Krassimir Atanassov | António E. Ruano | Jesús Medina | László T. Kóczy | Manuel Ojeda-Aciego

**Krassimir Atanassov**. Head of the Bioinformatics and Mathematical Modeling Dept., Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Corresponding Member of the Bulgarian Academy of Sciences, IFSA Fellow.

**Title: On Pseudo-fixed Points of the Intuitionistic Fuzzy Quantifiers and Operators**

**Abstract:** In this paper, the pseudo-fixed points of the intuitionistic fuzzy quantifiers

and operators from modal and level types, are described.

The first research in the area of intuitionistic fuzzy logics started 30 years ago. Sequentially, intuitionistic fuzzy propositional calculus, intuitionistic fuzzy predicate logic, intuitionistic fuzzy modal logic and intuitionistic fuzzy temporal logic were introduced and developed.

In intuitionistic fuzzy predicate logic, firstly, intuitionistic fuzzy quantifiers that are analogous of the standard logic quantifiers were defined and after this, a series of their extensions arised. In intuitionistic fuzzy modal logic, firstly, intuitionistic fuzzy modal operators that are analogues of standard modal logic operators “necessity” and “possibility” were introduced and after this, a series of their extensions and modifications were defned. Level operators, that are intuitionistic fuzzy analogues of the standard fuzzy set operators, were introduced, too. Here, the pseudo-fixed points of all these operators will be described.

**António E. Ruano**. Centre for Intelligent Systems, LAETA, Instituto Superior Técnico and Universidade do Algarve, Portugal.

Antonio Ruano was born in Espinho, Portugal, on the 14th September 1959. He holds a first degree in Electronic Eng. and Telecommunications (University of Aveiro – UA,1982), a MSc degree in Electrotechnical Eng. (University of Coimbra, 1989), a PhD in Electronic Eng. (University of Wales, 1992) and an Habilitation in Electronic Eng. and Computing (University of Algarve – UALg, 2004). He was a Lecturer (1982/83) at the Dep. of Mathematics, UA, Demonstrator (1981/82) and Lecturer (1984/1992) at the Dep. of Electronic Engineering and Telecommunications, UA, Auxiliar Professor (1993/96) and Associate Professor (1996/2004) at the Unit of Exact Sciences and Humanities – UCEH – of UALg. Since 2004 he is an Associate Professor with Habilitation at the Faculty of Sciences & Technology of UALg. In UALg, he has served in several management positions, such as Director of the Dep. of Electronic Eng. and Informatics, Vice-Dean, Dean and Scientific Council Chairman of UCEH, Pro-Rector of UALg, and Director of the Integrated Master on Electronic Eng. and Telecommunications, Master on Renewable Energy and Energy Management, and Master on Informatics Eng. His research activities are centred in Intelligent Control. He has been chairman of the IFAC Technical Committee on Computational Intelligence in Control for the last two trienniums (nowadays vice-chairman), has coordinated more than 25 national and international projects, has supervised more than 30 MSc, PhD and Pos-Doc students, and has published more than 250 articles, books and book chapters, that can be seen in ResearchID (B-4135-2008), Orcid (0000-0002-6308-8666), Scopus (7004284159) and GoogleScholar (wrYUbVgAAAAJ).

**Title: The IMBPC HVAC system: A complete MBPC solution for existing HVAC systems.**

**Abstract: **According to recent studies, energy consumption of buildings (residential and non-residential) represents approximately 40% of total world energy consumption, half of this energy consumed by HVAC systems operation. It is therefore of fundamental importance to control efficiently the existing HVAC systems, in order to decrease energy usage and to increase compliance with the European Directives on the energy performance of buildings and energy efficiency.

Model Based Predictive Control (MBPC) is perhaps the most proposed technique for HVAC control, since it offers an enormous potential for energy savings. This talk will introduce the Intelligent MBPC (IMBPC) HVAC system, a complete solution to enable MBPC of existing HVAC installations in a building. The IMPBC HVAC minimizes the economic cost needed to maintain controlled rooms in thermal comfort during the periods of occupation. The hardware and software components of the IMBPC system are described, with a focus on the MBPC algorithm employed, and the design of Computational Intelligence predictive models.

The installation of IMBPC HVAC solution in a University building by a commercial company is described, and the results obtained in terms of economical savings and thermal comfort obtained are compared with standard, temperature regulated control.

**Jesús Medina** received the M.S. degree in mathematics in 1998 from the University of Granada, Spain, and the Ph.D. degree in mathematics in 2002 from the University of Málaga, Spain. He is currently an Associate Professor at the Department of Mathematics, University of Cádiz, Cádiz, Spain, and evaluated by the Spanish National Agency ANECA as Full Professor, and the International Project Manager of the University of Cádiz. He is also the author or coauthor of more than 100 papers presented at conferences and published in scientific journals, including the Journal of Applied Logic, Applied Mathematics Letters, Information Sciences, Fuzzy Sets and Systems, and Computers and Mathematics with Applications. His is interested in the research areas of fuzzy sets, fuzzy rough sets, fuzzy logic, residuated and multi-adjoint logic programming, relational data analysis, and algebraic structures for soft computing. He is a Member of the European Association for Fuzzy Logic and Technology (EUSFLAT).

