Fuzzy Statistics and Computation on the Lexical Semantics : How Much Do You Think? and How Many?

Language, Information and Computation(PACLIC 11), 1996, 337-346 Fuzzy statistics and computation on the lexical semantics How much do you think? and how many? Berlin Wu and Ching-min Sun National Chengchi University and Jin-Wen College of Business and Technology, Taiwan Berlin@math.nccu.edu.tw Abstract In this paper, we investigated the fuzzy statistics analysis in lexical semantics and apply the fuzzy logic to compute some uncertain and ambiguous problems. The fuzzy propositional computation for the cognitive semantics can account for the degree of typicality and similarity. Which provide a more precise expression in human thought and human cognition. Some essential definitions for fuzzy statistics are proposed to implement these procedures. The empirical results by a sampling survey and fuzzy statistical analysis suggests that the fuzzy statistics and computation are potentially powerful heuristics in analyzing lexical semantics. 1. Introduction Procedures of semantic analysis may be one of the most complicated structures people have met with. Some conventional semantic theories presuppose the notion that natural language may be describable by a finite set of rules capable of generating an infinite set of sentences. The difficulty with this approach is that external features depends on being able to clearly determine for each relevant features whether or not an object processes it. Moreover, even those features which have been decided, such as 'heavy", 'short' or 'blue', might still be fuzzy since there are no clear cut boundaries distinguishing heavy from very heavy, short from a little short or blue from purple. A fundamental problem of lexical semantics is the fact that what Ruhl (1989) calls the perceived meaning of a word can vary so greatly from one context to another. Some disadvantages about computational (numerical) semantics are: (i) the danger of overstraining the empirical data to meet the requirement of numerical precision; (ii) the danger of overinterpreting the numerical results of a term. One possible way to diminish the required amount of precision is to use fuzzy statistics. However, Zadeh (1972) and (1983) have proposed certain alternative approaches where the linguistic aspects are mostly emphasized. Since then, many papers have also been published on this topic, for examples, see Joyce (1976), Rieger (1976) and Morgan and Pelletier (1977) Sanchez et al (1982) etc. For an extensive treatment of the theory of fuzzy sets with applied linguistics the interested reader may refer to see Dubois and Prade (1980) or Manton, Woodbury and Tolley (1994). In this paper, we will apply the fuzzy statistical analysis and computational lexical semantic method to investigate some uncertain and ambiguous problems. Especially we will discuss the degree of object's typicality and similarity, which 337 Especially we will discuss the degree of object's typicality and similarity, which provide a more precise expression in human cognition. . It should be pointed out that the concept of fuzzy statistical analysis applied in this research does not refer to the general notation of constructing certain theories, but to propose some alternative methods in computational lexical semantics. We hope that such analytic technique will be more reliable and significant …

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