Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions

Fuzzy Relational Systems

Fuzzy Sets in Information Retrieval and Cluster Analysis

Fuzzy sets in approximate reasoning, part 2: logical approaches

The intended purpose of this paper is twofold: proposing a common basis for the modeling of uncertainty and imprecision, and discussing various kinds of approximate and plausible reasoning schemes in this framework. Together with probability, different kinds of uncertainty measures (credibility and plausibility functions in the sense of Shafer, possibility measures in the sense of Zadeh and the dual measures of necessity, Sugeno's g?-fuzzy measures) are introduced in a unified way. The modeling of imprecision in terms of possibility distribution is then presented, and related questions such as the measure of the uncertainty of fuzzy events, the probability and possibility qualification of statements, the concept of a degree of truth, and the truth qualification of propositions, are discussed at length. Deductive inference from premises weighted by different kinds of measures by uncertainty, or by truth-values in the framework of various multivalued logics, is fully investigated. Then, deductive inferences from imprecise or fuzzy premises are dealt with; patterns of reasoning where both uncertainty and imprecision are present are also addressed. The last section is devoted to the combination of uncertain or imprecise pieces of information given by different sources. On the whole, this paper is a tentative survey of quantitative approaches in the modeling of uncertainty and imprecision including recent theoretical proposals as well as more empirical techniques such as the ones developed in expert systems such as MYCIN or PROSPECTOR, the management of uncertainty and imprecision in reasoning patterns being a key issue in artificial intelligence.

A Computational Approach to Approximate and Plausible Reasoning with Applications to Expert Systems

Special properties, closures and interiors of crisp and fuzzy relations

On nearness measures in fuzzy relational data models

Relational-product architectures for information processing

This paper attempts to give an overview of the way in which certain unconventional types of relational products (introduced by Bandler and Kohout in mid 1970s) work, both from the mathematical side and in concrete solution of problems of interest in knowledge engineering. The mathematical definitions of three families of fuzzy produets, namely of Triangle Subproduct x( R⊲ S)z, Triangle Superproduct x( R ⊳ S)z and Square product x(RDS)z are given, together with a theoretical semantic device called the checklist paradigm which gives the theoretical bounds on the performance of particular many-valued implication operators and other connectives used to define specijic produets of each of the above families. The paper is concluded with abrief survey of fast fuzzy relational algorithms for testing local relational properties, an up-to-date survey of applications, and a seleetive bibliography.

Fuzzy Relational Products in Knowledge Engineering

Properties of fuzzy implication operators

Wyllis Bandler

Papers

Special properties, closures and interiors of crisp and fuzzy relations

On nearness measures in fuzzy relational data models

Relational-product architectures for information processing

Fuzzy Relational Products in Knowledge Engineering

Properties of fuzzy implication operators