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 paper, we study the finitely many constraints of fuzzy relation inequalities problem and optimize the linear objective function on this region which is defined with fuzzy max-LUKASIEWICZ operator. In fact LUKASIEWICZ t-norm is one of the four basic t-norms. A new simplification technique is given to accelerate the resolution of the problem by removing the components having no effect on the solution process. Also, an algorithm and one numerical example are offered to abbreviate and illustrate the steps of the problem resolution ‎process.‎

The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gö del (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gö del logics, for showing that the intuitionistic logic is not finitely (many) valued. Now we know that the propositional intuitionistic logic is infinitely many valued (with a countably many logical values). In this paper we provide another proof for this result of Gö del, from the perspective of Kripke model theory. Š vejadr and Bendova (2000) proved that in Gö del fuzzy logic the conjunction and implication are not definable by the rest of the propositional CONNECTIVES (while disjunction is definable by conjunction and implication). In this paper, we show that disjunction is not definable by implication and negation in Gö del fuzzy logic; two proofs, one by Kripke models and one by fuzzy semantics, are provided for this new theorem.

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.