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A Field Theory of Words and Agents
Germano Resconi and Masoud Nikravesh

In this paper we assume that computation by words is equivalent to computation by fields. Any field is a word and computation by fields means computation of the words as fuzzy fields. Values of the fuzzy fields give us the semantic value of the words. Geometric image of the context H and of the field X in the Zadeh [12] form “H is r X” is given. Superposition of words (fields) to generate other words and filter rules to decompose a word in other words are given. Any word or field can be a basis field in the weighted superposition process to generate other words. The computation of the weights (sources) for which basis words are included in a given
word is a very important problem that we solve in this paper. A connection between Boolean fields (fields whose values are one or zero) and fuzzy fields (words) by the projection operator is given. In conclusion we establish a new computation of words as fuzzy fields with a suitable information system and its multidimensional geometric representation.

Keywords: computation by words, vector space, fields and words, membership function and fields, agents, reference space, space of the objects and space of the attributes.

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