Fuzzy Conditional Inference Research Articles

Some Considerations about Fuzzy Logic Based Decision Making by Autonomous Intelligent Actor

The article presents an approach toward an implementation of a fuzzy logic-based decision-making process by Autonomous Intelligent Actor (AIA) (© A. Tserkovny), when an input information is defined for its “strategic targeting” by a human operator in terms of a fuzzy incident geometry, whereas its “tactical” behavior (a navigation in space) is directed by fuzzy conditional inference rules. For implementing both elements of AIA decision-making a fuzzy logic [1] for formal geometric reasoning with extended objects is used. This fuzzy logic based fuzzification of axioms of an incidence geometry and a predicate apparatus [2] for AIA space orientation are also presented. The approach, offered in the article, extends predicates of a counter positioning of two objects and their mutual navigation into their fuzzy counterparts. The latter allows AIA to make certain “tactical” decisions.

MULTI-CRITERIONAL CHOICE OF AN ALTERNATIVE UNDER THE RULES OF FUZZY PRODUCTS WITH SOME RELIABILITY DEGREE

One of the main problems of decision-making tasks is the need to take into account subjective expert assessments, the complete consistency of which is rare, and the choice of the best alternative. The complexity of the connections between the many-sided aspects of the decision-making situation and the lack of an accurate forecast of the consequences leads to the fact that when assessing and choosing alternatives, it is possible, and often necessary, to use and process qualitatively fuzzy estimates. In decision-making situations, when at least one of the elements (outcomes, criteria, preferences, expert opinions, etc.) is described qualitatively, indistinctly, there are problems of multi-criteria decision-making with fuzzy initial information.
 Let’s consider the solution to the problem of multi-criteria choice based on the rules of fuzzy conditional inference, which have the form of fuzzy statements, the conditions and conclusions of which, along with expert assessments of the criteria, are presented in the form of interval fuzzy numbers of the second type (IT2FN). The convolution of private implications in each statement is made according to Lukasiewicz's rule. To reduce the type and defuzzify the resulting IT2FN, the Karrnik-Mendel algorithm was used to construct the minimum and maximum centroids of nested fuzzy sets of the first type, which give an estimate of the utility interval for each alternative. To refine the obtained utility estimates, under conditions of incomplete definiteness of statements, using the generalized Bayesian inference mechanism, adjusted estimates of the utility intervals of alternatives are constructed. By comparing these intervals, a larger interval is determined and the corresponding alternative is taken as a solution to the problem under consideration.
 The application of the proposed approach to solving the problem of multicriteria selection of the most corroded section of a gas pipeline with ambiguous expert opinions is shown. To date, specific practical and theoretical results have been obtained for decision-making problems with fuzzy initial information

New Method of Fuzzy Conditional Inference and Reasoning

ABSTRACT We consider fuzzy inference of the form ‘if ··· then ··· ’. ‘if ··· then ··· else ···’ and ‘if ··· and/or ··· and/or ··· then ···’. Muzomoto proposed logical constructs for ‘if. then.’ by applying Godelien and Standard Sequence methods. These method do not satisfy all the intuitions In this paper, We propose method of fuzzy inference and applied on logical constructs. We have shown that our fuzzy inference method satisfy all the intuitions under several criterions.

Generalized Fuzzy Data Mining for Incomplete Information

Defining data with fuzziness made the knowledge discovery process easy and secure to data in data mining. The fuzzy data bases may have linguistic variables. In this paper, fuzzy conditional inference and reasoning are studied for generalized fuzzy data mining. Generalized fuzzy data mining and reasoning is studied with two membership functions “Belief” and “Disbelief”. The fuzzy logic with two membership functions will give more evidence than single membership function. The fuzzy certainty factor is studied as difference between these functions and made it as single membership function. The fuzzy data mining methods are studied. The generalized data mining is studied with different fuzzy conditional inferences. The business intelligence is given as an example.

A t-Norm Fuzzy Logic for Approximate Reasoning

A t-norm fuzzy logic is presented, in which a triangular norm (t-norm) plays the role of a graduated conjunction operator. Based on this fuzzy logic we develop methods for fuzzy reasoning in which antecedents and consequents involve fuzzy conditional propositions of the form “If x is A then y is B”, with A and B being fuzzy concepts (fuzzy sets). In this study, we present a systemic approach toward fuzzy logic formalization for approximate reasoning. We examine statistical characteristics of the proposed fuzzy logic. As the matter of practical interest, we construct a set of fuzzy conditional inference rules on the basis of the proposed fuzzy logic. Important features of these rules are investigated.

Fuzzy Logic for Incidence Geometry.

The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points.

Regularizing the problem of monitoring the technical state of complex technical objects using program complexes for fuzzy conditional inference systems

Regularizing the problem of monitoring the technical state of complex technical objects in emergencies through drawing on additional semantic information is illustrated for a specific example.

