Title
THE MATHEMATICS OF FUZZINESS: MYTHS AND REALITIES: Value of fuzzy membership and fuzzy membership function are different things ,Used
Delivery time: 8-12 business days (International)
Two things we are aiming to discuss. First, it has been accepted that intersection of a fuzzy set and its complement is not the void set. Similarly it has also been accepted that the union of a fuzzy set and its complement is not the universal set.Accordingly, the fuzzy sets have been accepted not to form a field. However, can the intersection of anything, a fuzzy set or whatever else, and its complement be nonnull? Secondly, when it was seen that the fuzzy sets do not allow the additivity postulate for a measure to hold, a new definition of fuzzy measure was formalized. Can it not be so that possibility can be expressed in terms of something that is measure theoretic? Here in this monograph, we are going to show that the fuzzy sets do form a field. For that, we need to extend the definition of fuzziness just to define the complement of a fuzzy set. We are further going to establish that not one but two probability spaces are necessary and sufficient to define a possibility space. Hence in terms of two probability measures, possibility can be studied. We assure the readers that what we are proposing is absolutely mathematical. There is nothing fuzzy about it.
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Shipping & Returns
Shipping
We ship your order within 2–3 business days for USA deliveries and 5–8 business days for international shipments. Once your package has been dispatched from our warehouse, you'll receive an email confirmation with a tracking number, allowing you to track the status of your delivery.
Returns
To facilitate a smooth return process, a Return Authorization (RA) Number is required for all returns. Returns without a valid RA number will be declined and may incur additional fees. You can request an RA number within 15 days of the original delivery date. For more details, please refer to our Return & Refund Policy page.
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Warranty
We provide a 2-year limited warranty, from the date of purchase for all our products.
If you believe you have received a defective product, or are experiencing any problems with your product, please contact us.
This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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Your payment information is processed securely. We do not store credit card details nor have access to your credit card information.
We accept payments with :
Visa, MasterCard, American Express, Paypal, Shopify Payments, Shop Pay and more.