Aleksandar Takaci

Schur-concave triangular norms: Characterization and application in pFCSP

The concept of priority is often used in real time systems. Schur-concave t-norms are used to capture this concept within prioritized fuzzy constraint satisfaction problems (pFCSPs). We are dealing with a very strict notion of priority which favors the constraint with the larger priority regardless of its value.Also, some results on the characterization of Schur-concave t-norms are given.

Isotherms for the adsorption of Cu(II) onto lignin: Comparison of linear and non-linear methods

Equilibrium studies were carried out for the adsorption of Cu(II) onto Kraft lignin as an adsorbent. The experimental data were fitted to the Freundlich, Langmuir and Redlich-Peterson isotherms by linear and non-linear method. Comparison of linear and non-linear regression method was given in selecting the optimum isotherm for the experimental data. The coefficient of correlation r2 and Chi-square test χ2 was used to select the best linear theoretical isotherm. The best linear model is Redlich-Peterson isotherm model, where r2=0,985 and χ2=0,02. In order to predict the error ERRSQ, HYBRD, MPSD, ARE and EABS were used. Moreover, by minimizing these error functions the optimal values of parameters and also the optimum isotherm was found. The Redlich-Peterson isotherm was found to be the best representative for adsorption of Cu(II) on the adsorbent in the cases when ERRSQ, HYBRD, MPSD functions were used. There coefficients of determination are 0.986, 0.985, 0.984, respectively and Chi-square is 0.02 in all cases. Freundlich isotherms which were obtained by minimization of the ERRSQ, HYBRD, MPSD, ARE and EABS function showed very good agreement with experimental data. In all cases the coefficients of determination are greater than 0.91. Besides, it was observed that non-linear isotherm models were better for representation of equilibrium data than linearized models.

Prioritized fuzzy logic based information processing in relational databases

Many years of research related to fuzzy logic and fuzzy set theory extensions to relational databases have not lead to stable implementations, standardized languages or fuzzy relational database application development tools and methods. The main goal of this paper is the modelling and the implementation of a set of tools that allow usage of fuzzy logic enriched with priorities in relational database applications. In order to achieve that goal, at first, the relational data model is extended with the elements of fuzzy set theory. After that, a fuzzy extension of the SQL query language, called the PFSQL, is defined. An interpreter for that language is integrated inside an implementation of the fuzzy JDBC driver. An implementation of the CASE tool for modelling of fuzzy relational database schemas rounds up a set of tools for the implementation of Java fuzzy database applications. In this sense, this paper presents a step towards a methodology for the fuzzy relational database application development.

On the operational solutions of fuzzy fractional differential equations

Fuzzy fractional differential equations with fuzzy coefficients are analyzed in the frame of Mikusiński operators. Systems of fuzzy operational algebraic equations are obtained, in view of the definition of fuzzy derivatives. Their exact and approximate solutions are constructed and their characters are analyzed, considering them as the corresponding solutions of the given problem. The described procedure of the construction of solutions is illustrated on an example and the obtained approximate solutions of the considered problems are visualized by using the GeoGebra software package.

An Interpreter for Priority Fuzzy Logic Enriched SQL

In this paper we describe a query language called PFSQL (Priority Fuzzy Structured Query Language) that, beside basic fuzzy capabilities, adds the possibility to specify priorities for fuzzy statements. We give an analysis of possibilities to extend the SQL language and briefly describe the GPFCSP (Generalized Prioritized Fuzzy Constraint Satisfaction Problem) systems, a theoretical concept vital for the implementation of the PFSQL interpreter. In the following, we describe the most important ideas used in the process of the interpreter implementation. As one of the most innovative ideas we present the fuzzy JDBC (Java Database Connectivity) driver as a framework for the PFSQL interpreter.

The role of fuzzy sets in improving maximal covering location problem (MCLP)

In this paper an extension of fuzzy maximal covering location time problem (FMCLP) is presented. The travel times are considered to be linear, trapezoidal or Gaussian fuzzy numbers and the radius is considered to be a fuzzy set of a right shoulder type. For obtaining the distance a fuzzy ordering relation was used to compare distances to the radius. In order to solve the FMCLP problem we used discrete particle swarm optimization (DPSO) algorithm. Theoretical results show that the proposed DPSO algorithm is very competitive for FMCLP problem.

Formalising pfsql queries using ŁΠ fuzzy logic

Using the concept of a generalised priority constraint satisfaction problem, we previously found a way to introduce priority queries into fuzzy relational databases. The results were PFSQL (Priority Fuzzy Structured Query Language) together with a database independent interpreter for it. In an effort to improve the performance of the resolution of PFSQL queries, the aim of the current paper is to formalise PFSQL queries by obtaining their interpretation in an existing fuzzy logic. We have found that the ŁI logic provides sufficient elements. The SELECT line of PFSQL queries is semantically a formula of some fuzzy logic, and we show that such formulas can be naturally expressed in a conservative extension of the ŁI logic. Furthermore, we prove a theorem that gives the PSPACE containment for the complexity of finding a model for a given ŁI logic formula.

A note on the use of Choquet and Sugeno integrals in minimal and maximal covering location problems

The aim of this paper is to show a potential applicability of some well-known fuzzy integrals, i.e., of the Choquet integral and the Sugeno integral, in Minimal and Maximal Covering location problems, i.e., in MinCLP and MCLP. Possible benefits of the use of Choquet and Sugeno integrals lie in the flexibility of a monotone set function which is the core of the observed integrals and which is being used for modelling Decision Makers behavior. Mathematical models of Minimal and Maximal Covering location problems are given. Approach based on fuzzy integrals versus the standard two types of operators is discussed. Ideas for the future work and applications are presented.

On fixed point theorems involving altering distances in Menger probabilistic metric spaces

In this paper, we show by means of an example that the results of Babačev (Appl. Anal. Discrete Math. 6:257-264, 2012) do not hold for the class of t-norms T≤Tp. Further, we prove a fixed point theorem for quasi-type contraction involving altering distance functions which is weaker than that proposed by Babačev but for any continuous t-norm in a complete Menger space.MSC:47H10, 54H25.

The function for estimating the separation efficiency of the wheat flour milling process

Considering the significant differencies between the chemical composition of the kernel layers, distribution of chemical compounds in intermediate, final and subproducts of the milling process come as a result of the level of dissociation achieved during the milling process. These differences serve as a basis for the mill process control. Ash determination is probably the most widely used tool while even greater differencies exist in cellulose and especialy starch content. In this work efficiency function has been defined and used to evaluate the relative efficiency of the separation of endosperm from the outer pericarp leyers of the kernel. It is based on quantity rates (flour extraction and subproducts yield) and qulitative analyses (starch and cellulose content in the wheat, flour and subproducts).