I am very interested to describe, mathematical methods for solving multiple criteria decision making methods, combining probability theory and Zadeh membership functions theory.
We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart ... more We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart of a logic of problem solving. A Brouwerian D-algebra is defined by a subdirect product of a couple of algebras associated with a Heyting lattice and a Brouwer lattice. Then in this paper we introduce the notion of involutive Brouwerian D-algebra having as models direct products between the lattice of open sets and the lattice of closed sets of a topological space. Different properties including basic distributivity equations for complete Brouwerian D-algebras are presented. An extension of the real graded membership space for fuzzy sets is obtained. A connection with the notion of prelinear Heyting MV-algebra is also established.
In this paper, we consider the structure of residuated join semilattice monoid and we study its ÿ... more In this paper, we consider the structure of residuated join semilattice monoid and we study its ÿrst properties. The class of residuated join semilattice monoids is a variety of algebras. A representation of this structure as residuated mappings is given. Then we present the notion of normal ÿlter together with a characterization theorem of homomorphic images based on this notion. Di erent classes of residuated join semilattice monoids are introduced.
The notion of symmetric Boolean algebra is considered by Moisil [6] to define an algebra of elect... more The notion of symmetric Boolean algebra is considered by Moisil [6] to define an algebra of electrical circuits with valves. Then the notions of symmetric Heyting algebra and symmetric Lukasiewicz algebra are introduced by Monteiro and Iturrioz [3,4,7] to establish the relation between the intuitionistic logic and the Lukasiewicz logic. In connection with the Kolmogorov calculus of problems [5], the notions of D-algebra [8] and involutive Brouwerian D-algebra [9,10] are considered to express logical laws of reasoning in decision problem solving. In this paper a special subclass of involutive Brouwerian D-algebras with an additional structure of MV-algebra is presented to determine the algebraic counterpart of a Gödel-Dummett-Lukasiewicz modal logic. We consider the notion of Heyting MV-algebra introduced by Foullis [2]. A Heyting MV-algebra is a nonempty set H together with four binary operations ∨,∧,→,⊕, an unary operation ∗ and two constants 0, 1 such that the following condition...
We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart ... more We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart of a logic of problem solving. A Brouwerian D-algebra is defined by a subdirect product of a couple of algebras associated with a Heyting lattice and a Brouwer lattice. Then in this paper we introduce the notion of involutive Brouwerian D-algebra having as models direct products between the lattice of open sets and the lattice of closed sets of a topological space. Different properties including basic distributivity equations for complete Brouwerian D-algebras are presented. An extension of the real graded membership space for fuzzy sets is obtained. A connection with the notion of prelinear Heyting MV-algebra is also established.
Proceedings of the 6th Wseas International Conference on Systems Theory Scientific Computation, Aug 21, 2006
... Different properties including basic distributivity equations for complete Brouwerian D-algeb... more ... Different properties including basic distributivity equations for complete Brouwerian D-algebras are presented. ... Key-Words: - Brouwerian lattice; Heyting algebra; Topological space; De Morganalgebra; Fuzzy set; Residuated commutative monoid; Prelinear Heyting MV ...
We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart ... more We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart of a logic of problem solving. A Brouwerian D-algebra is defined by a subdirect product of a couple of algebras associated with a Heyting lattice and a Brouwer lattice. Then in this paper we introduce the notion of involutive Brouwerian D-algebra having as models direct products between the lattice of open sets and the lattice of closed sets of a topological space. Different properties including basic distributivity equations for complete Brouwerian D-algebras are presented. An extension of the real graded membership space for fuzzy sets is obtained. A connection with the notion of prelinear Heyting MV-algebra is also established.
The cellulose biodegradation process was performed using the pure cultures of Trichoderma viride,... more The cellulose biodegradation process was performed using the pure cultures of Trichoderma viride, Pleurotus ostreatus and Pleurotus florida strains, grown on cellulose substrata into a culture vessel of a batch bioreactor. Two types of kinetic models defined by differential equation systems for fungal biomass growth and cellulose biodegradation are presented: a Monod-Heukelekian model type describing the fungal growth rate as a linear combination of cellulose biodegradation rate and biomass concentration; a kinetic model with time variable structure describing the ratio between the fungal growth rate and cellulose biodegradation rate by a second degree rational fraction of time. Both types of kinetic models have in common a Monod type equation expressing the relative cellulose biodegradation rate. Some numerical simulation results based on the laboratory-scale data and a specific method for kinetic parameters evaluation are also given.
The variety of biresiduated algebras including the structures of D-algebra and MV-algebra was int... more The variety of biresiduated algebras including the structures of D-algebra and MV-algebra was introduced together with a corresponding logical system. A manyvalued space over a biresiduated algebra is a set equipped with an equivalence function and a distance function such that these functions are complementary. A cartesian closed category of many-valued spaces over a complete D-algebra is presented.
