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Computing with words (CWW) means different things to different people. This article is the start of a position paper, written by some of the members of the CIS Fuzzy Systems Technical Committee Task Force on CWW, that answers the question “What does CWW mean to me?” 1 Chairman of the CWW task force. All of the other authors are members of this task force. 2 This is a task force of the Fuzzy Systems Technical Committee of the IEEE Computational Intelligence Society. 3 Different acronyms have been used for Computing With Words—CW, CWW and CWP. The latter is short for Computing With Perceptions. Since the phrase Computing With Words has three words in it, I will use CWW in this article. Digital Object Identifier 10.1109/MCI.2009.934561 4 Taken from e-mail “CFP-Position Paper Submission for ICAART 2009,” (International Conference on Agents and AI), V. Rosario, ICAART Secretariat. © STOCKBYTE Authorized licensed use limited to: Univ of Calif Berkeley. Downloaded on March 04,2010 at 20:12:19 EST from IEEE Xplore. Restrictions apply. FEBRUARY 2010 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 21 description of perceptions. It is at this point that Computing with Words enters the picture. In essence, Computing with Words is a methodology for reasoning, computing and decision-making with information described in natural language. It is this methodology, described in my paper, “From Computing with Numbers to Computing with Words— From Manipulation of Measurements to Manipulation of Perceptions,” [IEEE Trans. on Circuits and Systems, vol. 45, no. 1, pp. 105–119, 1999] that is needed for computation with natural language descriptions of perceptions. Underlying Computing with Words are three principal rationales. First, much of human knowledge is described in natural language. Second, words are less precise than numbers—we use words when we do not know the numbers. In this perspective, Computing with Words may be viewed as a powerful formalism for dealing with imprecise information. And third, precision carries a cost. If there is a tolerance for imprecision, it can be exploited through the use of words in place of numbers. This is the key idea that underlies the machinery of linguistic variables and fuzzy if-then rules—a machinery which is employed in almost all applications of fuzzy logic, especially in the realms of consumer products and industrial systems. By adding to the armamentarium of AI an effective tool for reasoning and computing with information described in natural language, Computing with Words opens the door to a to a wideranging enlargement of the role of natural languages in science and engineering. Hani Hagras: I agree with the above definition and comments, however as mentioned above words are imprecise and uncertain and this is why as mentioned above “ we use words when we do not know the numbers”. Hence, can we say that when employing fuzzy sets, it will be better to employ higher order fuzzy sets like type-2 fuzzy sets rather than type-1 fuzzy sets where the higher order fuzzy sets will be able to better model the uncertainty rather than type-1 sets which use precise and crisp membership function. For example, for the word of “warm” temperature, it seems that using a type-1 set will constrain the uncertainty associated with this word across multiple users and even for the same user his concept of warm will change according to the location, season, location, etc. However using type-2 fuzzy sets will be able to better model the faced uncertainties associated with this word through the Footprint of Uncertainty and the third dimension of the type-2 fuzzy set. Sergio Guadarrama: You have said “a natural language is basically a system for description of perceptions.” It is usually said that a natural language is basically a system for communicating information. But we can communicate descriptions of perceptions, descriptions of actions, descriptions of intentions, descriptions of feelings. [Can you clarify this?] Lotfi Zadeh: There are many misconceptions about what Computing with Words (CW or CWW) is and what it has to offer. A common misconception is that CW and natural language processing are closely related. In reality, the opposite is the case. More importantly, what is widely unrecognized at this juncture is that moving from computation with numbers to computation with words has the potential for evolving into a basic paradigm shift—a paradigm shift which would open the door to a wide-ranging enlargement of the role of natural languages in scientific theories. The constructive comments of Sergio Guadarrama, Hani Hagras, Jonathan Lawry, Jerry M. Mendel, Enric Trillas and Ronald Yager serve to clarify what CW is and suggest new avenues for exploration of its applications. In the Appendix, I add to my earlier comment a brief updated exposition of the basic concepts and ideas that underlie CW. The updated version is a significant improvement over earlier versions. III. Enric Trillas on CWW CWW is not yet a well established field of research, but is one in course of development whose name cannot be still the subject of a clear-cut definition. It represents a good opportunity for extending fuzzy logic to copy with some complex problems related with linguistic, contextual, and