Fuzzy interval inference utilizing the checklist paradigm and BK-relational products.

*(English)*Zbl 0853.68163
Kearfott, R. Baker (ed.) et al., Applications of interval computations. Proceedings of an international workshop, El Paso, TX, USA, February 23-25, 1995. Dordrecht: Kluwer Academic Publishers. Appl. Optim. 3, 291-335 (1996).

Summary: In the first part of this paper, we explain how an interval fuzzy membership function can be derived within the checklist paradigm as an approximation of the crisp (Boolean) logical vector of \(n\) truth values simultaneously assigned to a proposition. It is seen that the checklist paradigm generates a variety of pairs of distinct connectives con of the same logical type (e.g. a pair of implication (ply) operators, and connectives, etc.). These pairs of many-valued logic connectives of the same type form the natural bounds contop and conbot within \([0, 1]\) fuzzy valuation space, thus determining the end points of intervals generated by fuzzy inference. The checklist paradigm provides the means for deriving systems of interval-valued fuzzy logics used for approximate inference. Thus a formal semantics for several kinds of interval logics is derived using the exact mathematical method based on the checklist paradigm.

Interrelationships between different MVL-connectives in interval logic systems can be captured with advantage in a more abstract way by groups of logical transformations of the MVL connectives. The basics of the theory of logic transformations characterizing MVL systems are briefly outlined in section 3. It is also shown that some systems of the checklist paradigm generated interval logics can by described by \({\mathcal S}_{2\times 2\times 2}\) symmetry group.

Inference in Knowledge-Based Systems (KBS) is performed by means of fuzzy relational compositions of special kind, the so-called triangle and square products of fuzzy relations. These are discussed in section 4. These fuzzy products use in their definitions many-valued logic systems as the base logics. Various pairs of many-valued connectives forming interval logics systems derived by means of the checklist paradigm can be used as the base logic systems for this purpose.

In additon to the theoretical analysis of interval logics presented here, an application of fuzzy interval inference in Knowledge-Engineering is also discussed in this paper. How the fuzzy interval inference is practically utilized in the design of Fuzzy Relational KBS is outlined in Section 5.2. Important epistemological reasons for using fuzzy interval inference in the medical domain are also briefly outlined there. This is followed by the presentation of a small portion of the relational knowledge base and some formulae for fuzzy relational interval inference, in order to illustrate the basic mechanism as used by a medical knowledge based system called CLINAID. The section is concluded by an illustrative sample of CLINAID’s inference. The paper is concluded with a brief discussion of the link of interval inference to soft computing.

For the entire collection see [Zbl 0836.00038].

Interrelationships between different MVL-connectives in interval logic systems can be captured with advantage in a more abstract way by groups of logical transformations of the MVL connectives. The basics of the theory of logic transformations characterizing MVL systems are briefly outlined in section 3. It is also shown that some systems of the checklist paradigm generated interval logics can by described by \({\mathcal S}_{2\times 2\times 2}\) symmetry group.

Inference in Knowledge-Based Systems (KBS) is performed by means of fuzzy relational compositions of special kind, the so-called triangle and square products of fuzzy relations. These are discussed in section 4. These fuzzy products use in their definitions many-valued logic systems as the base logics. Various pairs of many-valued connectives forming interval logics systems derived by means of the checklist paradigm can be used as the base logic systems for this purpose.

In additon to the theoretical analysis of interval logics presented here, an application of fuzzy interval inference in Knowledge-Engineering is also discussed in this paper. How the fuzzy interval inference is practically utilized in the design of Fuzzy Relational KBS is outlined in Section 5.2. Important epistemological reasons for using fuzzy interval inference in the medical domain are also briefly outlined there. This is followed by the presentation of a small portion of the relational knowledge base and some formulae for fuzzy relational interval inference, in order to illustrate the basic mechanism as used by a medical knowledge based system called CLINAID. The section is concluded by an illustrative sample of CLINAID’s inference. The paper is concluded with a brief discussion of the link of interval inference to soft computing.

For the entire collection see [Zbl 0836.00038].