Fuzzy logics based on triangular norms and their corresponding conorms are investigated. An aarmative answer to the question whether in such logics a speciic level of satissability of a set of formulas can be characterized by the same level of satissability of its nite subsets is given. Tautologies, contradictions and contingencies with respect to such fuzzy logics are studied, in particular fo...

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Intuitionistic fuzzy sets in the sense of Atanassov and interval-valued fuzzy sets can be seen as L-fuzzy sets w.r.t. a special lattice L . Deschrijver [2] introduced additive and multiplicative generators on L based on a special kind of addition introduced in [3]. Actually, many other additions can be introduced. In this paper we investigate additive generators on L as far as possible independ...

This report treats the relation between substructural logics and fuzzy logics, especially focuses on the noncommutativity of conjunctive operators i.e. substructural logics without the exchange rule. As the results, the authors show that fuzzy logics based on the left continuous pseudo-t-norms are the extensions of FLw. Also, we introduce the definition of pseudouninorms and give some methods t...

Recently, many works have appeared dealing with the distributivity of fuzzy implications over t-norms, tconorms and uninorms (see [2, 3, 4, 5, 12, 13, 14]). These equations have a very important role to play in efficient inferencing in approximate reasoning, especially fuzzy control systems (see [6]). In this work we present some results connected with two functional equations describing the di...

This paper deals with fuzzy quantities and relations in multi-objective minimum cost flow problem. When t-norms and t-conorms are available, the goal programming is applied tominimize the deviation among themultiple costs of fuzzy flows and the given targets when the fuzzy supplies and demands are satisfied. To obtain the most optimistic and the most pessimistic satisficing solutions of this pr...

Some fuzzy expert systems have used fuzzy rules with numerical values which represent degrees of conndence for rules. We discuss two kinds of interpretations for these numerical degrees of conndence for rules, called "di-rect degrees " and "indirect degrees". Then, we apply Zadeh's, Baldwin's, and Tsukamoto's reasoning method to the rules under the two interpretations using general T-norms, and...

Most normal forms for fuzzy logics are versions of conjunctive and disjunctive classical normal forms. Unfortunately, they do not always preserve either tautologies or contradictions which are fundamental for automatic theorem provers based on refutation methods. De Morgan implicative systems are triples like the De Morgan system, but considering fuzzy implications instead of t-conorms. These s...

Watermarking is done in digital images for authentication and to restrict its unauthorized usages. Watermarking is sometimes invisible and can be extracted only by authenticated party. Encrypt a text or information by public – private key from two fuzzy matrix and embed it in image as watermark. In this paper we proposed two fuzzy compositions Product-Mod-Minus, and Compliment-Product-Minus. Em...

Let I = ([0; 1];_;^; 0; 1), where _ and ^ are max and min, respectively. This algebra is the basic building block of fuzzy set theory and logic. Likewise, the algebra I = ([0; 1];_;^; 0; 1), where [0; 1] = f(a; b) : a; b 2 [0; 1], a bg, _, ^ are given coordinate-wise, and 0 and 1 are the bounds on [0; 1], is the relevant algebra for interval-valued fuzzy set theory and logic. A good share of th...