purpose-oriented meaning. In my view, Zadeh’s seminal ideas on CWW could lead to results with a big impact in science, technology, and society. In addition, CWW means a “challenge” for people working in both the theoretic and the technology sides of fuzzy logic. A challenge that eventually if successful, even could help to pose CWW itself as a new experimental science, managing the concepts and tools of computer science, and actually interacting with other disciplines. I think that a good mastering on current fuzzy logic is essential to work in CWW. On the theoretic side what right now seems extremely interesting is the design and realization of experiments within natural language related with the meaning’s representation of larger and more complex linguistic expressions than those currently considered in the applications of fuzzy logic. Experiments should pursue two goals: (i) Finding the limits of the current theoretic armamentarium of fuzzy logic, and (ii) Finding and developing new mathematical and algorithmic models, that could allow us to represent what cannot be done by means of, for instance, the standard algebras of fuzzy sets. Such experiments could also help to advance the comprehension of the uncertainty coming from imprecision. 5 Bracketed comment is by Mendel, made in order to expedite a reply. Computing with Words is a methodology for reasoning, computing and decision-making with information described in natural language. Authorized licensed use limited to: Univ of Calif Berkeley. Downloaded on March 04,2010 at 20:12:19 EST from IEEE Xplore. Restrictions apply. 22 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | FEBRUARY 2010 On the technology side I can foresee two overlapping lines corresponding to hardware and software to build up respectively, electronic devices endowed with sensors and soft computing based systems directed to perform actions for social, medical, economical, technological, etc. purposes. All that is to be accomplished with an extensive use of spoken or written natural language and for recognizing, understanding, answering, and, in the end, acting in or interacting with machines, animals, persons, and organizations of several types. Hani Hagras: Again, I agree with the above comments, and especially the comment “Experiments [should be] made with the goal of finding the limits of the current theoretic armamentarium of fuzzy logic, and new mathematical and algorithmic models [should be developed] that could allow us to represent what cannot be done by means of, for example, the standard algebras of fuzzy sets.” I think also besides exploring the limits of type-1 fuzzy sets, the limits of the higher order fuzzy sets and especially general type-2 fuzzy sets need to be explored as in my opinion they appear very promising to represent words in the CWW paradigm. Enric Trillas: I took for granted, of course, that type-2 fuzzy sets are in “the current theoretic armamentarium” of fuzzy logic. Anyway, I would like to make an additional and short comment at the respect. A good reason argued in pro of type-2 fuzzy sets is that of reaching some control on the uncertainty of the membership degrees. But, since in my view its objective control deserves again more scientific study, I also wrote “Such experiments could also help to advance the comprehension of the uncertainty coming from imprecision”. IV. Ronald Yager on CWW Human beings most naturally express and understand various types of information using language. One objective of Computing with Words (CWW) is to enable the inclusion of human sourced information in the formal computer based decision-making models that are becoming more and more pervasive. Central to CWW is a translation process. This process involves taking linguistically expressed information and translating into a machine manipulative format. The types of information that have to be translated are not restricted to the linguistic values of variables but must also include linguistically expressed information for processing information. The use of OWA provides an example of this translation of processing rules. Another objective of CWW is to help in the human understanding of the results of information acquisition and information processing. This involves techniques of linguistic summarization and retranslation. Retranslation involves taking the results of the manipulation of formal objects and converting them into linguistic terms understandable to the human. Here we are going in the opposite way of the previous objective. With linguistic summarization we are trying to summarize large sets of data, with the aid of words, in a way that a human can get a global understanding of the content of the data. Sergio Guadarrama: It is not clear how OWA is an example of translation. [Can you clarify this?] Ronald Yager: The OWA operator allows one to translate and implement aggregation rules expressed using linguistic quantifiers. For example, in the context of multi-criteria decision-making, consider the linguistically stated requirement “most criteria should be satisfied.” Here “most” is an example of a linguistic quantifier. We can represent “most” as a fuzzy subset M on the unit interval where M(p) indicates the degree to which the proportion p satisfies the concept “most”. In my paper “Quantifier