Interval-valued Fuzzy Inference Research Articles

Interval-valued fuzzy inference based on aggregation functions

Generalized modus ponens (GMP) and generalized modus tollens (GMT), as two basic patterns of approximate reasoning, aim to acquire some reasonable imprecise conclusions from a collection of imprecise premises using some inference rules. To solve the GMP and GMT problems under interval-valued fuzzy setting, an interval-valued A-compositional rule of inference (ACRI) method and quintuple implication principle (QIP) method with interval-valued implication generated by A under any partial order are presented in this paper, where A is an interval-valued aggregation function. In order to develop these methods, we firstly discuss interval-valued negation generated by an interval-valued aggregation function with any partial order. Some properties of interval-valued implications generated by interval-valued aggregation functions with an arbitrary order are then analyzed. We further investigate the ACRI method and quintuple implication principle (QIP) method with interval-valued implication generated by interval-valued aggregations to solve the interval-valued fuzzy modus ponens (IFMP) and interval-valued fuzzy modus tollens (IFMT). Finally, two examples are implemented to illustrate our proposed approaches using some special interval-valued aggregation functions.

Interval-valued quintuple implication principle of fuzzy reasoning

In this paper, we propose the quintuple implication principle based on interval-valued fuzzy inference for fuzzy modus ponens and fuzzy modus tollens, which explicitly use the closeness between A⁎ and A (or B⁎ and B) in the process of fuzzy reasoning. We first give the corresponding interval-valued R-type quintuple implication solutions and then investigate the robustness of quintuple implication algorithms based on interval-valued fuzzy inference. The sensitivity of quintuple implication algorithms based on two important interval-valued residuated implication operators is given.

Robustness of interval-valued fuzzy inference triple I algorithms based on normalized Minkowski distance

In this paper, we introduce the sensitivity of interval-valued fuzzy connectives and perturbation of interval-valued fuzzy sets based on normalized Minkowski distance in Hausdorff metrics. And then we calculate sensitivity of three typical interval-valued fuzzy connectives. The robustness of interval-valued fuzzy inference triple I algorithms is investigated.

Robustness of reverse triple I algorithms based on interval-valued fuzzy inference

In this paper, the robustness of reverse triple I algorithms based on interval-valued fuzzy inference is discussed. As corollaries of the main results, the sensitivities of interval-valued R -type [ α , β ] -reverse triple I solutions based on three well-known interval-valued residuated implication operators are given. • A new kind of full implication [ α , β ]-reverse triple I algorithm based on interval-valued fuzzy set is proposed. • The R-type [ α , β ]-reverse triple I solutions based on interval-valued fuzzy inference for the both model of IFMP and IFMT are given. • The reverse triple I algorithms based on interval-valued fuzzy set are robust. • The sensitivities of reverse triple I algorithms based on three important interval-valued residuated implications are given. • The robustness of interval-valued reverse triple I algorithms is directly linked to the selection of fuzzy connectives.

Robustness of full implication algorithms based on interval-valued fuzzy inference

• A new kind of full implication algorithm based on interval-valued fuzzy set is proposed. • The R -type triple I solutions based on interval-valued fuzzy reasoning are given. • The new triple I algorithms based on interval-valued fuzzy set are robust. • The sensitivity of some special algorithms based on four important interval-valued residuated implication is given. In this paper, a new full implication algorithm based on interval-valued fuzzy inference which extends the triple I principle for fuzzy inference based on fuzzy modus ponens and fuzzy modus tollens to the case of interval-valued fuzzy sets is presented. We first give the corresponding interval-valued R -type triple I solutions and then investigate the robustness of triple I algorithms based on interval-valued fuzzy sets for fuzzy inference. The sensitivity of some special algorithms based on four important interval-valued residuated implication is given. It is shown that the robustness of interval-valued full implication algorithms for fuzzy inference directly depends on the selection of interval-valued fuzzy connectives.

Robustness of interval-valued fuzzy inference

Since interval-valued fuzzy set intuitively addresses not only vagueness (lack of sharp class boundaries) but also a feature of uncertainty (lack of information), interval-valued fuzzy reasoning plays a vital role in intelligent systems including fuzzy control, classification, expert systems, and so on. To utilize interval-valued fuzzy inference better, it is very important to study the fundamental properties of interval-valued fuzzy inference such as robustness. In this paper, we first discuss the robustness of interval-valued fuzzy connectives. And then investigate the robustness of interval-valued fuzzy reasoning in terms of the sensitivity of interval-valued fuzzy connectives and maximum perturbation of interval-valued fuzzy sets. These results reveal that the robustness of interval-valued fuzzy reasoning is directly linked to the selection of interval-valued fuzzy connectives.

An interval-valued fuzzy inference method— Some basic properties

This paper presents a short analysis of formal properties of the interval-valued fuzzy inference method described in [5]. The analysis concerns the so-called good-mapping property (GMP) and α-good-mapping property (α-GMP) of this method. The considerations are illustrated by an example.

Interval-valued fuzzy inference involving uncertain (inconsistent) conditional propositions

This communication presents an extension of the interval-valued fuzzy inference method described in [4], to the case, when particular conditional propositions are characterized by different grades of credibility or consistency.