It is common in real life to find fuzzy information that comes from subjective judgments or the imprecision in measured data. Fuzzy approaches have been used to extend database systems in storing and updating imprecise information (data) and in processing imprecise queries. Consider a fuzzy query: find name, grade of quite good students and just tall students where age > 15. This query includes...

We present new tools for fuzzy arithmetic with fuzzy numbers, based on the parametric representation of fuzzy numbers and new fuzzy operations, the generalized difference and the generalized division of fuzzy numbers. The new operations are described in terms of the parametric LR and LU representations of fuzzy numbers and the corresponding algorithms are described. An application to the soluti...

We consider a fuzzy linear system with crisp coefficient matrix and with an arbitrary fuzzy number in parametric form on the right-hand side. It is known that the well-known existence and uniqueness theorem of a strong fuzzy solution is equivalent to the following: The coefficient matrix is the product of a permutation matrix and a diagonal matrix. This means that this theorem can be applicable...

In this paper we are going to introduce the notion of strong non-standard completeness (SNSC) for fuzzy logics. This notion naturally arises from the well known construction by ultraproduct. Roughly speaking, to say that a logic C is strong non-standard complete means that, for any countable theory Γ over C and any formula φ such that Γ 6`C φ, there exists an evaluation e of C-formulas into a C...

Introduction: Overexpression of Human Epidermal Growth factor Receptor-2 (HER-2) is one of the most important prognostic and predictive factors of breast cancer, observed in 25% - 30% of breast carcinoma patients leading to poor prognosis and feasible anti HER-2 antibody drugs. The objective of this study was to evaluate the HER-2 frequency in target population and its correlat...

Fuzzy Conceptual Maps have become an important means for describing a particular domain showing the concepts (variables) and the relationship between them. They have been used for several tasks like simulation processes, forecasting or decision support. In general, the task of creating Fuzzy Conceptual Maps is made by experts in a certain domain but it is very promising the automatic creation o...

This paper studies fuzzy relations in the graded framework of Fuzzy Class Theory (FCT). This includes (i) rephrasing existing work on graded properties of binary fuzzy relations in the framework of Fuzzy Class Theory and (ii) generalizing existing crisp results on fuzzy relations to the graded framework. Our particular aim is to demonstrate that Fuzzy Class Theory is a powerful and easy-to-use ...

Contrapositive symmetry (CPS) is a tautology in classical logic. In fuzzy logic, not all fuzzy implications have CPS with respect to a given strong negation. Given a fuzzy implication J , towards imparting contrapositive symmetry to J with respect to a strong negation N two techniques, viz., upper and lower contrapositivisation, have been proposed by Bandler and Kohout [Semantics of implication...

The notion of fuzzy function based on many-valued equivalence relations (many-valued similarity relations (equalities) [17, 18, 19], fuzzy equivalence relations [4, 6, 7, 21, 22, 26], similarity relations [1, 2, 3, 15, 28], indistinguishability operators [27], etc.) has been introduced by several authors, and applied to category theory [5], approximate reasoning and fuzzy control theory [8, 10,...