In this paper we combine determinization and state reduction methods into two-in-one algorithms t... more In this paper we combine determinization and state reduction methods into two-in-one algorithms that simultaneously perform determinization and state reduction. These algorithms perform better than all previous determinization algorithms for fuzzy finite automata, developed by Bělohlávek [Inform Sciences 143 (2002) 205–209], Li and Pedrycz [Fuzzy Set Syst 156 (2005) 68–92], Ignjatović et al. [Inform Sciences 178 (2008) 164–180], and Jančić et al. [Inform Sciences 181 (2011) 1358–1368], in the sense that they produce smaller automata, while require the same computation time. The only exception is the Brzozowski type determinization algorithm developed recently by Jančić and Ćirić [Fuzzy Set Syst (2014)], which produces a minimal crisp-deterministic fuzzy automaton, but the algorithms created here can also be used within the Brzozowski type algorithm and improve its performances.
The recently developed firefly algorithm has become one of the prominent population-based metaheu... more The recently developed firefly algorithm has become one of the prominent population-based metaheuristics due to its efficiency in solving a wide range of diverse real-world problems. In this paper an enhanced firefly algorithm to solve mixed variable structural optimization problems is presented. Two modifications related with the constraint handling method based on Deb's rules and the geometric progression reduction scheme mechanism are introduced in order to improve its performance in the constrained search space. The proposed algorithm is tested on four classical structural optimization problems taken from literature. The obtained results show that the proposed approach was very competitive in the considered problems, mostly outperforming the original firefly algorithm.
Abstract In this paper we provide improvements of determinization methods, based on factorization... more Abstract In this paper we provide improvements of determinization methods, based on factorization of fuzzy states, for fuzzy finite automata that accept fuzzy languages of infinite range. The improvements are based on the usage of the fuzzy relational calculus, namely, on the usage of the right invariant fuzzy quasi-orders. Our algorithms perform better in the sense that they produce smaller automata, while require the same computation time. In addition, they can produce finite deterministic automata in cases when previous algorithms result in infinite deterministic automata. We show that the weak representable-cycles property is necessary and sufficient condition for determinization of a fuzzy automaton via a maximal factorization of fuzzy states. This condition is more general than the representable-cycles property previously determined as the necessary and sufficient condition for determinization of a fuzzy automaton via a maximal factorization of fuzzy states.
ABSTRACT In this paper we study formal power series over a quantale with coefficients in the alge... more ABSTRACT In this paper we study formal power series over a quantale with coefficients in the algebra of all languages over a given alphabet, and representation of fuzzy languages by these formal power series. This representation generalizes the well-known representation of fuzzy languages by their cut and kernel languages. We show that regular operations on fuzzy languages can be represented by regular operations on power series which are defined by means of operations on ordinary languages. We use power series in study of fuzzy languages which are recognized by fuzzy finite automata and deterministic finite automata, and we study closure properties of the set of polynomials and the set of polynomials with regular coefficients under regular operations on power series.
Weakly linear systems of fuzzy relation inequalities and equations have recently emerged from res... more Weakly linear systems of fuzzy relation inequalities and equations have recently emerged from research in the theory of fuzzy automata. From the general aspect of the theory of fuzzy relation equations and inequalities homogeneous and heterogeneousweakly linear systems have been discussed in two recent papers. Here we give a brief overview of the main results from these two papers, as well as from a series of papers on applications of weakly linear systems in the state reduction of fuzzy automata, the study of simulation, bisimulation and equivalence of fuzzy automata, and in the social network analysis. Especially, we present algorithms for computing the greatest solutions to weakly linear systems.
In this paper we show that every fuzzy matrix with entries in a complete residuated lattice posse... more In this paper we show that every fuzzy matrix with entries in a complete residuated lattice possess the generalized inverses of certain types, and in particular, it possess the greatest generalized inverses of these types. We also provide an iterative method for computing these greatest generalized inverses, which terminates in a finite number of steps, for example, for all fuzzy matrices with entries in a Heyting algebra. For other types of generalized inverses we determine criteria for the existence, given in terms of solvability of particular systems of linear matrix equations. When these criteria are met, we prove that there is the greatest generalized inverse of the given type and provide a direct method for its computing.
The firefly algorithm (FA) has become one of the most prominent swarm intelligence methods due to... more The firefly algorithm (FA) has become one of the most prominent swarm intelligence methods due to its efficiency in solving a wide range of various real-world problems. In this paper, an upgraded firefly algorithm (UFA) is proposed to further improve its performance in solving constrained engineering optimization problems. The main modifications of the basic algorithm are the incorporation of the logistic map and reduction scheme mechanism in order to perform fine adjustments of its control parameters, and employing a mutation operator in order to provide useful diversity in the population. Also, the proposed approach uses certain feasibility-based rules in order to guide the search to the feasible region of the search space, the improved scheme to handle the boundary constraints and the method for handling equality constraints. The UFA is tested on a set of 24 benchmark functions presented in CEC’2006 and nine widely used constrained engineering optimization problems. Comprehensive experimental results show that the overall performance of the UFA is superior to the FA and its recently proposed variants. Moreover, it achieves highly competitive results compared with other state-of-the-art metaheuristic techniques.
In this paper we provide procedures for testing the existence of various types of generalized inv... more In this paper we provide procedures for testing the existence of various types of generalized inverses in involutive residuated semigroups and involutive quantales defined by the Moore-Penrose equations, and for computing the extreme inverses whenever they exist. We also determine certain instances when a? = a*, whenever a? exists. The obtained results can be applied to a wide class of quantales of fuzzy relations and fuzzy matrices, as well as to Gelfand quantales.
