Fuzzy Concept - Analysis

Analysis

In mathematical logic, programming, philosophy and linguistics fuzzy concepts can be analyzed and defined more accurately or comprehensively, by describing or modelling the concepts using the terms of fuzzy logic. More generally, techniques can be used such as:

• specifying a range of conditions to which the concept applies (for example, in computer programming of a procedure).
• classifying or categorizing all or most cases or uses to which the concept applies (taxonomy).
• probing the assumptions on which a concept is based, or which are associated with its use (Critical thought).
• identifying operational rules for the use of the concept, which cover all or most cases.
• allocating different applications of the concept to different but related sets (e.g. using Boolean logic).
• examining how probable it is that the concept applies, statistically or intuitively.
• examining the distribution or distributional frequency of (possibly different) uses of the concept.
• some other kind of measure or scale of the degree to which the concept applies.
• specifying a series of logical operators (an inferential system or algorithm) which captures all or most cases to which the concept applies.
• mapping or graphing the applications of the concept using some basic parameters.
• applying a meta-language which includes fuzzy concepts in a more inclusive categorical system which is not fuzzy.
• reducing or restating fuzzy concepts in terms which are simpler or similar, and which are not fuzzy or less fuzzy.
• relating the fuzzy concept to other concepts which are not fuzzy or less fuzzy, or simply by replacing the fuzzy concept altogether with another, alternative concept which is not fuzzy yet "works exactly the same way".

In this way, we can obtain a more exact understanding of the use of a fuzzy concept, and possibly decrease the amount of fuzziness. It may not be possible to specify all the possible meanings or applications of a concept completely and exhaustively, but if it is possible to capture the majority of them, statistically or otherwise, this may be useful enough for practical purposes.

A process of defuzzification is said to occur, when fuzzy concepts can be logically described in terms of (the relationships between) fuzzy sets, which makes it possible to define variations in the meaning or applicability of concepts as quantities. Effectively, qualitative differences may then be described more precisely as quantitative variations or quantitative variability (assigning a numerical value then denotes the magnitude of variation).

The difficulty that can occur in judging the fuzziness of a concept can be illustrated with the question "Is this one of those?". If it is not possible to clearly answer this question, that could be because "this" (the object) is itself fuzzy and evades definition, or because "one of those" (the concept of the object) is fuzzy and inadequately defined.

Thus, the source of fuzziness may be in the nature of the reality being dealt with, the concepts used to interpret it, or the way in which the two are being related by a person. It may be that the personal meanings which people attach to something are quite clear to the persons themselves, but that it is not possible to communicate those meanings to others except as fuzzy concepts.