Computing with words and perceptions
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Computing with words (CWW) is a methodology in which the objects of computation are words and propositions drawn from a natural language. It is inspired by the remarkable human capability to perform a wide variety of physical and mental tasks without any measurements and any computations. CWW may have an important bearing on how humans make perception-based rational decisions in an environment of imprecision, uncertainty and partial truth.
Definition
Professor Zadeh coined the phrase “computing with words” (CWW) in his 1996 paper “Fuzzy Logic = Computing with Words.” It has grown in visibility and recognition since then. Zadeh pointed out that there are two basic rationales for the use of computing with words. First, when we have to use words because we do not know the numbers. And second, when we know the numbers but the use of words is simpler and cheaper, or when we use words to summarize numbers. In large measure, the importance of computing with words derives from the fact that much of human knowledge is described in natural language. In one way or another, the fuzzy-logic-based machinery of computing with words opens the door to a wide-ranging enlargement of the role of natural languages in scientific theories, including scientific theories which relate to economics, medicine, law, and decision analysis.
Of course, Zadeh did not mean that computers would actually compute using words—single words or phrases—rather than numbers. He meant that computers would be activated by words, which would be converted into a mathematical representation using fuzzy sets, and that these fuzzy sets would be mapped by a CWW engine into some other fuzzy set, after which the latter would be converted back into a word.
Guidelines for calling something CWW
Many different approaches have been proposed under the name of CWW, e.g., perceptual computing, the 2-tuple fuzzy linguistic representation model, linguistic summarization, etc. Wu and Mendel proposed the following guidelines for calling something “CWW” in the form of three tests. A fourth test is optional but is strongly suggested.
1. A word must lead to a membership function rather than a membership function leading to a word.
When one begins with a fuzzy set, one begins with the membership function of that set, i.e. a mathematical description of that set. It matters not what that fuzzy set is called because the same membership function is associated with each and every name chosen for the set, and when the fuzzy set is programmed for a computer, the computer does not care about the name of the fuzzy set---it only implements the mathematical formula of the membership function. For example, if temperature is partitioned into three overlapping intervals, and fuzzy sets are established for the three partitions, these sets could be called low, medium and high, T1, T2 and T3, or any other three names.
On the other hand, when one begins with a word and wants to use a fuzzy set to model it, then some knowledge or information about the word has to lead to the fuzzy set. Just as there can be different kinds of models that describe a dynamical system, there can be different kinds of fuzzy set models that describe a word. When physical laws are used to model a dynamical system, then one obtains an internal representation of the system. When only data are available about a dynamical system, then one obtains an external representation of the system. Similarly, when some laws about words are used to model them, then one obtains an internal representation of the words. When data are available about words, then one obtains an external representation about the words.
2. Numbers alone may not activate the CWW engine (e.g., IF-THEN rules).
Numbers are modeled as singleton fuzzy sets and there is nothing fuzzy about them. At least one word must activate the CWW engine and it must be modeled by a non-singleton fuzzy set, e.g. a fuzzy number. If the CWW engine is comprised of rules, then singleton fuzzification alone is not permitted, because a fuzzy singleton is not a legitimate model of a word. Rules must be activated by fuzzy sets, and so in CWW one is always in the so-called non-singleton fuzzification situation. This is very different from a rule-based fuzzy logic system that is used for function approximation kinds of applications, where almost everyone uses singleton fuzzification to keep things simple.
3. The output from CWW must be at least a word and not just a number.
CWW implies ``words in and words out; however, people also like to get data to back up the words (e.g., if your supervisor tells you your performance is unsatisfactory, then you ask ``why? and the answer to this has to be backed up with data), so words and data are okay as outputs from CWW. Words alone are okay for CWW, but data alone are not okay as outputs from CWW, e.g., for a rule-based CWW engine, if the output is only a defuzzified number, then this is not CWW (it's a fuzzy logic system or a fuzzy logic controller, etc.). If, however, that defuzzified number is somehow mapped into a word, then this is CWW, and the combined defuzzified number and its associated word are also CWW. An example of a mapping that leads to both a number and a word is ranking, e.g. proposals A, B, C, and D are ranked 2 (next-to-the best), 4 (worst), 1 (best) and 3 (next-to-the worst), respectively. Of course, in CWW something other than defuzzification may be used to aggregate fired-rule output-sets, e.g., a fuzzy weighted average or a linguistic weighted average, leading to another fuzzy set that is mapped into the word it most closely resembles.
4. Because words mean different things to different people, they should be modeled using at least interval type-2 fuzzy sets.
A consequence of using at least interval type-2 fuzzy sets as models for words is that all computations performed by a CWW engine will then be for at least interval type-2 fuzzy sets. Another consequence of this requirement is that researchers who have developed novel and interesting ideas for CWW in the framework of type-1 fuzzy sets could re-examine those ideas using at least interval type-2 fuzzy sets. This test is ``optional so as not to exclude much research on CWW that uses type-1 fuzzy sets.
See also
References
F. Herrera and L. Martinez, “A 2-tuple fuzzy linguistic representation model for computing with words,” IEEE Trans. on Fuzzy Systems, vol 8, no. 6, pp. 746 – 752, 2000.
Janusz Kacprzyk and Sawomir Zadrony, “Computing with words in intelligent database querying: standalone and Internet-based applications,” Information Sciences, vol 134, no. 1-4, pp. 71-109, 2001.
Sankar Kumar Pal, Lech Polkowski and Andrzej Skowron (Eds), Rough-Neural Computing: Techniques For Computing With Words, Springer, 2003.
J. Lawry, “An alternative to computing with words,” Int’l. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 9, Suppl., pp. 3–16, 2001.
J.M. Mendel, “Computing with words and its relationships with fuzzistics,” Information Sciences, vol. 177, pp. 988–1006, 2007.
J.M. Mendel, "Computing With Words: Zadeh, Turing, Popper and Occam," IEEE Computational Intelligence Magazine, Vol. 2, pp. 10-17, November 2007.
J.M. Mendel, J. Lawry, L.A. Zadeh, “Foreword to the Special Section on Computing With Words,” IEEE Trans. on Fuzzy Systems, vol 18, no 3, pp. 437-440, 2010.
J. M. Mendel and D. Wu, Perceptual Computing: Aiding People in Making Subjective Judgments. Hoboken, NJ: Wiley-IEEE Press, 2010.
Jerry M. Mendel, Lotfi A. Zadeh, Enric Trillas, Ronald Yager, Jonathan Lawry, Hani Hagras, Sergio Guadarrama, “What Computing with Words Means to Me,” IEEE Computational Intelligence Magazine, Vol. 2, pp. 20-26, November 2010.
S.H. Rubin, “Computing with words,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol 29, no 4, pp. 518 – 524, 1999.
Huaiqing Wang and Daowen Qiu, “Computing with words via Turing machines: a formal approach,” IEEE Trans. on Fuzzy Systems, vol 11, no 6, pp. 742 – 753, 2003.
P.P. Wang (Ed.), Computing With Words, John Wiley & Sons, Inc., New York, 2001.
L.A. Zadeh, “Fuzzy logic = computing with words,” IEEE Trans. on Fuzzy Systems, vol. 4, pp. 103–111, 1996.
L.A. Zadeh, “From computing with numbers to computing with words—from manipulation of measurements to manipulation of perceptions,” IEEE Trans. on Circuits and Systems–I: Fundamental Theory and Applications, vol. 4, pp. 105–119, 1999.
L.A. Zadeh and J. Kacprzyk (Eds.), Computing With Words in Information/Intelligent Systems 1 & 2, Physica-Verlag, New York, 1999.
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