In this paper we combine determinization and state reduction methods into two-in-one algorithms t... more In this paper we combine determinization and state reduction methods into two-in-one algorithms that simultaneously perform determinization and state reduction. These algorithms perform better than all previous determinization algorithms for fuzzy finite automata, developed by Bělohlávek [Inform Sciences 143 (2002) 205–209], Li and Pedrycz [Fuzzy Set Syst 156 (2005) 68–92], Ignjatović et al. [Inform Sciences 178 (2008) 164–180], and Jančić et al. [Inform Sciences 181 (2011) 1358–1368], in the sense that they produce smaller automata, while require the same computation time. The only exception is the Brzozowski type determinization algorithm developed recently by Jančić and Ćirić [Fuzzy Set Syst (2014)], which produces a minimal crisp-deterministic fuzzy automaton, but the algorithms created here can also be used within the Brzozowski type algorithm and improve its performances.
The recently developed firefly algorithm has become one of the prominent population-based metaheu... more The recently developed firefly algorithm has become one of the prominent population-based metaheuristics due to its efficiency in solving a wide range of diverse real-world problems. In this paper an enhanced firefly algorithm to solve mixed variable structural optimization problems is presented. Two modifications related with the constraint handling method based on Deb's rules and the geometric progression reduction scheme mechanism are introduced in order to improve its performance in the constrained search space. The proposed algorithm is tested on four classical structural optimization problems taken from literature. The obtained results show that the proposed approach was very competitive in the considered problems, mostly outperforming the original firefly algorithm.
Abstract In this paper we provide improvements of determinization methods, based on factorization... more Abstract In this paper we provide improvements of determinization methods, based on factorization of fuzzy states, for fuzzy finite automata that accept fuzzy languages of infinite range. The improvements are based on the usage of the fuzzy relational calculus, namely, on the usage of the right invariant fuzzy quasi-orders. Our algorithms perform better in the sense that they produce smaller automata, while require the same computation time. In addition, they can produce finite deterministic automata in cases when previous algorithms result in infinite deterministic automata. We show that the weak representable-cycles property is necessary and sufficient condition for determinization of a fuzzy automaton via a maximal factorization of fuzzy states. This condition is more general than the representable-cycles property previously determined as the necessary and sufficient condition for determinization of a fuzzy automaton via a maximal factorization of fuzzy states.
ABSTRACT In this paper we study formal power series over a quantale with coefficients in the alge... more ABSTRACT In this paper we study formal power series over a quantale with coefficients in the algebra of all languages over a given alphabet, and representation of fuzzy languages by these formal power series. This representation generalizes the well-known representation of fuzzy languages by their cut and kernel languages. We show that regular operations on fuzzy languages can be represented by regular operations on power series which are defined by means of operations on ordinary languages. We use power series in study of fuzzy languages which are recognized by fuzzy finite automata and deterministic finite automata, and we study closure properties of the set of polynomials and the set of polynomials with regular coefficients under regular operations on power series.
Weakly linear systems of fuzzy relation inequalities and equations have recently emerged from res... more Weakly linear systems of fuzzy relation inequalities and equations have recently emerged from research in the theory of fuzzy automata. From the general aspect of the theory of fuzzy relation equations and inequalities homogeneous and heterogeneousweakly linear systems have been discussed in two recent papers. Here we give a brief overview of the main results from these two papers, as well as from a series of papers on applications of weakly linear systems in the state reduction of fuzzy automata, the study of simulation, bisimulation and equivalence of fuzzy automata, and in the social network analysis. Especially, we present algorithms for computing the greatest solutions to weakly linear systems.
In this paper we show that every fuzzy matrix with entries in a complete residuated lattice posse... more In this paper we show that every fuzzy matrix with entries in a complete residuated lattice possess the generalized inverses of certain types, and in particular, it possess the greatest generalized inverses of these types. We also provide an iterative method for computing these greatest generalized inverses, which terminates in a finite number of steps, for example, for all fuzzy matrices with entries in a Heyting algebra. For other types of generalized inverses we determine criteria for the existence, given in terms of solvability of particular systems of linear matrix equations. When these criteria are met, we prove that there is the greatest generalized inverse of the given type and provide a direct method for its computing.
The firefly algorithm (FA) has become one of the most prominent swarm intelligence methods due to... more The firefly algorithm (FA) has become one of the most prominent swarm intelligence methods due to its efficiency in solving a wide range of various real-world problems. In this paper, an upgraded firefly algorithm (UFA) is proposed to further improve its performance in solving constrained engineering optimization problems. The main modifications of the basic algorithm are the incorporation of the logistic map and reduction scheme mechanism in order to perform fine adjustments of its control parameters, and employing a mutation operator in order to provide useful diversity in the population. Also, the proposed approach uses certain feasibility-based rules in order to guide the search to the feasible region of the search space, the improved scheme to handle the boundary constraints and the method for handling equality constraints. The UFA is tested on a set of 24 benchmark functions presented in CEC’2006 and nine widely used constrained engineering optimization problems. Comprehensive experimental results show that the overall performance of the UFA is superior to the FA and its recently proposed variants. Moreover, it achieves highly competitive results compared with other state-of-the-art metaheuristic techniques.
In this paper we provide procedures for testing the existence of various types of generalized inv... more In this paper we provide procedures for testing the existence of various types of generalized inverses in involutive residuated semigroups and involutive quantales defined by the Moore-Penrose equations, and for computing the extreme inverses whenever they exist. We also determine certain instances when a? = a*, whenever a? exists. The obtained results can be applied to a wide class of quantales of fuzzy relations and fuzzy matrices, as well as to Gelfand quantales.
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Papers by Jelena Ignjatovic