# [Vortrag] Computing with Words and its Applications to Information Processing, Decision and Control

Die FAKULTÃ„T FÃœR INFORMATIK in Zusammenarbeit mit der FAKULTAET FÃœR MATHEMATIK UND GEOWISSENSCHAFTEN an der TU Wien lÃ¤dt zu folgendem Vortrag ein:

# Computing with Words and its Applications to Information Processing, Decision and Control

Fuzzy logic has been Â and to some extent still is Â an object of controversy.

Some are turned-off by its name. But,more importantly, fuzzy logic is tolerant of imprecision and partial truth.

It is this tolerance that is in conflict with thedeep-seated Cartesian tradition of aiming at truth which isbivalent, with no shades of gray allowed.

There are many misconceptions about fuzzy logic. In large measure, the misconceptions reflect the fact that

the term fuzzy logic has two distinct interpretations. More specifically, in a narrowsense, fuzzy logic is the logic of approximate reasoning:

But in a wider sense Â which is in dominant use today Â fuzzylogic, denoted as FL, is coextensive with the theory of fuzzysets, and contains fuzzy logic in its narrow sense as one ofits branches.

In fact, most applications of FL involve modes of analysis which are computational rather than logical innature.

Fuzzy logic, FL, has four principal facets. First, thelogical facet, FL , which is fuzzy logic in its narrow sense. Second, the set-theoretic facet, FLs, which is concerned with classes having unsharp boundaries, that is, with fuzzy sets. Third, the relational facet, FLr, which is concerned with linguistic variables, fuzzy if-then rules and fuzzy relations.

It is this facet that underlies almost all applications of fuzzylogic in control, decision analysis, industrial systems andconsumer products. And fourth, the epistemic facet, FLe,which is concerned with knowledge, meaning and linguistics.

One of the important branches of FLe is possibility theory.

A concept which has a position of centrality in FL is thatof fuzzy granularity or, simply, f-granularity.

F-granularity reflects the bounded ability of human sensory organs and, ultimately, the brain, to resolve detail and store information.

In particular, human perceptions are, for the most part, f-granular in the sense that (a) the boundaries of perceivedclasses are fuzzy, and (b) the perceived attributes are granu-lated, with a granule being a clump of values drawn togetherby indistinguishability, similarity, proximity or functionality.

In this perspective, the colors red, blue, green, etc., maybe viewed as labels of granules of perception of color.

Precision carries a cost. This is the main reason why in most ofits applications, the machinery of fuzzy logic is employed to exploit the tolerance for imprecision for achieving tractability, robustness and low solution cost.

In fact, it is the tolerance for imprecision that underlies the remarkable humancapability to perform a wide variety of physical and mental tasks, e.g., drive in city traffic,

based solely on perceptions, without any measurements and any computations.

It is this capability that motivated the development of fuzzy-logic-based computational theory of perceptions (CTP).

Existing theories and, in particular, probability theory, do not have the capability to operate on perception-based information.

The computational theory of perceptions is a branchof the fuzzy-logic-based methodology of computing with words and perceptions (CWP).

Development of the methodology of computing with words is an important event in theevolution of fuzzy logic.

Eventually, it may lead to a radical enlargement of the role of natural languages in information processing, decision, and control.