzy variant of Shannon Entropy method for criteria weight determination in multi criteria decision making in management problem. BTW your paper is different. Thanks
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