We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart ... more We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart of a logic of problem solving. A Brouwerian D-algebra is defined by a subdirect product of a couple of algebras associated with a Heyting lattice and a Brouwer lattice. Then in this paper we introduce the notion of involutive Brouwerian D-algebra having as models direct products between the lattice of open sets and the lattice of closed sets of a topological space. Different properties including basic distributivity equations for complete Brouwerian D-algebras are presented. An extension of the real graded membership space for fuzzy sets is obtained. A connection with the notion of prelinear Heyting MV-algebra is also established.
In this paper, we consider the structure of residuated join semilattice monoid and we study its ÿ... more In this paper, we consider the structure of residuated join semilattice monoid and we study its ÿrst properties. The class of residuated join semilattice monoids is a variety of algebras. A representation of this structure as residuated mappings is given. Then we present the notion of normal ÿlter together with a characterization theorem of homomorphic images based on this notion. Di erent classes of residuated join semilattice monoids are introduced.
The notion of symmetric Boolean algebra is considered by Moisil [6] to define an algebra of elect... more The notion of symmetric Boolean algebra is considered by Moisil [6] to define an algebra of electrical circuits with valves. Then the notions of symmetric Heyting algebra and symmetric Lukasiewicz algebra are introduced by Monteiro and Iturrioz [3,4,7] to establish the relation between the intuitionistic logic and the Lukasiewicz logic. In connection with the Kolmogorov calculus of problems [5], the notions of D-algebra [8] and involutive Brouwerian D-algebra [9,10] are considered to express logical laws of reasoning in decision problem solving. In this paper a special subclass of involutive Brouwerian D-algebras with an additional structure of MV-algebra is presented to determine the algebraic counterpart of a Gödel-Dummett-Lukasiewicz modal logic. We consider the notion of Heyting MV-algebra introduced by Foullis [2]. A Heyting MV-algebra is a nonempty set H together with four binary operations ∨,∧,→,⊕, an unary operation ∗ and two constants 0, 1 such that the following condition...
We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart ... more We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart of a logic of problem solving. A Brouwerian D-algebra is defined by a subdirect product of a couple of algebras associated with a Heyting lattice and a Brouwer lattice. Then in this paper we introduce the notion of involutive Brouwerian D-algebra having as models direct products between the lattice of open sets and the lattice of closed sets of a topological space. Different properties including basic distributivity equations for complete Brouwerian D-algebras are presented. An extension of the real graded membership space for fuzzy sets is obtained. A connection with the notion of prelinear Heyting MV-algebra is also established.
Proceedings of the 6th Wseas International Conference on Systems Theory Scientific Computation, Aug 21, 2006
... Different properties including basic distributivity equations for complete Brouwerian D-algeb... more ... Different properties including basic distributivity equations for complete Brouwerian D-algebras are presented. ... Key-Words: - Brouwerian lattice; Heyting algebra; Topological space; De Morganalgebra; Fuzzy set; Residuated commutative monoid; Prelinear Heyting MV ...
We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart ... more We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart of a logic of problem solving. A Brouwerian D-algebra is defined by a subdirect product of a couple of algebras associated with a Heyting lattice and a Brouwer lattice. Then in this paper we introduce the notion of involutive Brouwerian D-algebra having as models direct products between the lattice of open sets and the lattice of closed sets of a topological space. Different properties including basic distributivity equations for complete Brouwerian D-algebras are presented. An extension of the real graded membership space for fuzzy sets is obtained. A connection with the notion of prelinear Heyting MV-algebra is also established.
The cellulose biodegradation process was performed using the pure cultures of Trichoderma viride,... more The cellulose biodegradation process was performed using the pure cultures of Trichoderma viride, Pleurotus ostreatus and Pleurotus florida strains, grown on cellulose substrata into a culture vessel of a batch bioreactor. Two types of kinetic models defined by differential equation systems for fungal biomass growth and cellulose biodegradation are presented: a Monod-Heukelekian model type describing the fungal growth rate as a linear combination of cellulose biodegradation rate and biomass concentration; a kinetic model with time variable structure describing the ratio between the fungal growth rate and cellulose biodegradation rate by a second degree rational fraction of time. Both types of kinetic models have in common a Monod type equation expressing the relative cellulose biodegradation rate. Some numerical simulation results based on the laboratory-scale data and a specific method for kinetic parameters evaluation are also given.
The variety of biresiduated algebras including the structures of D-algebra and MV-algebra was int... more The variety of biresiduated algebras including the structures of D-algebra and MV-algebra was introduced together with a corresponding logical system. A manyvalued space over a biresiduated algebra is a set equipped with an equivalence function and a distance function such that these functions are complementary. A cartesian closed category of many-valued spaces over a complete D-algebra is presented.
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