Browsing by Author "KHENICHE, Azzedine"

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    Compatibility of fuzzy relations
    (Université de M'sila, 2016-01-19) KHENICHE, Azzedine
    : The first aim of the present thesis is to strip the compatibility property of its originating context of fuzzy equivalence relations, since only the notion of compatibility of a fuzzy relation with respect to a fuzzy equality (equivalence) was introduced in the early years. Indeed, we have generalized this compatibility property to arbitrary fuzzy relations; this property is dissected here into left and right compatibility and studied in detail in the context of arbitrary fuzzy relations. Relying on the notions of left and right traces of a fuzzy relation, the main findings of the first part of the thesis is that the left and right compatibility can be expressed in terms of inclusions, which facilitates their understanding. On the other hand, we have shown that although there exists no non-trivial (fuzzy) tolerance relation a partial order relation is compatible with, the situation is quite different when considering its strict part. Indeed, We provide a characterization of all fuzzy tolerance (and, in particular, fuzzy equivalence) relations a strict order relation is left compatible, right compatible and compatible with, by using the notion of the clone relation associated with a partially ordered set introduced here and discuss its basic propertiesDate
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    Compatibility of fuzzy relations
    (Université de M'sila, 2016) KHENICHE, Azzedine
    This thesis is an output of several years of research that was started at the university of m’sila with collaboration of the KERMIT laboratory of Gent university in Belgium. Since that time I have worked with many people whose support and cooperation in various and different ways contributed to the great success of my thesis. It is a pleasure to convey my gratitude to all my humble gratitude. I am highly indebted to my supervisors Prof. dr. Bernard De Baets, Prof. dr. Abdelaziz Amroune, who taught and supervised me during these years of research. Bernard and L. Zedam, it is a great honor to work with you. Without any doubt, your efforts were putting me on the right path. I will never forget your guidance and the help you gave me even during weekends, holidays and all other opportunities. I sincerely thank the chairman of the jury committee, Prof.A. Boudaoud and the jury members, prof. N-s Touafak, Prof.L. Naoui, Prof.L. Zedam and our guest Prof.D. Mihoubi. I would like to express my gratitude to all my colleagues in Msila university who have helped me during my study. I would like to express my gratitude to all my colleagues in Guelma university who have helped me during my study, especially Pr. C. Ghiat, Dr. T. Ben chikh, Pr. MAATALLAH Kheireddine, M. A. bouchemella. I would like to express my gratitude to my colleague and friend Dr. Kolli Elhadj in Guelma university. I wish also to express my appreciation to my colleagues at BIOMATH of Gent university in Belgium for the friendly atmosphere, especially Tarad jowaid, Hamchou and my friend of my box Jose Garcia (Mexico). I also wish to send my sincere gratitude to the M.S.E.R.S who supported me to pursue my stay and traineeship in Belgium for 18 months to finalize this thesis. I am very grateful to my mother ‘Zouina’ and my father ‘Ibrahim’. Their prayers, passionate encouragements and generosities have followed me everywhere to give me a lot of power. My deepest gratitude goes to my sister and my brothers. Specific gratitude goes to my brother ‘Nabil’ who passed away during my stay in Belgium, God have mercy on them. I wish to send my best regards to my wife’s family especially mother and father-in-low. I wish all of you a prosperous life full of happiness and health. My lovely wife ‘Zedjiga’ you were the main supporter of me along my entire PhD thesis. I am deeply grateful for your patience and sacrifices. I hope I can compensate you with all my love for all the moments which I spent far away from you