Fuzzy Geometry-Based Decision Making with Unprecisiated Visual Information

Abstract

Decision making is conditioned by relevant information. This information very seldom has reliable numerical representation. Usually, decision-relevant information is perception-based. A question arises of how to proceed from perception-based information to a corresponding mathematical formalism. When perception-based information is expressed in natural language, the fuzzy set theory can be used as a corresponding mathematical formalism for decision analysis. However, perception-based decision-relevant information is not always sufficiently clear to be modeled by means of membership functions. In contrast, it remains at a level of some cloud images which are difficult to be caught by words. This imperfect information caught in perceptions cannot be precisiated by numbers or fuzzy sets and is referred to as unprecisiated information. Humans are able to make decisions based on unprecisiated visual perceptions. Modeling of this outstanding capability, even to some limited extent, becomes a difficult yet a highly promising research area. In this study, we use fuzzy geometry and the extended fuzzy logic to cope with uncertain situations coming with unprecisiated information. In this approach, the objects of computation and reasoning are geometric primitives which model human perceptions when the latter cannot be defined in terms of membership functions. For this aim, the fuzzified axioms of the incidence geometry are used. An approach to decision making with outcomes and probabilities described by geometrical primitives is developed. Examples of application of the approach to decision making on a short term investment decision and marketing decision are given. The obtained results prove the validity of the suggested approach.