guided aggregation using OWA operators” [Int’l. J. of Intelligent Systems, vol. 11, pp. 49–73, 1996] I show how this fuzzy set can be used to obtain the weights of an OWA operator that can be used to provide an aggregation function that combines the satisfactions of the individual criteria to determine how well they have met the stated requirement. V. Mendel on CWW I begin with Zadeh’s seminal statement that 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. This statement is very general and means that “CWW” is a broad overarching methodology, which makes it very rich because it is open to interpretations and different instantiations. As an engineer, I begin by asking the question “How can I solve a specific (class of) problem(s) using CWW? If I am able to do this, then CWW will have been interpreted/defined (for me) for this class of problems. In this question, the word “solve” is very important because to me it contains two important steps—formulate [a solution] and implement [that solution]. Unless both steps can be accomplished, then CWW will remain a fantasy for the solution of the specific class of problems. Although the formulation of a CWW solution to a specific class of problems may appear to be quite generic, in that it may be applicable to a broad spectrum of problems, and not just the one that I am presently interested in, it is the implementation of the formulation that distinguishes one kind of CWW instantiation from another for different classes of problems. Let me be specific. I am interested in CWW for assisting people in making subjective judgments (this is a class CWW means a “challenge” for people working in both the theoretic and the technology sides of fuzzy logic. Authorized licensed use limited to: Univ of Calif Berkeley. Downloaded on March 04,2010 at 20:12:19 EST from IEEE Xplore. Restrictions apply. FEBRUARY 2010 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 23 of problems). I call my CWW formulation a Perceptual Computer (Per-C). The Per-C has three components: (1) Encoder that maps words into fuzzy set models; (2) CWW Engine that maps its input fuzzy sets into its output fuzzy sets; and, (3) Decoder that maps the CWW Engine’s output fuzzy sets into a linguistic recommendation. This formulation is quite generic, and, as I mentioned above, may be applicable to other classes of problems. In order to implement this three-stage formulation, I: (1) Establish a vocabulary of words that is application dependent; (2) Collect data from a group of subjects about all of the words in the vocabulary; (3) Map that data into a fuzzy set model for each word [the results of Steps (1)–(3) lead to the Codebook for the application, and Steps (2) and (3) implement the Encoder]; (4) Establish which CWW Engine will be used for the specific application of the Per-C (e.g., IF-THEN rules, Linguistic Weighted Average, linguistic summarization, etc.); (5) Implement the specific CWW Engine, i.e. develop (or, if it is already available, use) the mathematics for its input–output relationships; (6) Map the fuzzy set outputs of the CWW Engine into a recommendation (e.g., words, a mixture of words and numerical data that explain the words, linguistic rankings, linguistic classes) [the results of this step implement the Decoder, and make very heavy use of similarity, ranking or classification]. For this class of problems, there are, in my opinion, some guidelines for when its solution should be branded “CWW.” Without such guidelines “CWW” will just be a re-labeling of what we are already doing. The following proposed guidelines are in the form of three tests all of which I propose must be passed or else the work should not be called CWW. A word must lead to a membership 1) function rather than a membership function leading to a word. Numbers alone may not activate the 2) CWW engine. The output from CWW must be at 3) least a word and not just a number. A fourth test is optional but is strongly suggested. It is “optional” so as not to exclude much research on CWW that uses type-1 fuzzy sets, even though I strongly believe that this test should also be a requirement for CWW. Because words mean different things to 4) different people, they should be modeled using at least interval type-2 fuzzy sets. These tests are easy to apply to any paper that uses CWW in its title or claims to be about CWW. If tests 1–3 are passed, then using the phrase CWW is okay; otherwise, it is not. Failing any one or all of these tests does not diminish the work’s importance; it serves to distinguish the work from works about CWW. In this way, a clear distinction will appear between FL as in CWW and FL as not in CWW. Confusion will be reduced and this will benefit the entire FL field. Hani Hagras: I think the tests mentioned above are a good way forward to formalize the CWW paradigm. Sergio Guadarrama: Although words could mean different things to different people, I don’t know why it is required for them to be modeled by type-2 fuzzy sets. Jerry Mendel: I believe that words mean different things to different people. In my papers “Fuzzy Sets for Words: a New Beginning,” [Proc. IEEE FUZZ Conf., St. Louis, MO, May 26–28, 2003, pp. 37–42] and “Computing with words: Zadeh, Turing, Popper and Occam,” [IEEE Computational Intelligence Magazine, vol. 2, pp. 