James F. Baldwin

Support logic programming

This article describes a support logic programming system which uses a theory of support pairs to model various forms of uncertainty. It should find application to designing expert systems and is of a query language type like Prolog. Uncertainty associated with facts and rules is represented by a pair of supports and uses ideas from Zadehs fuzzy set theory and Shafers evidence theory. A calculus is derived for such a system and various models of interpretation given. the article provides a form of knowledge representation and inference under uncertainty suitable for expert systems and a closed world assumption is not assumed. Facts not in the knowledge base are uncertain rather than assumed to be false.

Fuzzy logic and fuzzy reasoning

The concepts of truth value restriction and fuzzy logical relation are used to give a general approach to fuzzy logic and also fuzzy reasoning involving propositions with imprecise or vague description.

A model of fuzzy reasoning through multi-valued logic and set theory

Various interpretations of conditional propositions are considered, which include relational definitions using Łukasiewicz logical implication rule and Zadehs Maximin rule. Theorems are presented which describe the relationship between the interpretations. An example of reasoning in ordinary set theory is presented as a special case of the method used for approximate reasoning with fuzzy propositions. Models of reasoning from multiple conditional propositions of high dimensional state are constructed and theorems for reducing dimensionality are presented. Problems of dimensionality using the Łukasiewicz implication rule are discussed and an alternative method based on fuzzy logic is indicated briefly.

Fuzzy logic and approximate reasoning for mixed input arguments

In this paper we extend the method of approximate reasoning based upon fuzzy logic as proposed by Baldwin (1978) to arguments of a more complex nature, namely those with mixed inputs. Two approaches are given, both of which have their analogies in ordinary two valued logic.

A Theory of Mass Assignments for Artificial Intelligence

We present a theory of mass assignments for evidential reasoning under uncertainty which allows for fuzzy[15, 16, 17], probabilistic and incomplete probabilistic specifications[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. The theory is applicable to fuzzy control, expert systems, decision support systems, knowledge engineering and represents a general theory of uncertainty in AI.

A mass assignment based ID3 algorithm for decision tree induction

A mass assignment based ID3 algorithm for learning probabilistic fuzzy decision trees is introduced. Fuzzy partitions are used to discretize continuous feature universes and to reduce complexity when universes are discrete but with large cardinalities. Furthermore, the fuzzy partitioning of classification universes facilitates the use of these decision trees in function approximation problems. Generally the incorporation of fuzzy sets into this paradigm overcomes many of the problems associated with the application of decision trees to real‐world problems. The probabilities required for the trees are calculated according to mass assignment theory applied to fuzzy labels. The latter concept is introduced to overcome computational complexity problems associated with higher dimensional mass assignment evaluations on databases. ©1997 John Wiley & Sons, Inc.

Fuzzy truth definition of possibility measure for decision classification

A new definition of possibility measure is presented which is calculated on truth space and is shown to be equivalent to Zadehs original definition. This alternative formulation is shown to be the more natural in the context of decision classification because it clearly demonstrates the need for determining both the possibility of a category and not that category in a selection criterion. A number of useful possibility theorems are presented and their application to decision classification is demonstrated in a simplistic medical diagnosis problem, which also employs entropy measure as an additional parameter. The truth space formulation of possibility measure is shown to be of further value in problems of high dimensional state and an important possibility theorem relating to such problems is presented.

Towards soft computing object-oriented logic programming

Logic programming, object-oriented programming and soft computing have provided advantageous methodologies and techniques for computer-based problem solving. This paper proposes a framework that combines these three disciplines to exploit their own advantages in dealing with real world problems. The framework is a logic-based one in which class and object properties are represented by clauses. Vague data in properties are represented by fuzzy sets interpreted as possibility distributions. Uncertain applicability of a property to a class or an object is represented either by a support pair defining probability lower and upper bounds, or by a certainty lower bound. Fundamental issues of uncertain membership and inheritance are then discussed and solutions to them are proposed. The result forms a basis for development of soft computing object-oriented programming systems.

Knowledge from data using fuzzy methods

The basic concept of a data browser is explained and some methods are described which are suitable for extracting knowledge from data as an induction process. The data browser gives data mining capabilities but also provides a stage for computers and users to act out their parts in this knowledge discovery process.

Asymmetric Triangular Fuzzy Sets for Classification Models

Decision trees have already proved to be important in solving classification problems in various fields of application in the real world. The ID3 algorithm by Quinlan is one of the well-known methods to form a classification tree. Baldwin introduced probabilistic fuzzy decision trees in which fuzzy partitions were used to discretize continuous feature universes. Here, we have introduced a way of fuzzy partitioning in which we can have asymmetric triangular fuzzy sets for mass assignments approach to fuzzy logic. In this paper we have shown with example that the use of asymmetric and unevenly spaced triangular fuzzy sets will reduce the number of fuzzy sets and will also increase the efficiency of probabilistic fuzzy decision tree.