There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Formal concept analysis via multi-adjoint concept lattices

Multi-adjoint t-concept lattices

Multi-adjoint property-oriented and object-oriented concept lattices

Fuzzy systems have been used widely thanks to their ability to successfully solve a wide range of problems in different application fields. However, their replication and application require a high level of knowledge and experience. Furthermore, few researchers publish the software and/or source code associated with their proposals, which is a major obstacle to scientific progress in other disciplines and in industry. In recent years, most fuzzy system software has been developed in order to facilitate the use of fuzzy systems. Some software is commercially distributed, but most software is available as free and open-source software, reducing such obstacles and providing many advantages: quicker detection of errors, innovative applications, faster adoption of fuzzy systems, etc. In this paper, we present an overview of freely available and open-source fuzzy systems software in order to provide a well-established framework that helps researchers to find existing proposals easily and to develop well-founded future work. To accomplish this, we propose a two-level taxonomy, and we describe the main contributions related to each field. Moreover, we provide a snapshot of the status of the publications in this field according to the ISI Web of Knowledge. Finally, some considerations regarding recent trends and potential research directions are presented.

/pdf/a-survey-of-fuzzy-systems-software-taxonomy-current-research-13ece2jf0f.pdf

A Survey of Fuzzy Systems Software: Taxonomy, Current Research Trends, and Prospects

https://titan.inf-cr.uclm.es/www/pjulian/publications/FSS05/fss05.pdf

On fuzzy unfolding: A multi-adjoint approach

During the last two years, our developments regarding the design of the FLOPER tool ("Fuzzy LOgic Programming Environment for Research"), have been devoted to implant in its core a rule-based, easy representation of lattices representing fuzzy notions of truth degrees beyond the boolean case, in order to work with flexible programs belonging to the so-called multi-adjoint logic approach. Now, the system improves its initial running/debugging/tracing capabilities for managing this kind of fuzzy logic programs, with new options for manipulating in a classical Prolog style the mathematical foundations of the enrichment introduced by multi-adjoint lattices. In particular, we show that for a given program and query, many different answers can be obtained when changing the assumption of truth in a single work session. The experience related here evidences the expressive power of Prolog rules (i.e., clauses) for implementing rich versions of multi-adjoint lattices in a very easy way, as well as its crucial role in further fuzzy logic computations.

A practical management of fuzzy truth-degrees using FLOPER

Multi-adjoint logic programming represents a very recent, extremely flex- ible attempt for introducing fuzzy logic into logic programming. In this setting, the execution of a goal w.r.t. a given program is done in two separate phases. During the operational one, admissible steps are systematically applied in a similar way to classi- cal resolution steps in pure logic programming, thus returning a computed substitution together with an expression where all atoms have been exploited. This last expression is then interpreted under a given lattice during the so called interpretive phase, hence returning a value which represents the fuzzy component (truth degree) of the computed answer. On the other hand, unfolding is a well known transformation rule widely used in declar- ative programming for optimizing and specializing programs, among other applications. In essence, it is usually based on the application of operational steps on the body of program rules. The novelty of this paper consists in showing that this process can also be made in terms of interpretive steps. We present two strongly related kinds of unfolding (operational and interpretive), which, apart from exhibiting strong correct- ness properties (i.e. they preserve the semantics of computed substitutions and truth degrees) they are able to significantly simplify the two execution phases when solving goals.

/pdf/operational-interpretive-unfolding-of-multi-adjoint-logic-5dunqe1bwe.pdf

Operational/Interpretive Unfolding of Multi-adjoint Logic Programs

Time and space variations in mercury and other trace element contents in olive tree leaves from the Almadén Hg-mining district

The "Fuzzy LOgic Programming Environment for Research", FLOPER in brief, that we have implemented in our research group, is intended to help the development of rule-based applications supporting fuzzy logic and approximated reasoning. The system is able to directly translate a powerful kind of fuzzy logic programs (belonging to the so-called multi-adjoint logic approach ) into Prolog code which can be directly executed inside any standard Prolog interpreter in a completely transparent way for the final user. The system also generates a low-level representation of the fuzzy code offering debugging (tracing) capabilities with close connections to other program manipulation tasks (optimization, specialization, etc). Our approach focuses on practical and technical aspects on rule-based reasoning with uncertain and fuzzy information.

Ginés Moreno

Papers

On fuzzy unfolding: A multi-adjoint approach

A practical management of fuzzy truth-degrees using FLOPER

Operational/Interpretive Unfolding of Multi-adjoint Logic Programs

Time and space variations in mercury and other trace element contents in olive tree leaves from the Almadén Hg-mining district

Programming with Fuzzy Logic Rules by Using the FLOPER Tool