Managerial decision-making

Linguistic fuzzy IF-THEN make it possible to distinguish sufficiently subtly and, at the same time, aptly, various degrees of fulfilling of the respective criteria, their various importance and, moreover, it may also overcome possible discrepancies. Degrees of importance are naturally included in the linguistic characterization and so, the usual problem of assigning weights to the criteria disappears. This is a great advantage because the methods for weights assignment, though sophisticated, are rather intricate and still much subjective.

The decision problem is usually decomposed into a hierarchy of linguistic descriptions which helps to deeper understanding to structure of the decision problem and reduces the number of variables (criteria) in the respective fuzzy IF-THEN rules.

Demonstration

A company wants to buy a new building. The decision is influenced by economical conditions of the company and by several characteristics, some of them being difficult or impossible to quantify.

Important decision characteristics

Economical conditions of the company – they can be characterized using, e.g., gain over several years. Its trend can be estimated using fuzzy transform. Evaluation of the trend can be done using the following fuzzy IF-THEN rules: IF GainChange(t-3) is + Small AND GainChange(t-2) is + Medium AND GainChange(t-1) is + Big THEN Economical Conditions is +Very Big
Economical characteristics of the new building that may consist of the following detailed characteristics: – Price, – Reconstruction costs, – Maintenance costs, – Taxes, etc.
Technical characteristics of the new building – Total living area in square m, – No. of floors, etc.
Aesthetical characteristics – Global appearance, – Stylishness, etc.
Infrastructure characteristics (place, etc.)

One can see our way of elaboration of linguistic descriptions allows us to include easily also characteristics that are practically impossible to quantify (but people are able to assign them certain degrees of quality).

Global evaluation of each building can be done using linguistic description consisting of fuzzy IF-THEN rules of the following form:

IF EconConditions is + Big AND EconChar is + More or less Big AND
TechChar is + Roughly Big AND AestChar is + Very Big
THEN GlobEval is + More or less Big

Results of practical computation

Economical conditions of the company have been evaluated as Good (0.9)

Variant	Global evaluation		Economical characteristics	Technical characteristics	Aesthetical characteristics
	numerically	verbally	numerically	numerically	numerically
Building 1	0.49	very roughly good	0.53	0.47	0.77
Building 2	0.54	very roughly good	0.54	0.78	0.77
Building 3	0.85	good	0.9	0.78	0.77
Building 4	0.92	significantly good	0.9	0.78	0.93

On the basis of our computation we will choose Building 4 as the best fitting all our requirements.
[2] NOVÁK, V. Foundations of fuzzy modeling (Základy fuzzy modelování). Praha: BEN-technická literatura, 2000. 166 pp. ISBN 80-7300-009-1 (in Czech).
[3] NOVÁK, V., KOVÁŘ, J. Linguistic IF-THEN Rules in Large Scale Application of Fuzzy Control. In Fuzzy If-Then Rules in Computational Intelligence: Theory and Applications. Boston : Kluwer, 2000. ISBN 0-7923-7820-2. pp. 223-241.

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