**Title: Multi-adjoint Frameworks, towards a More Flexible Formal World**

**Abstract:** Multi-adjoint logic programming, multi-adjoint fuzzy rough sets, multi-adjoint concept lattices, multi-adjoint fuzzy relation equations, etc. These are different frameworks in which the common factor is the multi-adjoint philosophy. This is based on the consideration of an general algebraic structure, called multi-adjoint lattices or algebras, in which the adjoint triples are the underline operators, and the possibility of considering different adjoint triples at the same time.

These operators are defined on general posets or lattices, depend on the specific considered framework, and they do not need to be commutative and/or associative. These general properties together with the consideration of several adjoint triples provides an extra level of flexibility in the framework in which this structure is considered.

This work will present the multi-adjoint algebras, introduce diverse examples, analyze the main features and properties in the main frameworks in which they have been considered and show the first demo of a software which involves different of these frameworks.

**László T. Kóczy. **Faculty of Engineering Sciences. Univ. Széchenyi István, Hungary.

**Title: Fuzzy Signature Sets Are L-fuzzy**

**Abstract:** When Zadeh introduced the concept of fuzzy sets where μ(x) : X → [0, 1], soon his that time student Goguen extended the idea to L-fuzzy sets where the unit interval [0, 1] was replaced by arbitrary algebraic lattice in the manner that the membership degrees are defined by *μ*(*x*) : *X* → *L*. In the late 1970s, we introduced a practical extension to fuzzy sets: vector valued Fuzzy (VVF) sets *μ*(*x*) : *X* → [0, 1]* ^{n}*. The

*n*-dimensional unit hypercube may be certainly interpreted as a lattice under the usual partial ordering ≤. This concept was necessary for a certain industrial application, classifying microscopic images of steel alloys.

Much later we proposed a further extension of the idea by allowing the vectorial

membership degree components being vectorial themselves, the new concept called

Fuzzy Signature (FSig). This way the degree of *x* belonging to a FSig set is expressed

by a nested membership degree vector (with arbitrary depth), or illustrated by a rooted

tree graph where each leaf has a membership degree. As in the following various

applications (medical diagnosis, built construction evaluation, fuzzy communication of

robots, warehouse optimization, etc.) it was necessary to manipulate partly different FSig-s at the same time, the internal nodes of the graphs were attached fuzzy aggregations so partial reduction and transformation of the FSig becomes possible, in order to combine FSig-s of partially different, but essentially similar structure. While many applications were completed and they worked all right, the algebraic structure of FSig-s has never been analysed as far.

The present keynote talk is an attempt to define a series of operations, such as lattice meet and join, and two variations of partial ordering among FSig-s belonging to a certain “family”. Based on these it is possible to define an algebraic lattice over the set of nested vectors (within a family), and so, it will be proved that Fuzzy Signature Sets are a special case of Goguen’s L-fuzzy sets, thus the “new” concept is in fact a possible realisation of an “old” definition and thus it fits in the existing mathematical system of the fuzzy theory.

**Manuel Ojeda-Aciego** holds a MSc in Mathematics (1990) and a PhD in Computer Science (1996). He is currently Full Professor in the Department of Applied Mathematics, University of Málaga. He is the president of the Computer Science Committee of the Royal Spanish MathematicalSociety (2005), Area Editor of Fuzzy Fundamentals of the Intl J on Uncertainty and Fuzziness in Knowledge-based Systems, member of the Editorial Board of the IEEE Tr on Fuzzy Systems, member of the Steering Committee of the Intl Conf onConcept Lattices and their Applications (CLA) and the Intl Conf on Information Processing and Management of Uncertainty in knowledge-based systems (IPMU), member of EUSFLAT, and senior member of the IEEE. As a member of the Research Group of Applied Mathematics in Computing, his current research interests include residuated and multi-adjoint logic programming, fuzzy answer set semantics, fuzzy formal concept analysis, logical approaches to qualitative reasoning, and algebraic structures for computer science. He has authored or coauthored more than 120 papers in scientific journals and proceedings of international conferences. He has co-edited the book Foundations of Reasoning under Uncertainty (Springer-Verlag, 2010), as well as several special issues in scientific journals on mathematical and logical foundations of non-classical reasoning, and on concept lattices and their applications.

**Title: Bonds in a Fuzzy Environment**

**Abstract:** Formal Concept Analysis (FCA) has become a very active research topic, both theoretical and practical; its wide applicability justifies the need of a deeper knowledge of its underlying mechanisms, and one important way to obtain this extra knowledge turns out to be via generalization.

Several fuzzy variants of generalized FCA have been introduced and developed both from the theoretical and the practical side. Most of the generalizations focus on including extra features (fuzzy, possibilistic, rough, etc.); however, not much have been published on the suitable general version of certain specific notions, such as the bonds between formal contexts.

One of the motivations for introducing the notion of bond was to provide a tool for studying mappings between formal contexts, somehow mimicking the behavior of Galois connections between their corresponding concept lattices. In this talk we will deal with generalizations of the notion of bond in an L-fuzzy setting..