A Fuzzy measure of Openness

Peter Henderson

8th February 2012

This paper is still in preparation. The most recent draft is available from http://openpdq.com/OpenSystems.

The author can be contacted at mailto:p.henderson@ecs.soton.ac.uk

1 Summary

A measure of openness is defined that is based on an estimate of the number of independent companies that make use of an apparently open interface.

For each apparently open interface, we count two things: (i) the number of independent companies that supply modules that produce that interface and (ii) the number of independent companies that supply modules that consume that interface.

From these two pieces of data, we then calculate a measure of openness, using a straightforward fuzzy lookup table.

2 Openness

The measure of openness that we suggest (tabulated below) ranges from Very Low to Very High. The definitions and supporting arguments follow.

 Low Consumers  Medium Consumers  High Consumers
    up to a dozen          dozens          hundreds
Low Producers (one or two) Very Low Medium High
Medium Producers (a few) Low Medium High Very High
High Producers (dozens) Medium Low High Very High

It is not claimed that this measure covers all aspects of openness. We comment on other aspects of openness in our analysis at the end of this report. The benefits of openness are well established and have been discussed in an earlier paper.

3 Definitions

The systems we are interested in are very large and complex and typically supplied by a network of companies. Good examples of such systems are telecomms platforms such as mobile phones, any web-based commercial application or any large public-sector procurement.

We assume a complex modular structure for a system of interest and assume that we can identify the interfaces across which modules are connected. Modules are supplied by Companies. Modules have Interfaces. Modules are connected to each other over these interfaces. In a market, a company will choose to develop a module in order to supply a particular interface. It will do so in the context of being able to rely on other modules (from independent companies) being able to supply other interfaces on which this new product depends.

Many interfaces will be proprietary. Some however will be Open in the sense that their precise details are published and fixed, in the sense that their established capabilities can be relied upon to continue through a lifetime of capability enhancement. This fixedness might be assured by the interface adhering to some standard governed by a standards body. Equally often however, an open interface will simply be de facto open, the market supports it. For example, many operating systems for computers or mobile phone systems are the property of single companies (or legally conjoined companies). Their market depends on them maintaining fixedness of their capabiliies (enhancements being backwards compatible). So, although the interface is owned by one company, other independent companies can confidently base a business case on its continued availability.

4 Calculating the Measure

The measure tabulated above purports to measure the openness of an interface, the degree to which we can trust the interface to continue to supply the capabilities that we need. The measure is based on an assumption that we can estimate the number of independent companies that supply modules producing the interface and we can estimate the number of independent companies that supply modules consuming the interface.

The scale for estimating producers is fuzzily one-or-two, a-few, dozens. These categories intentionally overlap. Choose the one which you think best captures your confidence in the market. For example for Microsoft Windows, you'd have to choose one-or-two, while for Linux you would probably choose a-few. For an interface giving the capability of displaying video, for example, you might choose dozens.


The scale for estimating consumers is different. First, we are not referring here to end-users, but to companies that supply product that depend on the interface we are measuring. Again we estimate fuzzily using the categories up-to-a-dozen, dozens, hundreds. These categories intentionally overlap, so again choose the one which you think best captures your confidence in the market. For example for Microsoft Windows and for Linux, you'd have to choose hundreds, while for some specialised operating system, such as those supplied in specialist areas such as defence you would probably choose up-to-a-dozen.


Clearly, we could have chosen narrower categories and for any particular application area it may be appropriate to do that. We believe the categories chosen here are sufficient to illustrate our intention.

The scale for representing openess is finer. We use the categories Very-Low, Low, Medium Low, Medium, Medium High, High and Very High. Again these categories intentionally overlap. For example for Microsoft Windows, our openness would be characterised as High, while for Linux it would be Very High. A specialised operating system, such as those supplied in defence you would probably only rank Very Low.