in this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where a~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisti...

By means of theory of truth degrees of formulas, according to deduction theorems and completeness theorems, the new concepts of consistency degrees and polar index for general theories in Łukasewicz fuzzy and n-valued propositional logic systems are introduced. Moreover, sufficient and necessary conditions for a theory Γ to be consistent, inconsistent, and fully divergent are obtained. Finally,...

This paper describes the mathematical basis for a computer language which can be used for representing natural human reasoning with imprecise linguistic information. The approach to doing this employs a collection of abstraction mechanisms which are based on the concept of a linguistic variable first introduced by Zadeh [1975]. The present semantics differs from that of Zadeh, however, in that ...

This is an extended abstract of the published paper “Approximate Similarity and Poincaré Paradox to be published in Notre Dame Journal of Formal Logic, 49, 2008”. The startin point is an observation by De Cock and Kerre, in which, in considering Poincaré paradox, one observes that the intuitive notion of “approximate similarity” cannot be adequately represented by the fuzzy equivalence relation...

This paper is concerned with a natural deduction system for First Degree Entailment (FDE). First, we exhibit a brief history of FDE and of combined systems whose underlying idea is used in developing the natural deduction system. Then, after presenting the language and a semantics of FDE, we develop a natural deduction system for FDE. We then prove soundness and completeness of the system with ...

Data cleaning deals with the detection and removal of errors and inconsistencies in data, gathered from distributed sources. This process is essential for drawing correct conclusions from data in decision support systems. Eliminating fuzzy duplicate records is a fundamental part of the data cleaning process. The vagueness and uncertainty involved in detecting fuzzy duplicates make it a niche, f...

We present the fully automatic partial deduction system ecce, which can be used to specialise and optimise logic programs. We describe the underlying principles of ecce and illustrate some of the potential application areas. Interesting possibilites of crossfertilisation with other elds such as reachability analysis of concurrent systems and inductive theorem proving are highlighted and substan...

The performance of an automated forward deduction system is crucial to its applicability. Since a forward deduction system working for discovery has no explicitly specified proposition or theorem given previously as goal, it often deduces many redundant intermediates, i.e., instances of those that have previously deduced. Therefore, how to reduce redundant intermediates is a general and difficu...

in this paper, new definitions of $l$-fuzzy closure operator, $l$-fuzzy interior operator, $l$-fuzzy remote neighborhood system, $l$-fuzzy neighborhood system and $l$-fuzzy quasi-coincident neighborhood system are proposed. it is proved that the category of $l$-fuzzy closure spaces, the category of $l$-fuzzy interior spaces, the category of $l$-fuzzy remote neighborhood spaces, the category of ...