A logical approach to fuzzy truth hedges

The starting point of this paper are the works of Hájek and Vychodil on the axiomatization of truth-stressing and-depressing hedges as expansions of Hájek's BL logic by new unary connectives. They showed that their logics are chain-complete, but standard completeness was only proved for the expansions over Gödel logic. We propose weaker axiomatizations over an arbitrary core fuzzy logic which have two main advantages: (i) they preserve the standard completeness properties of the original logic and (ii) any subdiagonal (resp. superdiagonal) non-decreasing function on [0, 1] preserving 0 and 1 is a sound interpretation of the truth-stresser (resp. depresser) connectives. Hence, these logics accommodate most of the truth hedge functions used in the literature about of fuzzy logic in a broader sense. © 2013 Elsevier Inc. All rights reserved.The authors acknowledge partial support of the MICINN projects TASSAT (TIN2010-20967-C04-01) and ARINF (TIN2009-14704-C03-03), and the FP7-PEOPLE-2009-IRSES project MaToMUVI (PIRSES-GA-2009-247584). Carles Noguera also acknowledges support of the research contract “Juan de la Cierva” JCI-2009-05453.Peer Reviewe

Multivalued logic systems for technical applications

Velmi často je vyžadováno, aby automatizovaná zařízení byla jistým způsobem "inteligentní", tedy aby jejich řídicí systémy uměly emulovat rozhodovací proces. Tato diplomová práce poskytuje obecný formální popis vícehodnotových logických systémů schopných zmíněné emulace a jejich souvislost s teorií fuzzy množin. Jsou uvedeny způsoby vytváření matematických modelů založených na lingvistických datech. Dále se práce zabývá znalostními bázemi a jejich vlastnostmi. Součástí této práce je také počítačový program sloužící k tvorbě slovních modelů.Automated devices are very often required to exhibit some kind of an intelligent behaviour, which means that their control systems must be able to emulate the reasoning process. This diploma thesis provides a general formal description of multivalued logic systems capable of such an emulation and their connection with the fuzzy set theory. Ways of constructing mathematical models based on linguistic data are described. Also, knowledge bases and their properties are discussed. A computer program serving as a linguistic model development tool is a part of this thesis.

Parameterizing the semantics of fuzzy attribute implications by systems of isotone Galois connections

We study the semantics of fuzzy if-then rules called fuzzy attribute implications parameterized by systems of isotone Galois connections. The rules express dependencies between fuzzy attributes in object-attribute incidence data. The proposed parameterizations are general and include as special cases the parameterizations by linguistic hedges used in earlier approaches. We formalize the general parameterizations, propose bivalent and graded notions of semantic entailment of fuzzy attribute implications, show their characterization in terms of least models and complete axiomatization, and provide characterization of bases of fuzzy attribute implications derived from data

Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics, fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. In this paper, we use the triangular fuzzy numbers for matrix domains of sequence spaces with infinite matrices. We construct the new space with triangular fuzzy numbers and investigate to structural, topological and algebraic properties of these spaces.Comment: 10 pages, 17 reference

Neuro-fuzzy software for intelligent control and education

Tese de mestrado integrado. Engenharia Electrotécnica e de Computadores (Major Automação). Faculdade de Engenharia. Universidade do Porto. 200

Ordering based decision making: a survey

Decision making is the crucial step in many real applications such as organization management, financial planning, products evaluation and recommendation. Rational decision making is to select an alternative from a set of different ones which has the best utility (i.e., maximally satisfies given criteria, objectives, or preferences). In many cases, decision making is to order alternatives and select one or a few among the top of the ranking. Orderings provide a natural and effective way for representing indeterminate situations which are pervasive in commonsense reasoning. Ordering based decision making is then to find the suitable method for evaluating candidates or ranking alternatives based on provided ordinal information and criteria, and this in many cases is to rank alternatives based on qualitative ordering information. In this paper, we discuss the importance and research aspects of ordering based decision making, and review the existing ordering based decision making theories and methods along with some future research directions