{"id":{"repo_id":"greece","oai_identifier":"oai:10442/1419"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/1419","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΜΙΑ ΜΠΟΥΛΙΑΝΗ ΓΕΝΙΚΕΥΣΗ ΤΗΣ ΑΠΕΙΡΟΣΤΙΚΗΣ ΑΝΑΛΥΣΗΣ ΜΕ ΕΦΑΡΜΟΓΕΣ ΣΤΑ ΑΣΑΦΗ ΣΥΝΟΛΑ","abstract":"IT IS WELL KNOWN THAT NON STANDARD ANALYSIS IS BASED ON A TRIVIAL 0-1 PROBABILITY SPACE (IN, P(IN), MK). IN THIS THESIS WE GENERALIZE IT TO A GENERAL PROBABILITY SPACE (Ω, Α, Ρ), THAT LOADS US TO THE BOOLEAN ANALYSIS. INTERNAL-EXTERNAL SETS, MOSTOWSKI'S COLLAPSING TRANSFER PRINCIPLE AND OTHER NOTIONS OF NON STANDARD ANALYSIS ARE ALSO GENERALIZED. WE USE THE THEORY OF BOOLEAN POWERS AND FINALLY WE GET A BOOLEAN- VALUED MODEL OF THE REALS (IR#), THAT IS ISOMORPHIC TO THE ELEMENTARY STOCHASTIC SPACE E OF KAPPOS. FINALLY, APPLICATIONS OF OUR MODEL TO FUZZY SETS (QUALITATIVE OR B-FUZZY SETS) ARE GIVEN.","abstract_html":"IT IS WELL KNOWN THAT NON STANDARD ANALYSIS IS BASED ON A TRIVIAL 0-1 PROBABILITY SPACE (IN, P(IN), MK). IN THIS THESIS WE GENERALIZE IT TO A GENERAL PROBABILITY SPACE (Ω, Α, Ρ), THAT LOADS US TO THE BOOLEAN ANALYSIS. INTERNAL-EXTERNAL SETS, MOSTOWSKI'S COLLAPSING TRANSFER PRINCIPLE AND OTHER NOTIONS OF NON STANDARD ANALYSIS ARE ALSO GENERALIZED. WE USE THE THEORY OF BOOLEAN POWERS AND FINALLY WE GET A BOOLEAN- VALUED MODEL OF THE REALS (IR#), THAT IS ISOMORPHIC TO THE ELEMENTARY STOCHASTIC SPACE E OF KAPPOS. FINALLY, APPLICATIONS OF OUR MODEL TO FUZZY SETS (QUALITATIVE OR B-FUZZY SETS) ARE GIVEN.","abstract_has_math":false,"creators":["Μαρκάκης, Γεώργιος"],"institution":"University of Patras","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1990,"date_issued":"1990","date_published":"1990","updated_at":"2026-07-24T02:24:56Z","subjects":["ΑΛΓΕΒΡΑ BOOLE","Ασαφή σύνολα","Θεωρία μοντέλων","ΜΗ ΣΥΜΒΑΤΙΚΗ ΑΝΑΛΥΣΗ","ΜΠΟΥΛΙΑΝΑ ΜΟΝΤΕΛΑ","ΜΠΟΥΛΙΑΝΕΣ ΔΥΝΑΜΕΙΣ","ΠΟΙΟΤΙΚΗ ΠΙΘΑΝΟΘΕΩΡΙΑ","ΣΤΟΧΑΣΤΙΚΟΙ ΧΩΡΟΙ","ΤΥΧΑΙΑ ΜΑΤΑΒΛΗΤΗ","Υπερδομές","BOOLEAN ALGEBRA","BOOLEAN POWERS","BOOLEAN-VALUED MODELS","Fuzzy sets","Model theory","NON STANDARD ANALYSIS","QUALITATIVE PROBABILITY THEORY","Random variables","STOCHASTIC SPACES","Superstructures","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1419"],"render_values":[{"text":"10.12681/eadd/1419","href":"https://doi.org/10.12681/eadd/1419","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/1419","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Μαρκάκης, Γεώργιος"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1990"]},{"key":"dc:publisher","label":"Institution","values":["University of Patras","Πανεπιστήμιο Πατρών"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ΑΛΓΕΒΡΑ BOOLE","Ασαφή σύνολα","Θεωρία μοντέλων","ΜΗ ΣΥΜΒΑΤΙΚΗ ΑΝΑΛΥΣΗ","ΜΠΟΥΛΙΑΝΑ ΜΟΝΤΕΛΑ","ΜΠΟΥΛΙΑΝΕΣ ΔΥΝΑΜΕΙΣ","ΠΟΙΟΤΙΚΗ ΠΙΘΑΝΟΘΕΩΡΙΑ","ΣΤΟΧΑΣΤΙΚΟΙ ΧΩΡΟΙ","ΤΥΧΑΙΑ ΜΑΤΑΒΛΗΤΗ","Υπερδομές","BOOLEAN ALGEBRA","BOOLEAN POWERS","BOOLEAN-VALUED MODELS","Fuzzy sets","Model theory","NON STANDARD ANALYSIS","QUALITATIVE PROBABILITY THEORY","Random variables","STOCHASTIC SPACES","Superstructures","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1419","http://hdl.handle.net/10442/hedi/1419"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["IT IS WELL KNOWN THAT NON STANDARD ANALYSIS IS BASED ON A TRIVIAL 0-1 PROBABILITY SPACE (IN, P(IN), MK). IN THIS THESIS WE GENERALIZE IT TO A GENERAL PROBABILITY SPACE (Ω, Α, Ρ), THAT LOADS US TO THE BOOLEAN ANALYSIS. INTERNAL-EXTERNAL SETS, MOSTOWSKI'S COLLAPSING TRANSFER PRINCIPLE