The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theori...

Based on the NM propositional logic system of nilpotent minimum logic, concept integral truth degree formula is firstly proposed by integrating function induced formula, and MP rule HS are proved means invariance. Secondly, in similarity pseudo-distance introduced into set general formulas system, some good properties about proved. Finally, terms divergence degrees diameter, a new membership fo...

By means of the function induced by a logical formula A, the concept of truth degree of the logical formula A is introduced in the 3-valued pre-rough logic in this paper. Moreover, similarity degrees among formulas are proposed and a pseudometric is defined on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in 3-value logic pre-rough logi...

The modern geographic information retrieval technology is based on quantitative models and methods. The semantic information in web documents and queries cannot be effectively represented, leading to information lost or misunderstanding so that the results are either unreliable or inconsistent. A new qualitative approach is thus proposed for supporting geographic information retrieval based on ...

Similarity measures play an important role in data mining, pattern recognition, decision making, machine learning, image process etc. Then, single valued neutrosophic sets (SVNSs) can describe and handle the indeterminate and inconsistent information, which fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. Therefore, the paper proposes new similarity meas-ures between SVNS...

Context. The development of effective distance metrics and similarity measures for categorical features is an important task in data analysis, machine learning, decision theory since a significant portion object properties described by non-numerical values. Typically, the dependence between may be more complex than simply comparing them equality or inequality. Such attributes can relatively sim...