Ph.D. Tezi Görüntüleme | |||||||||||||||||||||
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| Summary: The main aim of present thesis is to give the characterization of uninorms on bounded lattices and investigate the properties of idempotent uninorms that is obtained in reaction to this characterization. This thesis consists of two chapters. In the first chapter, by making a general study of literature about the equivalence and order relations, lattices, triangular norms and triangular conorms, it is mentioned some main results obtained concerning uninorms on the unit interval [0,1], the lattice L^I, the lattice L^* and the bounded lattice L.The second chapter consists of four sections. In the first section, it is given two methods to construct a uninorm on a bounded lattice L with the neutral element e∈L{0,1} and as a by-product these methods, the smallest and the greatest idempotent uninorms on L with the neutral element e are obtained. In the second section, for the bounded lattice L, e∈L{0,1} and a=U(0,1)∥e, it is shown that there does not always exist a uninorm on L with neutral element e. In the third section, it is extended locally internal concept given on unit interval [0,1] to bounded lattices and by showing an idempotent uninorm on every bounded lattice need not be locally internal, it is given a sufficient condition to an idempotent uninorm on L be locally internal. In the last section, it is given a method for constructing idempotent uninorms on a bounded lattice L by means of a decreasing function under some assumptions on L. Key Words: Uninorm, Idempotent uninorm, T-norm, T-conorm, Bounded lattice. | |||||||||||||||||||||