Outline of a Computational Theory of Perceptions Based on Computing with Words

Fuzzy Optim Decis Making

2006

Two related aggregation operators called copulas and co-copulas are introduced and various properties are described. The relationship, of these operators to t-norms and t-conorms is noted. Generalizations of these, respectively, called conjunctors and disjunctors, are introduced. We suggest the use of disjunctor operators for modeling the multi-valued implication operator in fuzzy logic. We point out that the selection of operators used in fuzzy logic, in addition to having appropriate pointwise properties, should be holistic, this requires consideration of the nature of the resulting fuzzy set as a whole. Focusing on the protoform of fuzzy modus ponens and looking at the information contained in the inferred fuzzy set we show that the use of co-copulas has some desirable properties. Taking advantage of the fact that the weighted sum of co-copulas is a co-copula we consider the problem of constructing customized implication operators.

Section: Implication Operators and Disjunctorsmentioning

confidence: 99%

Modeling holistic fuzzy implication using co-copulas

Fuzzy Optim Decis Making

2006

“…We now introduce another operation that will play an important role in the process of question answering, the Zadeh extension principle (Zadeh 1965(Zadeh , 1999Yager, 1986;Xu, Kerre, Ruan, & Song, 2001).…”

Section: Notementioning

confidence: 99%

“…Thus, if a joint variable has q components, its domain is a set of q-tuples. It is implicitly assumed, unless otherwise stated, that the variables of interest can assume only one value in its base set (see Zadeh, 1999, for a discussion of different variable types).A categorical proposition (or statement) in the theory of approximate reasoning is of the form V is A; here V is a joint variable and A is a fuzzy subset 3 of the domain of V. A proposition that involves only one variable is called a canonical proposition; those involving two or more variables are called relational or joint propositions. A large variety of types of knowledge can be represented by propositions of the preceding form.…”

mentioning

confidence: 99%

Knowledge trees and protoforms in question‐answering systems

2006

J. Am. Soc. Inf. Sci.

We point out that question-answering systems differ from other information-seeking applications, such as search engines, by having a deduction capability, an ability to answer questions by a synthesis of information residing in different parts of its knowledge base. This capability requires appropriate representation of various types of human knowledge, rules for locally manipulating this knowledge, and a framework for providing a global plan for appropriately mobilizing the information in the knowledge to address the question posed. In this article we suggest tools to provide these capabilities. We describe how the fuzzy set-based theory of approximate reasoning can aid in the process of representing knowledge. We discuss how protoforms can be used to aid in deduction and local manipulation of knowledge. The idea of a knowledge tree is introduced to provide a global framework for mobilizing the knowledge base in response to a query. We look at some types of commonsense and default knowledge. This requires us to address the complexity of the nonmonotonicity that these types of knowledge often display. We also briefly discuss the role that Dempster-Shafer structures can play in representing knowledge. IntroductionThe widespread availability of the Internet has generated considerable interest in electronic sources of information. Various types of software applications have been developed to support this interest. We can generically refer to these as applications useful for seeking information (AUSIN). One widely used class of these AUSINs are search engines. These applications retrieve pointers to pages or files based on their matching some keywords specified by the user.Another widely used class ofAUSINs are database systems. In some ways database applications and search engines are opposite extremes of these AUSINs. Database applications give precise information; however, they only work in highly structured environments. The search engines, although only giving imprecise responses, pointers, are capable of functioning in highly unstructured, almost chaotic environments. However, neither of these two applications typically has reasoning capacity.Another class of AUSINs are question-answering systems (Chaudri & Fikes, 1999;Clark, Thompson, & Porter, 1999;Maybury, 2003;Zadeh, 2004b). An important dimension along which question-answering systems differ from search engines and most databases is reasoning ability (Zadeh, 2004b). A fundamental characteristic of question-answering systems is their ability to reason over an information base. This facility leads to a fundamental difference in the nature of the response to query. In particular, the response from a search engine is a pointer to a document (file or Web page) resident in its library.1 The database responds essentially by providing some value already resident in the database. A question-answering system, because of its reasoning capacity, can construct new knowledge that is not resident in its knowledge base in response to a query. Although currently less commo...

“…One of these is that fuzzy set theory and particularly Zadeh's paradigm of computer with words 7,8 was especially developed for the task of representing human linguistic concepts in terms of a mathematical object, a fuzzy subset. Fuzzy logic has large repertoire of operations that allows for the combination of these sets in ways that mimic the logic of human reasoning and deduction.…”

Section: Introductionmentioning

confidence: 99%

Intelligent social network analysis using granular computing

2008

Int. J. Intell. Syst.

An introduction to some basic ideas of graph (relational network) theory is first provided. We then discuss some concepts from granular computing in particular the fuzzy set paradigm of computing with words. The natural connection between graph theory and granular computing, particularly fuzzy set theory, is pointed out. This connection is grounded in the fact that these are both setbased technologies. Our objective here is to take a step toward the development of intelligent social network analysis using granular computing. In particular one can start by expressing in a human-focused manner concepts associated with social networks then formalize these concepts using fuzzy sets and then evaluate these concepts with respect to social networks that have been represented using set-based relational network theory. We capture this approach in what we call the paradigm for intelligent social network analysis, PISNA. Using this paradigm, we provide definitions of a number of concepts related to social networks. C 2008 Wiley Periodicals, Inc.