10–17, Nov. 2007], I apply Karl Popper’s Falsificationism to show that it is scientifically incorrect to model a word using a type-1 fuzzy set, and that an interval type-2 fuzzy set is a scientifically correct first-order uncertainty model for a word. I also believe that fuzzy set models for words must be derived from data that are collected from a group of subjects. Such data will collectively contain each subject’s (intra-) uncertainty about a word as well as the group’s (inter-) uncertainty about the word (words mean different things to different people). The intraand inter-uncertainties about a word can be modeled by an interval type-2 fuzzy set but cannot be modeled by a type-1 fuzzy set. What has been largely missing from the CWW literature is the connection between data and fuzzy set model. I believe that this connection should be made at the start of works about CWW because those works need to incorporate the uncertainties about words. Since a type-1 fuzzy set is a special case of a type-2 fuzzy set, it seems to me that it is more appropriate to develop new ideas about CWW in the setting of type-2 fuzzy sets than in the setting of type-1 fuzzy sets, since the former can reduce to the latter, but the latter can not be generalized to the former. VI. Lawry on CWW Here is my definition partly borrowed from the cover material for my recent book: very short definition: ❏ computing with words = The incorporation of vague linguistic concepts into intelligent computer systems. Slightly longer definition: ❏ Vagueness is central to the flexibility and robustness of natural language descriptions. Vague concepts are robust to the imprecision of our perceptions, while still allowing us to convey useful, and sometimes vital, information. 6 Examples of CWW Engines are Linguistic Weighted Averages and IF-THEN Rules. What has been largely missing from the CWW literature is the connection between data and fuzzy set model. This connection should be made at the start of works about CWW because those works need to incorporate the uncertainties about words. Authorized licensed use limited to: Univ of Calif Berkeley. Downloaded on March 04,2010 at 20:12:19 EST from IEEE Xplore. Restrictions apply. 24 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | FEBRUARY 2010 Computing with words is therefore motivated by the desire to incorporate this robustness and flexibility into intelligent computer systems. Such a goal, however, re quires a formal model of vague concepts that will allow us to quantify and manipulate the uncertainty resulting from their use as a means of passing information between autonomous agents. Lotfi Zadeh: A word about vagueness. Lawry uses the term “vague” in the same sense as fuzzy. Actually, vague and fuzzy have different meanings. Fuzzy relates to un-sharpness of class boundaries, while vagueness relates to insufficient specificity. As an illustration, “I’ll be back in a few minutes,” is fuzzy but not vague. While “I’ll be back sometime,” is both fuzzy and vague. Similarly, “Meet me at the lobby at about 6pm,” is fuzzy but not vague. Usually, what is vague is fuzzy but not vice-versa. Jonathan Lawry: For me vagueness refers to uncertainty concerning the conventions for the use of linguistic terms across a population of communicating agents. From this perspective the term “few minutes” is vague since for a given number of minutes x there is uncertainty as to whether the assertion “x is a few minutes” can be appropriately used (based on linguistic convention). I do agree that there is a dis tinction between vagueness and imprecision though. So, for example, given the assertion “the exam was between 20 and 40 minutes long” we have imprecision and not vagueness, i.e., there is no concept level uncertainty but rather the information provided is imprecise in that it does not tell us the exact length of the exam. Hani Hagras: Would vagueness be associated with words and what they mean to different people or would it be associated with how humans can compute with words and move from inputs words to output actions? Hence, would the framework of type-2 fuzzy systems be more appropriate to handling the uncertainty in CWWs? Jonathan Lawry: Second order vagueness may be important, however in my view the central issue is that uncertainty concerning the meaning of linguistic terms arises from the distributed way that meaning is communicated through communications between agents across a population. Sergio Guadarrama: Al though vagueness is an important feature of words it is not the only one. Jonathan Lawry: I agree but I think that the fundamental aim of computing with words is to enable representation and reasoning with granular models, where information granules are represented by linguistic concepts. For this an effective representation of concept vagueness is of central importance since it allows for the development of robust and transparent granular models. VII. Hagras on CWW Computing with words relates to developing intelligent systems that are able to receive as input words, perceptions, and propositions drawn from the natural language and can then produce a decision or output based on these words. Computing with words involve different needed components which are: Developing the mechanisms that can ❏ handle the uncertainties existing with