Interval-valued Fuzzy Reasoning Research Articles

The Relationship between Fuzzy Reasoning Methods Based on Intuitionistic Fuzzy Sets and Interval-Valued Fuzzy Sets

Two important basic inference models of fuzzy reasoning are Fuzzy Modus Ponens (FMP) and Fuzzy Modus Tollens (FMT). In order to solve FMP and FMT problems, the full implication triple I algorithm, the reverse triple I algorithm and the Subsethood Inference Subsethood (SIS for short) algorithm are proposed, respectively. Furthermore, the existing reasoning algorithms are extended to intuitionistic fuzzy sets and interval-valued fuzzy sets according to different needs. The purpose of this paper is to study the relationship between intuitionistic fuzzy reasoning algorithms and interval-valued fuzzy reasoning algorithms. It is proven that there is a bijection between the solutions of intuitionistic fuzzy triple I algorithm and the interval-valued fuzzy triple I algorithm. Then, there is a bijection between the solutions of intuitionistic fuzzy reverse triple I algorithm and the interval-valued fuzzy reverse triple I algorithm. At the same time, it is shown that there is also a bijection between the solutions of intuitionistic fuzzy SIS algorithm and interval-valued fuzzy SIS algorithm.

Interval-valued fuzzy reasoning full implication algorithms based on the t-representable t-norm

Interval-valued fuzzy reasoning plays a vital role in intelligent systems with the performance of effectively reducing the loss of fuzzy information and reflecting the vagueness and uncertainty in information processing. However the existing reasoning algorithms were developed based on some special interval-valued t-norms which limits the usability and adaptation of these algorithms. This study proposes general reasoning algorithms on the basis of interval-valued fuzzy sets, that is the interval-valued fuzzy reasoning triple I algorithms based on the left-continuous t-representable t-norm TT1,T2. Furthermore, the interval-valued R-type triple I solutions of the interval-valued fuzzy reasoning triple I algorithms are given. We show that the proposed algorithms possess the reducibility. Finally, some robustness results of the interval-valued fuzzy reasoning triple I algorithms based on the left-continuous interval-valued t-representable t-norm are proved.

Interval-valued fuzzy reasoning algorithms based on Schweizer–Sklar t-norms and its application

Based on the normalized Minkowski distance in Hausdorff metrics, we study the sensitivity of interval-valued Schweizer-Sklar t-norms and their corresponding residual implications. Moreover, we investigate the robustness of interval-valued fuzzy reasoning triple I algorithms based on Schweizer–Sklar operators and illustrate the feasibility of the algorithms by a numerical example. Finally, the interval-valued fuzzy reasoning triple I algorithms are applied to medical diagnosis.

The quintuple implication principle of fuzzy reasoning based on interval-valued S-implication

Interval-valued fuzzy reasoning is an important issue in approximate reasoning and decision making under fuzzy and uncertainty. To improve the quality of interval-valued fuzzy reasoning, this paper proposes the quintuple implication principle (QIP) of fuzzy reasoning based on interval-valued S-implication in order to solve interval-valued fuzzy modus ponens (IFMP) and interval-valued fuzzy modus tollens (IFMT). We first present the QIP solutions of IFMP and IFMT for interval-valued S-implications, then discuss the reductivity and continuity of fuzzy reasoning with QIP method for interval-valued S-implications. Finally, we also provide several examples to illustrate and substantiate our theoretical developments.

The Suitable Two Kinds of Interval-valued Fuzzy Metric Spaces for Interval-valued Fuzzy Reasoning

In this paper, a new definition of distance of interval-valued fuzzy sets is presented. Four interval-valued fuzzy metric spaces respectively induced by four specific interval-valued implication operators are established. By discussing and comparing the structures of four specific interval-valued fuzzy metric spaces, it can be concluded that interval-valued fuzzy metric spaces induced by interval-valued Łukasiewicz implication and interval-valued Goguen implication respectively are suitable for interval-valued fuzzy reasoning.

Robustness of Fuzzy Reasoning Based on Schweizer–Sklar Interval-valued [formula omitted]-Norms

In this paper, we focus on the parametric triple I algorithms by the combination of Schweizer–Sklar interval-valued operators and triple I principles for fuzzy reasoning. Firstly, we give the interval-valued triple I solutions based on Schweizer–Sklar interval-valued operators. Then, we investigate the sensitivity of Schweizer–Sklar interval-valued fuzzy connectives. Finally, we study the robustness of the triple I algorithms based on Schweizer–Sklar interval-valued t-norms (m∈(0,∞)). It shows that the quality of interval-valued fuzzy reasoning algorithms depends on the selection of interval-valued fuzzy connectives.

Multi-attribute group decision making approach based on interval-valued intuitionistic fuzzy sets and evidential reasoning methodology

In multi-attribute group decision making methods, team often needs to deal with both quantitative data and qualitative information with uncertainty. It is essential to properly represent and use uncertain information to conduct rational decision analysis. Having regarded this fact many approaches have been proposed for solving group decision-making problems, especially in fuzzy environments, but due to their drawbacks they get an unreasonable preference order of the alternatives in some situation. Thus in this paper based on interval-valued intuitionistic fuzzy sets and evidential reasoning methodology, a new approach has been proposed for supporting such decision situation. The experimental results are examined using the proposed approach. Computation steps and analysis results are provided to demonstrate its implementation process. The proposed method can overcome the drawbacks of the existing methods for fuzzy multi-attribute group decision making in intuitionistic fuzzy environments.

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.

Multidimensional Interval-valued Fuzzy Reasoning Approach Based on Weighted Similarity Measure

This paper focuses on presentation of a method to bidirectional interval-valued fuzzy approximate reasoning by employing a weighted similarity measure between the fact and the antecedent (or consequent) portion of production rule in which the vague terms are represented by interval-valued fuzzy concepts rather than plain fuzzy sets. The proposed method is more reasonable and flexible than the one presented in the paper by Chen [Fuzzy Sets and Systems, 91(1997), 339–353] due to the fact that it not only can deal with multidimensional interval-valued fuzzy reasoning scheme, but also consider the different importance degree of linguistic variables in production rule and that of elements in each universe.

An Interval-Valued Fuzzy Reasoning Approach Based on Weighted Similarity Measure

This paper presents a new approach for bidirectional interval-valued fuzzy reasoning by employing a weighted similarity measure between the fact and the antecedent portion of production rule, in which the vague terms appearing are represented by interval-valued fuzzy concepts. One numeric example is given to demonstrate the reasonability and flexibility of our proposed approach.

구간값 퍼지집합 추론의 퍼지 Pr/T 네트 표현

This paper proposes a fuzzy Pr/T net representation of interval-valued fuzzy set reasoning, where fuzzy production rules are used for knowledge representation, and the belief of fuzzy production rules are represented by interval-valued fuzzy sets. The presented interval-valued fuzzy reasoning algorithm is much closer to human intuition and reasoning than other methods because this algorithm uses the proper belief evaluation functions according to fuzzy concepts in fuzzy production rules.

Interval-valued fuzzy backward reasoning

The importance and efficiency of backward reasoning in nonfuzzy reasoning has been stressed for a long time, especially in the case of expert systems and decision-support systems. The extension of this reasoning method to fuzzy theory, however, has never been considered. In this paper, the authors propose a definition of fuzzy backward reasoning based on the generalized modus ponens and show the necessity of considering interval-valued fuzzy backward reasoning. Then, the authors propose solving methods for fuzzy backward reasoning in the case of a rule with one or several conditions as well as in the case of several rules.