AND OTHER NOTIONS OF NON STANDARD ANALYSIS ARE ALSO GENERALIZED. WE USE THE THEORY OF BOOLEAN POWERS AND FINALLY WE GET A BOOLEAN- VALUED MODEL OF THE REALS (IR#), THAT IS ISOMORPHIC TO THE ELEMENTARY STOCHASTIC SPACE E OF KAPPOS. FINALLY, APPLICATIONS OF OUR MODEL TO FUZZY SETS (QUALITATIVE OR B-FUZZY SETS) ARE GIVEN.","ΕΙΝΑΙ ΓΝΩΣΤΟ ΟΤΙ Η ΜΗ-ΣΥΜΒΑΤΙΚΗ ΑΝΑΛΥΣΗ ΜΠΟΡΕΙ ΝΑ ΒΑΣΙΣΤΕΙ ΣΕ ΕΝΑΝ ΤΕΤΡΙΜΕΝΟ 0-1 ΠΙΘΑΝΟΘΕΩΡΗΤΙΚΟ ΧΩΡΟ (ΙΝ, Π(ΙΝ)Ρ, ΜΚ). ΣΤΗ ΔΙΑΤΡΙΒΗ ΑΥΤΗ ΓΙΝΕΤΑΙ Η ΓΕΝΙΚΕΥΣΗ ΤΗΣ ΣΕ ΕΝΑΝ ΤΥΧΟΝΤΑ ΠΙΘΑΝΟΘΕΩΡΗΤΙΚΟ ΧΩΡΟ, (Ω, Α, Ρ) Η ΟΠΟΙΑ ΟΔΗΓΕΙ ΣΤΗΝ ΜΠΟΥΛΙΑΝΗ ΑΝΑΛΥΣΗ. ΓΕΝΙΚΕΥΟΝΤΑΙ ΑΝΤΙΣΤΟΙΧΕΣ ΕΝΟΟΙΕΣ ΤΗΣ ΜΗ ΣΥΜΒΑΤΙΚΗΣ ΑΝΑΛΥΣΗΣ, ΔΗΛ. ΕΣΩΤΕΡΙΚΑ-ΕΞΩΤΕΡΙΚΑ ΣΥΝΟΛΑ, ΣΥΝΑΡΤΗΣΗ ΣΥΝΘΛΙΨΗΣ ΤΟΥ MOSTOWSKI, ΑΡΧΗ ΜΕΤΑΦΟΡΑΣ. ΗΓΕΝΙΚΕΥΣΗ ΓΙΝΕΤΑΙ ΜΕ ΤΗ ΧΡΗΣΗ ΤΩΝ ΜΠΟΥΛΙΑΝΩΝ ΔΥΝΑΜΕΩΝ ΚΑΙ ΟΔΗΓΕΙ ΤΕΛΙΚΑ ΣΕ ΕΝΑΜΠΟΥΛΙΑΝΟ ΜΟΝΤΕΛΟ ΠΡΑΓΜΑΤΙΚΩΝ ΑΡΙΘΜΩΝ (IR#) ΠΟΥ ΕΙΝΑΙ ΙΣΟΜΟΡΦΟ ΜΕ ΤΟΝ ΣΤΟΙΧΕΙΩΔΗ ΣΤΟΧΑΣΤΙΚΟ ΧΩΡΟ Ε ΤΟΥ ΚΑΠΠΟΥ. ΤΕΛΟΣ ΔΙΝΟΝΤΑΙ ΕΦΑΡΜΟΓΕΣ ΤΟΥ ΜΟΝΤΕΛΟΥ ΑΥΤΟΥ ΣΤΑ ΑΣΑΦΗ ΣΥΝΟΛΑ (ΠΟΙΟΤΙΚΑ 'Η IB-ΑΣΑΦΗ ΣΥΝΟΛΑ) ."]},{"key":"dc:title","label":"Title","values":["ΜΙΑ ΜΠΟΥΛΙΑΝΗ ΓΕΝΙΚΕΥΣΗ ΤΗΣ ΑΠΕΙΡΟΣΤΙΚΗΣ ΑΝΑΛΥΣΗΣ ΜΕ ΕΦΑΡΜΟΓΕΣ ΣΤΑ ΑΣΑΦΗ ΣΥΝΟΛΑ","A BOOLEAN GENERALIZATION OF NON STANDARD ANALYSIS WITH APPLICATIONS TO FUZZY SETS"]}]}],"canonical_facts":{"dc:creator":["Μαρκάκης, Γεώργιος"],"dc:date":["1990"],"dc:description":["IT IS WELL KNOWN THAT NON STANDARD ANALYSIS IS BASED ON A TRIVIAL 0-1 PROBABILITY SPACE (IN, P(IN), MK). IN THIS THESIS WE GENERALIZE IT TO A GENERAL PROBABILITY SPACE (Ω, Α, Ρ), THAT LOADS US TO THE BOOLEAN ANALYSIS. INTERNAL-EXTERNAL SETS, MOSTOWSKI'S COLLAPSING TRANSFER PRINCIPLE AND OTHER NOTIONS OF NON STANDARD ANALYSIS ARE ALSO GENERALIZED. WE USE THE THEORY OF BOOLEAN POWERS AND FINALLY WE GET A BOOLEAN- VALUED