Enriched fuzzy relational algebras based on BK-products of relations have representational and computational means for handling both, concrete numerical representations of relations extensively used in applications, as well as high level symbolic forms. Such forms can be used for symbolic manipulation of relations that have been abstracted from numerical representations. Symbolic forms can be handled equationally. Equations over BK-products can characterise relational properties in a universal way. The described tool facilitates transformations between these different forms.

This paper continues investigation of systems of fuzzy interval logics based on the checklist paradigm semantics of Bandler and Kohout (1993). While the previous work was mainly concerned with the interval systems containing commutative AND and OR, this paper describes the system in which these connective types are non-commutative. While the commutative systems can be sufficiently characterized by an 8-element group of transformations, the non-commutative require the symmetric 16 element group S2times2times2times2

We present a general framework for solving fuzzy relational equations in monoidal logics. This framework yields the general solution equations for relational systems based on large family of many-valued logics. The proofs use as a tool certain relational inequalities that we call BK-residuated bootstrap. First we extend to the realm of relational systems in monoidal logics the previous results concerning the BK-residuated bootstrap that were obtained by Kohout for relational inequalities based on fuzzy basic logic systems (BL) of Hajek (published in Proceedings of FUZZ-IEEE 2000) and also for relational systems based on left-continuous t-norms. Then we use the BK-residuated bootstrap for proving the results concerning relational equations. It should be noted that solutions for relational systems based on linear logics and intuitionistic logics are included as special cases.

We are involved in the construction of problem solving environments for coupled climate modeling. Numerical simulations of climate models that include atmospheric, oceanographic, geological, and other sub-models need to coordinate information along the boundaries between the sub-models in order to model correctly the interaction between the disparate sub-systems. Conventional high performance computing programming paradigms make it difficult for users to integrate existing model components such as atmosphere, oceans, and chemistry because of the absence of uniform model development; no mechanism for integrating research results exists. This situation can be substantially remedied by the use of problem solving environments (PSE) : A PSE is a computer system that provides all the computational facilities necessary to solve a target class of problems. These features include advanced solution methods, automatic and semi-automatic selection of solution methods, and ways to easily incorporate novel solution methods. This application area leads us to the components that a PSE of this kind requires.

The paper outlines the employment of fuzzy relational computations and fuzzy BK-products of relations in building architectures of intelligent geographic information systems (GIS) and decision support. The purpose of such systems is to analyse and interpret data to be used in geographic research. Our emphasis is on digital satellite imagery, a data stream that is commonly used to generate land use and land cover maps with which other GIS data are integrated. In order to efficiently apply methods of computational intelligence and soft computing to the project, a new conceptual framework is needed, in which the data, knowledge and activities of computing systems and human participants are jointly considered. Our framework distinguishes objects, properties, attributes, observers, contexts and perspectives and relations between these. The formal specification methods employ semiotic descriptors combined with fuzzy relational systems, algebraically defined by means of nonassociative BK-products of relation. BK-products are used not only for specifications but also in parallel computations in evaluation of data.

This paper shows how temporal Allen algebra relations can be embedded into a recursive structure called RATA (Recursive Allen Temporal Algebra). This structure is required in order to allow the maximal representational power of temporal relations. The question of the fuzzification of RATA is also discussed.

Relational computing structures make it possible to perform knowledge representation as well as all the computations in intelligent systems in a unified way. When crisp computations are replaced by fuzzy relational computations, it is possible to improve significantly handling of indeterminacy and incompleteness of information. Fuzzy computational structures in which cuts commute with closures over relational properties, provide in addition the means for significant data compression, resulting in significant speedup of computations. BK-relational products provide axiomatics necessary for constructive computational procedures that rigorously satisfy the above formulated requirements. This paper provides the mathematical overview of concepts needed for fuzzy relational computations and the rigorous mathematical proofs of inequalities relating triangle BK-products to standard t-norm based compositions of relations. The proofs of correctness of these crucial computational relationships is performed in basic logic of Hajek (1996, 1998), which is the fuzzy predicate logic axiomatization of t-norm based residuated fuzzy logics. The paper concludes with a survey of the use of BK-products in scientific, medical, engineering and business applications, information retrieval, automated reasoning, etc.

This paper describes the method we have developed for cost/performance comparison of technological objects using fuzzy interval ranking computation method. First, fuzzy logics, RE-fuzzy relational products and fast fuzzy relational algorithms implemented in the TRISYS software are used to compute the fuzzy pre-ordering of technological objects. Next, fuzzy interval ranking computation method, called FIRE, is applied to thus obtained fuzzy relational structures in order to compute the ranks of technological objects, representing these as fuzzy intervals. The choice of fuzzy interval logics for FIRE method has to be supported by adequate epistemic theory of algorithms that compute fuzzy interval results. For this purpose FIRE combines the checklist paradigm semantics of fuzzy logic with a ranking aggregation method which yields fuzzy intervals. The algorithm of FIRE method is described in detail and a case study of its application to high technology problems of the aviation industry is presented.