Ph.D. Tezi Görüntüleme | |||||||||||||||||||||
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| Summary: The main aim of this thesis is to investigate properties of t-partial order, denoted by ≼_T, defined on a bounded lattice L, to define on the set of all incomparable elements with arbitrary but fixed c∈[0,1] according to ≼_T for any t-norm T on [0,1] to study on this set and to construct a t-norm T such that ([0,1],≼_T ) is a lattice. This study consists of two main chapters. In Chapter 1, some definitions and theorems which are crucial for our study are stated. Chapter 2 contains four parts. In the first part, it is defined that the notions order-strong and order-weak for t-norms on a bounded lattice L and it is determined the order-weakest and the order strongest t-norms. In the second part, it is defined that an equivalence relation β on the class of t-norms on [0,1] and it is investigated properties of this relation. In the third part, it is defined the set of all incomparable elements with arbitrary but fixed c∈[0,1] according to ≼_T, denoted by 〖I_T〗^((c) ), and this set is determined for some particular t-norms. In the last part, it is constructed a family (T_λ )_(λ∈(0,1) ) of t-norms on [0,1] with the help of any t-norm T on [0,1]. Also, if T is a divisible t-norm, then it is shown that ([0,1],≼_(T_λ ) ) is a complete lattice. So, it is shown that there exists a t-norm T_λ which is different from T_W such that (L,≼_(T_λ ) ) is a lattice for L=[0,1] whence an answer is given to the open problem in [35]. Also, it is shown that if T is non-divisible t-norm, then (L,≼_(T_λ ) ) need not to be a lattice.
Key Words: Bounded lattice, T-Norm, T-partial order | |||||||||||||||||||||