Ασαφείς Αρνήσεις , ασαφείς συνεπαγωγές και εφαρμογές

Fuzzy negations , fuzzy implications and applications (Αγγλική)

  1. MSc thesis
  2. ΠΑΝΑΓΙΩΤΗΣ ΜΑΓΓΕΝΑΚΗΣ
  3. Μεταπτυχιακές Σπουδές στα Μαθηματικά (ΜΣΜ)
  4. 14 Μαίου 2023
  5. Ελληνικά
  6. 78
  7. ΠΑΠΑΔΟΠΟΥΛΟΣ ΒΑΣΙΛΕΙΟΣ
  8. ΑΝΟΥΣΗΣ, ΜΙΧΑΗΛ
  9. ασαφείς αρνήσεις , συνεπαγωγές , εφαρμογές, οικονομική οδήγηση, κατασκευή
  10. ΜΣΜ 50
  11. 5
  12. 4

    • Στην προαναφερθήσα διπλωματική εργασία αφού πρώτα παρατέθηκε μία εισαγωγή που αφορούσε την έννοια και κατασκευή των ασαφών συνόλων στη συνέχεια δόθηκαν οι βασικές πράξεις μεταξύ κλασικών και κατ επέκταση ασαφών συνόλων . Μελετήθηκαν εξ ορισμού οι ασαφείς αρνήσεις , αυστηρές και δυνατές . Δόθηκε ένας τρόπος-θεώρημα κατασκευής δυνατών αρνήσεων με χρήση 1-1 και αντιστρέψιμων συναρτήσεων . Πάνω σε αυτή την μέθοδο παρουσιάζεται μία πρωτότυπη κατασκευή μίας οικογένειας ασαφών αρνήσεων με πολύ ενδιαφέρουσες προεκτάσεις. Στην συνέχεια αναλύεται η μελέτη των ασαφών συνεπαγωγών . Αφού δώθούν ο ορισμός και η αξιωματική θεμελίωση των συνεπαγωγών , παρουσιάζεται και πάλι μια πρωτότυπη κατασκευή ασαφούς συνεπαγωγής  βασισμένη στην οικογένεια ασαφών αρνήσεων που προαναφέρθηκε. Τέλος παρουσίαζονται 2 νεοφυή προβλήματα που αφορούν την οικονομική οδήγηση. Δίνεται μία συνεπαγωγή που αφορά την σχέση ταχύτητα αυτοκινήτου => κατανάλωση καυσίμου . Με την χρήση της δικής μας συνεπαγωγής κατασκευάζουμε συναρτήσεις συμετοχής με τρόπο που να ευνοείται η αλλαγή των σχέσεων ταχυτήτων στο χρονικό σημείο - στιγμιαία ταχύτητα όταν η κατανάλωση βρίσκεται στο ολικό ελάχιστο της .  

    • In the aforementioned thesis after first an introduction concerning the concept and construction of fuzzy sets was given, then the basic operations between classical and by extension fuzzy sets were given. Fuzzy negations, strict and possible, were studied by definition. A method-theorem for the construction of possible negations using 1-1 and invertible functions was given. On this method an original construction of a family of fuzzy negations with very interesting implications is presented. Then the study of fuzzy implications is discussed . After giving the definition and the axiomatic foundation of implications , an original construction of fuzzy implication based on the family of fuzzy negations mentioned above is again presented. Finally, 2 novel problems concerning economic driving are presented. An entailment is given concerning the relation : car speed => fuel consumption . Using our own implication we construct membership functions in a way that favors changing the gear ratios at the time point - instantaneous speed when the consumption is at its total minimum .












      In the aforementioned thesis after first an introduction concerning the concept and construction of fuzzy sets was given, then the basic operations between classical and by extension fuzzy sets were given. Fuzzy negations, strict and possible, were studied by definition. A method-theorem for the construction of possible negations using 1-1 and invertible functions was given. On this method an original construction of a family of fuzzy negations with very interesting implications is presented. Then the study of fuzzy implications is discussed . After giving the definition and the axiomatic foundation of implications , an original construction of fuzzy implication based on the family of fuzzy negations mentioned above is again presented. Finally, 2 novel problems concerning economic driving are presented. An entailment is given concerning the relation : car speed => fuel consumption . Using our own implication we construct membership functions in a way that favors changing the gear ratios at the time point - instantaneous speed when the consumption is at its total minimum .












      In the aforementioned thesis after first an introduction concerning the concept and construction of fuzzy sets was given, then the basic operations between classical and by extension fuzzy sets were given. Fuzzy negations, strict and possible, were studied by definition. A method-theorem for the construction of possible negations using 1-1 and invertible functions was given. On this method an original construction of a family of fuzzy negations with very interesting implications is presented. Then the study of fuzzy implications is discussed . After giving the definition and the axiomatic foundation of implications , an original construction of fuzzy implication based on the family of fuzzy negations mentioned above is again presented. Finally, 2 novel problems concerning economic driving are presented. An entailment is given concerning the relation : car speed => fuel consumption . Using our own implication we construct membership functions in a way that favors changing the gear ratios at the time point - instantaneous speed when the consumption is at its total minimum .












      In the aforementioned thesis after first an introduction concerning the concept and construction of fuzzy sets was given, then the basic operations between classical and by extension fuzzy sets were given. Fuzzy negations, strict and possible, were studied by definition. A method-theorem for the construction of possible negations using 1-1 and invertible functions was given. On this method an original construction of a family of fuzzy negations with very interesting implications is presented. Then the study of fuzzy implications is discussed . After giving the definition and the axiomatic foundation of implications , an original construction of fuzzy implication based on the family of fuzzy negations mentioned above is again presented. Finally, 2 novel problems concerning economic driving are presented. An entailment is given concerning the relation : car speed => fuel consumption . Using our own implication we construct membership functions in a way that favors changing the gear ratios at the time point - instantaneous speed when the consumption is at its total minimum .









  14. Hellenic Open University
  15. Αναφορά Δημιουργού 4.0 Διεθνές