We present some model theoretic results for LUKASIEWICZ predicate logic by using the methods of continuous model theory developed by Chang and Keisler. We prove compactness theorem with respect to the class of all structures taking values in the LUKASIEWICZBL-algebra. We also prove some appropriate preservation theorems concerning universal and inductive theories.Finally, Skolemization and Morleyization in this framework are discussed and some natural examples of fuzzy theories are presented.

The notion of (closed) LUKASIEWICZ fuzzy ideal is introduced, and several properties are investigated.The relationship between LUKASIEWICZ fuzzy subalgebra and LUKASIEWICZfuzzy ideal is discussed, and characterization of a LUKASIEWICZ fuzzy ideal is considered.Conditions for a LUKASIEWICZ fuzzy subalgebra to be a LUKASIEWICZ fuzzy ideal are provided, andconditions for the $\in$-set, $q$-set and $O$-set to be ideals are explored.

In this work, we examine several widely-used interval-valued fuzzy logical CONNECTIVES with respect to admissible orders. We are concerned with interval-valued fuzzy negations, automorphisms, fuzzy implications and aggregation functions with respect to $K_{\alpha,\beta}$ orders and arbitrary intervals on $L([0, 1])$. We also make a discussion of width-preserving interval-valued fuzzy equivalence functions and fuzzy dissimilarity functions with respect to arbitrary admissible orders and the intervals with the same width on $L([0, 1])$. Then we bring some approaches to constructing the proposed interval-valued fuzzy logical CONNECTIVES with respect to admissible orders.