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We remark that the functor \(\varGamma \) maps a non-equational class of groups, the category of abelian \(\ell \)-groups with strong unit, to an equational class , the variety of all MV-algebras.
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In this paper, we have introduced the notion of local and semilocal triangle algebras and propose the theorems that characterize these algebraic structures. Additionally, we have established the new properties of these algebraic... more
In this paper, we have introduced the notion of local and semilocal triangle algebras and propose the theorems that characterize these algebraic structures. Additionally, we have established the new properties of these algebraic structures and discussed the relations between local triangle algebras and some interval valued residuated lattice (IVRL)-filters, such as n-fold IVRL-extended integral filters and IVRL-extended maximal filters. The obtained results proved that the MTL-triangle algebra is a subdirect product of local triangle algebras. Moreover, a correlation was observed between the set of the dense elements and local triangle algebras. Finally, semilocal triangle algebras were introduced and assessed in detail, and an association was observed between the semilocal triangle algebras and quotient triangle algebras.
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Research Interests:
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New methods, like fuzzy logic, are coming into the field of adaptive traffic signal control. Development of the fuzzy control can roughly be divided into two research approaches: development of fuzzy control functions, and development of... more
New methods, like fuzzy logic, are coming into the field of adaptive traffic signal control. Development of the fuzzy control can roughly be divided into two research approaches: development of fuzzy control functions, and development of fuzzy inference methods. Both approaches are discussed in this paper. First, a lately developed fuzzy inference method, called maximal fuzzy similarity, is introduced. Second, two fuzzy traffic signal control functions, phase selector and green extender, are presented and their performance is evaluated by simulations. Third, the applicability of the maximal fuzzy similarity inference method in traffic control systems is compared to the traditional Mamdani inference method. The comparison is made using them separately in the above mentioned control functions. In the simulations, the phase selector function improved significantly the control performance, while the fuzzy green extender worked better than the non-fuzzy control only with high volumes. Th...
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Abstract: We present three fundamental tools from soft computing realm to solve real world problems that are vague in nature and not easy to handle with classical mathematical methods. We show by several real world examples how such... more
Abstract: We present three fundamental tools from soft computing realm to solve real world problems that are vague in nature and not easy to handle with classical mathematical methods. We show by several real world examples how such problems are solved.
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In 2013 Li and Jin studied a particular type of fuzzy relational equations on finite sets, where the introduced min-bi-implication composition is based on Łukasiewicz equivalence. In this paper such fuzzy relation equations are studied on... more
In 2013 Li and Jin studied a particular type of fuzzy relational equations on finite sets, where the introduced min-bi-implication composition is based on Łukasiewicz equivalence. In this paper such fuzzy relation equations are studied on a more general level, namely complete residuated lattice valued fuzzy relation equations of type ⋀ y ∈ Y ( A ( x , y ) ↔ X ( y ) = B ( x ) are analyzed, and the existence of solutions S is studied. First a necessary condition for the existence of solution is established, then conditions for lower and upper limits of solutions are given, and finally sufficient conditions for the existence of the smallest and largest solutions, respectively, are characterized. If such general or global solutions do not exist, there might still be partial or point wise solutions; this is a novel way to study fuzzy relation equations. Such point wise solutions are studied on Łukasiewicz, Product and Godel t-norm based residuated lattices on the real unit interval.
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ABSTRACT Zadeh's Fuzzy Logic was introduced as a mathematical tool for deduction working with different degrees of truth, instead of the two truth degrees of Classical Logic. The next step taken by Pavelka was to admit assumptions... more
ABSTRACT Zadeh's Fuzzy Logic was introduced as a mathematical tool for deduction working with different degrees of truth, instead of the two truth degrees of Classical Logic. The next step taken by Pavelka was to admit assumptions and theorems which are also satisfied only to some truth degree, as well as deduction rules transferring these degrees to the deduced formulas. In the semantics these possibly, but not necessarily, correspond to the degrees of satisfaction of formulas. A significant consequent progress towards this direction was achieved by Hajek's work on Rational Pavelka Logic; it forms formulas with graded truth as couples of a formula and a rational truth value. The success of the Rational Pavelka Logic follows from the properties of the standard MV-algebra, i.e. the real unit interval with the Łukasiewicz operations, which was used as its semantical interpretation. The main mathematical result is that the Rational Pavelka Logic is sound and complete in the sense that the syntactical provability degree and the semantical degree of satisfaction coincide. In this paper an alternative to Pavelka's approach is investigated. Instead of the standard MV-algebra, the truth values are taken from a perfect MV-algebra, in particular, Chang's MV-algebra. This is the opposite extreme among MV-algebras, it admits only infinitesimals besides the two classical truth degrees. We argue that such an example also has a motivation in deduction imitating human reasoning. As Chang's MV-algebra is not complete, the provability degree need not exist. Nevertheless, as the main result the following weak completeness theorem is proved: If the provability degree of a formula exists, it coincides with the degree of satisfaction. This result is obtained by adding to Pavelka's original approach a new rule of inference, Hájek's book-keeping axioms and an axiom valid in Chang's MV-algebra. An example that clarifies the differences between Classical Logic, Rational Pavelka Logic and Perfect Pavelka Logic is given, and some new fuzzy rules of inference are introduced.
