By Tru Hoang Cao

During this quantity, first we formulate a framework of fuzzy forms to symbolize either partial fact and uncertainty approximately thought and relation varieties in conceptual graphs. Like fuzzy characteristic values, fuzzy varieties additionally shape a lattice laying a typical flooring for lattice-based computation of fuzzy granules. moment, for automatic reasoning with fuzzy conceptual graphs, we advance foundations of order-sorted fuzzy set good judgment programming, extending the idea of annotated good judgment courses of Kifer and Subrahmanian (1992). 3rd, we convey a few fresh purposes of fuzzy conceptual graphs to modelling and computing with quite often quantified statements, approximate wisdom retrieval, and common language question realizing.

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**Additional resources for Conceptual Graphs and Fuzzy Logic: A Fusion for Representing and Reasoning with Linguistic Information (Studies in Computational Intelligence)**

**Sample text**

It satisfies the intuition that, if β = 1 then τβ = absolutely true and if β = 0 then τβ = absolutely unknown. Similarly, “p is possible at most to degree γ” can be represented by “p is τγ” such that Π(absolutely true | τγ) ≤ γ, whence the least specific solution for τγ is: μτγ(1) = γ and μτγ(u) = 1 for all u ≠ 1. 2. A fuzzy type is defined to be a pair (t, v) where t is a basic type in a partially ordered set of basic types and v is a fuzzy truth-value in a fuzzy truthvalue lattice. The intuitive meaning of a fuzzy type assertion “x is of fuzzy type (t, v)” is “It is v that x is of t”.

Conjunctive fuzzy types that express (partial) inconsistency are also allowed, such as {(TALL_MAN, false), (HANDSOME_MAN, more or less true)}. On the basis of the fuzzy subtype relation, the conjunctive fuzzy subtype relation is defined in a straightforward manner as follows. 5. Given two conjunctive fuzzy types T1 and T2, T2 is said to be a conjunctive fuzzy subtype of T1, denoted by T1 ≤ι T2, iff ∀τ1∈T1 ∃τ2∈T2: τ1 ≤ι τ2. 1, one has: {(TALL_MAN, true), (HANDSOME_MAN, more or less false)} ≤ι {(TALL_MAN, very true), (YOUNG_MAN, false)} because (TALL_MAN, true) ≤ι (TALL_MAN, very true) and (HANDSOME_MAN, more or less false) ≤ι (YOUNG_MAN, false), provided that true ≤ι very true and more or less false ≤ι false.

Other properties of the fuzzy set mismatching degree function Δ that are used in this volume are stated in the following proposition. 3. Let A, A*, A1 and A2 be fuzzy sets on the same domain. Then the following properties hold: 26 2 Fuzzy Conceptual Graphs 1. , A* ⊆ A. 2. If A1 ≤ι A2 then Δ(A | A2) ≤ Δ(A | A1). 3. A+ε ≤ι A* iff Δ(A | A*) ≤ ε, for every ε∈[0, 1]. 6 Fuzzy Types Objects in the real world are naturally associated with types, sorts, or classes. g. a type hierarchy, has become important part of knowledge bases and advanced information systems.