Axiomatic Theory of Complex Fuzzy Logic and Complex Fuzzy Classes

Complex fuzzy sets, classes, and logic have an important role in applications, such as prediction of periodic events and advanced control systems, where several fuzzy variables interact with each other in a multifaceted way that cannot be represented effectively via simple fuzzy operations such as union, intersection, complement, negation, conjunction and disjunction. The initial formulation of these terms stems from the definition of complex fuzzy grade of membership. The problem, however, with these definitions are twofold: 1) the complex fuzzy membership is limited to polar representation with only one fuzzy component. 2) The definition is based on grade of membership and is lacking the rigor of axiomatic formulation. A new interpretation of complex fuzzy membership enables polar and Cartesian representation of the membership function where the two function components carry uncertain information. Moreover, the new interpretation is used to define complex fuzzy classes and develop an axiomatic based theory of complex propositional fuzzy logic. Additionally, the generalization of the theory to multidimensional fuzzy grades of membership has been demonstrated. In this paper we propose an axiomatic framework for first order predicate complex fuzzy logic and use this framework for axiomatic definition of complex fuzzy classes. We use these rigorous definitions to exemplify inference in complex economic systems. The new framework overcomes the main limitations of current theory and provides several advantages. First, the derivation of the new theory is based on axiomatic approach and does not assume the existence of complex fuzzy sets or complex fuzzy classes. Second, the new form significantly improves the expressive power and inference capability of complex fuzzy logic and class theory. The paper surveys the current state of complex fuzzy sets, complex fuzzy classes, and complex fuzzy logic; and provides an axiomatic basis for first order predicate complex fuzzy logic and complex class theory

An evaluation methodology for ergonomic design of electronic consumer products based on fuzzy axiomatic design

This article is posted with permission of OCP Science imprint. Copyright @ 2008 Old City Publishing Group.The development life cycle of software and electronic products has been shortened by the growth of rapid prototyping techniques. The evaluation of electronic consumer products should consider hardware and software as well as the ergonomic usability, emotional appeal and aesthetic integrity of the design. This research follows a systematic approach to develop an evaluation methodology for electronic mobile products on ergonomic design. The proposed methodology is based on fuzzy multi attribute decision making and fuzzy axiomatic design realized in three steps; determination of ergonomic attributes for electronic consumer products, determination of a representative set of alternatives, and selection of the best alternative in terms of ergonomic design by utilizing fuzzy axiomatic design. A case study is also provided to support the proposed methodology

On the Origin of Abstraction : Real and Imaginary Parts of Decidability-Making

International audienceThe behavioral tradition has largely anchored on Simon's early conception of bounded rationality, it is important to engage more explicitly cognitive approaches particularly ones that might link to the issue of identifying novel competitive positions. The purpose of the study is to describe the cognitive processes by which decision-makers manage to work, individually or collectively, through undecidable situations and design innovatively. Most widespread models of rationality developed for preference-making and based on a real dimension should be extended for abstraction-making by adding a visible imaginary one. A development of a core analytical/conceptual apparatus is proposed to purposely account this dual form of reasoning, deductive to prove (then make) equivalence and abstractive to represent (then unmake) it. Complex numbers, comfortable to describe repetitive, expansional and superimposing phenomena (like waves, envelope of waves, interferences or holograms, etc.) appear as generalizable to cognitive processes at work when redesigning a decidable space by abstraction (like relief vision to design a missing depth dimension, Loyd's problem to design a missing degree of freedom, etc.). This theoretical breakthrough may open up vistas capacity in the fields of information systems, knowledge and decision

Fuzzy Logic in Clinical Practice Decision Support Systems

Computerized clinical guidelines can provide significant benefits to health outcomes and costs, however, their effective implementation presents significant problems. Vagueness and ambiguity inherent in natural (textual) clinical guidelines is not readily amenable to formulating automated alerts or advice. Fuzzy logic allows us to formalize the treatment of vagueness in a decision support architecture. This paper discusses sources of fuzziness in clinical practice guidelines. We consider how fuzzy logic can be applied and give a set of heuristics for the clinical guideline knowledge engineer for addressing uncertainty in practice guidelines. We describe the specific applicability of fuzzy logic to the decision support behavior of Care Plan On-Line, an intranet-based chronic care planning system for General Practitioners