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... Organizers Stefano Aguzzoli (Milan), Brunella Gerla (Varese), Vincenzo Marra (Milan). ... mapping on B-structures Ioana Leustean A notion of independence for probability MV-algebras Enrico Marchioni Possibilistic States: A Logical... more
... Organizers Stefano Aguzzoli (Milan), Brunella Gerla (Varese), Vincenzo Marra (Milan). ... mapping on B-structures Ioana Leustean A notion of independence for probability MV-algebras Enrico Marchioni Possibilistic States: A Logical Formalization Kalina Martin Comparison of ...
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics,... more
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
En We present three fundamental tools from soft computing realm to solve real world problems that are vague in nature and not easy to handle with classical mathematical methods. We show by several real world examples how such problems are... more
En We present three fundamental tools from soft computing realm to solve real world problems that are vague in nature and not easy to handle with classical mathematical methods. We show by several real world examples how such problems are solved.
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In this work we have managed to find parameters for defining athlete’s aerobic and anaerobic thresholds. Thresholds which are of vital importance for top athletes. It is shown how differential evolution and different similarity measures... more
In this work we have managed to find parameters for defining athlete’s aerobic and anaerobic thresholds. Thresholds which are of vital importance for top athletes. It is shown how differential evolution and different similarity measures has been used to tune computational model for threshold definitions. From our results it is obvious that the use of right parameter values for this kind expert system is of vital importance.
We investigate the applicability and usefulness of the GUHA data mining method and its computer implementation LISp-Miner for driver characterization based on digital vehicle data on gas pedal position, vehicle speed, and others. Three... more
We investigate the applicability and usefulness of the GUHA data mining method and its computer implementation LISp-Miner for driver characterization based on digital vehicle data on gas pedal position, vehicle speed, and others. Three analytical questions are assessed: (1) Which measured features, also called attributes, distinguish each driver from all other drivers? (2) Comparing one driver separately in pairs with each of the other drivers, which are the most distinguishing attributes? (3) Comparing one driver separately in pairs with each of the other drivers, which attributes values show significant differences between drivers? The analyzed data consist of 94,380 measurements and contain clear and understandable patterns to be found by LISp-Miner. In conclusion, we find that the GUHA method is well suited for such tasks.
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The primary aim of this paper is to establish a formal connection between a particular many–valued paraconsistent logic and the logic of a KDD method, namely the GUHA data mining method by introducing a new quantifier called... more
The primary aim of this paper is to establish a formal connection between a particular many–valued paraconsistent logic and the logic of a KDD method, namely the GUHA data mining method by introducing a new quantifier called Paraconsistent Separation quantifier. This quantifier is implemented to LISp–Miner Software. The secondary aim is to demonstrate a possible usefulness of this quantifier in social and other applied sciences by examples taking from family planning context.
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The 20 January 2005 solar energetic particle (SEP) event was one of the hardest on record with the largest ground level (neutron monitor) event since 1956. On this day, the MINIS balloon campaign had one payload with electric field... more
The 20 January 2005 solar energetic particle (SEP) event was one of the hardest on record with the largest ground level (neutron monitor) event since 1956. On this day, the MINIS balloon campaign had one payload with electric field instrumentation aloft in the stratosphere above Antarctica at 71° S, 10° W geographic. When the SEPs arrived at earth, the horizontal
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... completeness for first order structures Majid M. Ali Multiplication von Neumann regular modules Jorge Almeida Decision problems ... in Mal'cev algebras: properties and applications Bertalan Pécsi Weakly representable relation... more
... completeness for first order structures Majid M. Ali Multiplication von Neumann regular modules Jorge Almeida Decision problems ... in Mal'cev algebras: properties and applications Bertalan Pécsi Weakly representable relation algebras form a variety Agata Pilitowska Complex ...
We introduce an axiomatic extension of Höhle’s Monoidal Logic called Semi–divisible Monoidal Logic, and prove that it is complete by show-ing that semi–divisibility is preserved in MacNeille completion. Moreover, we introduce Strong... more
We introduce an axiomatic extension of Höhle’s Monoidal Logic called Semi–divisible Monoidal Logic, and prove that it is complete by show-ing that semi–divisibility is preserved in MacNeille completion. Moreover, we introduce Strong semi– divisible Monoidal Logic and conjecture that a pred-icate formula α is derivable in Strong Semi–divisible Monadic logic if, and only if its double negation ¬¬α is derivable in Łukasiewicz ∗ logic.