MODEL OF THE REALS (IR#), THAT IS ISOMORPHIC TO THE ELEMENTARY STOCHASTIC SPACE E OF KAPPOS. FINALLY, APPLICATIONS OF OUR MODEL TO FUZZY SETS (QUALITATIVE OR B-FUZZY SETS) ARE GIVEN.","ΕΙΝΑΙ ΓΝΩΣΤΟ ΟΤΙ Η ΜΗ-ΣΥΜΒΑΤΙΚΗ ΑΝΑΛΥΣΗ ΜΠΟΡΕΙ ΝΑ ΒΑΣΙΣΤΕΙ ΣΕ ΕΝΑΝ ΤΕΤΡΙΜΕΝΟ 0-1 ΠΙΘΑΝΟΘΕΩΡΗΤΙΚΟ ΧΩΡΟ (ΙΝ, Π(ΙΝ)Ρ, ΜΚ). ΣΤΗ ΔΙΑΤΡΙΒΗ ΑΥΤΗ ΓΙΝΕΤΑΙ Η ΓΕΝΙΚΕΥΣΗ ΤΗΣ ΣΕ ΕΝΑΝ ΤΥΧΟΝΤΑ ΠΙΘΑΝΟΘΕΩΡΗΤΙΚΟ ΧΩΡΟ, (Ω, Α, Ρ) Η ΟΠΟΙΑ ΟΔΗΓΕΙ ΣΤΗΝ ΜΠΟΥΛΙΑΝΗ ΑΝΑΛΥΣΗ. ΓΕΝΙΚΕΥΟΝΤΑΙ ΑΝΤΙΣΤΟΙΧΕΣ ΕΝΟΟΙΕΣ ΤΗΣ ΜΗ ΣΥΜΒΑΤΙΚΗΣ ΑΝΑΛΥΣΗΣ, ΔΗΛ. ΕΣΩΤΕΡΙΚΑ-ΕΞΩΤΕΡΙΚΑ ΣΥΝΟΛΑ, ΣΥΝΑΡΤΗΣΗ ΣΥΝΘΛΙΨΗΣ ΤΟΥ MOSTOWSKI, ΑΡΧΗ ΜΕΤΑΦΟΡΑΣ. ΗΓΕΝΙΚΕΥΣΗ ΓΙΝΕΤΑΙ ΜΕ ΤΗ ΧΡΗΣΗ ΤΩΝ ΜΠΟΥΛΙΑΝΩΝ ΔΥΝΑΜΕΩΝ ΚΑΙ ΟΔΗΓΕΙ ΤΕΛΙΚΑ ΣΕ ΕΝΑΜΠΟΥΛΙΑΝΟ ΜΟΝΤΕΛΟ ΠΡΑΓΜΑΤΙΚΩΝ ΑΡΙΘΜΩΝ (IR#) ΠΟΥ ΕΙΝΑΙ ΙΣΟΜΟΡΦΟ ΜΕ ΤΟΝ ΣΤΟΙΧΕΙΩΔΗ ΣΤΟΧΑΣΤΙΚΟ ΧΩΡΟ Ε ΤΟΥ ΚΑΠΠΟΥ. ΤΕΛΟΣ ΔΙΝΟΝΤΑΙ ΕΦΑΡΜΟΓΕΣ ΤΟΥ ΜΟΝΤΕΛΟΥ ΑΥΤΟΥ ΣΤΑ ΑΣΑΦΗ ΣΥΝΟΛΑ (ΠΟΙΟΤΙΚΑ 'Η IB-ΑΣΑΦΗ ΣΥΝΟΛΑ) ."],"dc:identifier":["10.12681/eadd/1419","http://hdl.handle.net/10442/hedi/1419"],"dc:language":["gre"],"dc:publisher":["University of Patras","Πανεπιστήμιο Πατρών"],"dc:subject":["ΑΛΓΕΒΡΑ BOOLE","Ασαφή σύνολα","Θεωρία μοντέλων","ΜΗ ΣΥΜΒΑΤΙΚΗ ΑΝΑΛΥΣΗ","ΜΠΟΥΛΙΑΝΑ ΜΟΝΤΕΛΑ","ΜΠΟΥΛΙΑΝΕΣ ΔΥΝΑΜΕΙΣ","ΠΟΙΟΤΙΚΗ ΠΙΘΑΝΟΘΕΩΡΙΑ","ΣΤΟΧΑΣΤΙΚΟΙ ΧΩΡΟΙ","ΤΥΧΑΙΑ ΜΑΤΑΒΛΗΤΗ","Υπερδομές","BOOLEAN ALGEBRA","BOOLEAN POWERS","BOOLEAN-VALUED MODELS","Fuzzy sets","Model theory","NON STANDARD ANALYSIS","QUALITATIVE PROBABILITY THEORY","Random variables","STOCHASTIC SPACES","Superstructures","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"dc:title":["ΜΙΑ ΜΠΟΥΛΙΑΝΗ ΓΕΝΙΚΕΥΣΗ ΤΗΣ ΑΠΕΙΡΟΣΤΙΚΗΣ ΑΝΑΛΥΣΗΣ ΜΕ ΕΦΑΡΜΟΓΕΣ ΣΤΑ ΑΣΑΦΗ ΣΥΝΟΛΑ","A BOOLEAN GENERALIZATION OF NON STANDARD ANALYSIS WITH APPLICATIONS TO FUZZY SETS"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:24:56Z"}