Systemic approach to fuzzy logic formalization for approximate reasoning

L.A. Zadeh, E.H. Mamdani, M. Mizumoto, et al., R.A. Aliev and A. Tserkovny have proposed methods for fuzzy reasoning in which antecedents and consequents involve fuzzy conditional propositions of the form “If x is A then y is B”, with A and B being fuzzy concepts (fuzzy sets). A formulation of fuzzy antecedent/consequent chains is one of the most important topics within a wide spectrum of problems in fuzzy sets in general and approximate reasoning, in particular. From the analysis of relevant research it becomes clear that for this purpose, a so-called fuzzy conditional inference rules comes as a viable alternative. In this study, we present a systemic approach toward fuzzy logic formalization for approximate reasoning. For this reason, we put together some comparative analysis of fuzzy reasoning methods in which antecedents contain a conditional proposition with fuzzy concepts and which are based on implication operators present in various types of fuzzy logic. We also show a process of a formation of the fuzzy logic regarded as an algebraic system closed under all its operations. We examine statistical characteristics of the proposed fuzzy logic. As the matter of practical interest, we construct a set of fuzzy conditional inference rules on the basis of the proposed fuzzy logic. Continuity and stability features of the formalized rules are investigated.

Averaging linguistic truth values in fuzzy approximate reasoning

The properties of a new rule for fuzzy conditional inference are presented and discussed. The rule is based on the extended mean operator defined on fuzzy numbers. The related propositions have the form “X is A is τ,” where τ is an element of the term set of the linguistic variable truth. The results obtained via the rule match with Fukami's and with the critical analysis carried out by Mizumoto and Zimmermann about the generalized modus ponens. © 1998 John Wiley & Sons, Inc.

Averaging linguistic truth values in fuzzy approximate reasoning

The properties of a new rule for fuzzy conditional inference are presented and discussed. The rule is based on the extended mean operator defined on fuzzy numbers. The related propositions have the form “X is A is τ,” where τ is an element of the term set of the linguistic variable truth. The results obtained via the rule match with Fukami's and with the critical analysis carried out by Mizumoto and Zimmermann about the generalized modus ponens. © 1998 John Wiley & Sons, Inc.

Coimplication and its application to fuzzy expert systems

In two-valued logic or classical logic, an evaluation takes each of a given set of propositions into one of the extreme truth values 0 or 1, subject to certain consistency rules. In fuzzy logic or multiple-valued logic, the truth value of a formula can assume any value in the interval [0, 1] and is used to indicate the degree of truth represented by the formula. Many of the present expert systems use two-valued logic and probability. Since much of the information in the knowledge base of a typical expert system is imprecise and vague, it is well known that we cannot handle those kinds of uncertainties using those tools. In a fuzzy conditional inference of the fuzzy expert systems, the problem is that, given values, for A → B and A′, we have to find a consistent value for B′ through the modus ponens. In this paper we propose to use the equivalence relation for modus ponens of the inference in fuzzy expert systems instead of fuzzy implication and introduce the concept of coimplication as a new approach to approximate reasoning of expert systems using the new concept of modus ponens.

Linguistic Hedges and Reasonable Fuzzy Inferences

In many cases of human reasoning, the reasoning ways based on vague statements and loose concepts is often considerable. Furthermore, some vague concepts are often represented by transformations of another vague concepts. In order to make such a fuzzy inference and a transformation with fuzzy concepts, some fuzzy conditional inference rules and various linguistic hedges are proposed by Zadeh, Mamdani and Mizumoto. The relationship between the linguistic hedges and some fuzzy inference rules are reported by Mizumoto. However, the only intuitive discussion about the reasonableness for such fuzzy inference has been made. This paper introduces the concept of inference reasonableness with respect to “fuzzy modus ponens” and “fuzzy modus tollens”. Then, the necessary and sufficient conditions for the reasonable fuzzy inference by the max-min composition of the fuzzy sets and the fuzzy relations is derived. Furthermore, the property of linguistic hedge which induce quite reasonable inference results for several fuzzy conditional inference rules is investigated.

Fuzzy Reasoning with Various Fuzzy Inputs

This paper compares inference results of a fuzzy conditional inference with a fuzzy input A' and a fuzzy conditional A ⇒ B under several translating rules for the conditional A ⇒ B by Zadeh, Mamdani and Mizumoto when a fuzzy input A' is a fuzzy set obtained by attaching to the fuzzy set A a linguistic hedge such as slightly, sort of, highly and so on. It is shown that the translating rule Rs proposed before by the author can get reasonable inference results which fit our intuition. Moreover, a new composition called “max-∧ composition” is introduced and it is shown that the inference results for various fuzzy inputs A' are better than those under the ordinal compositional rule of inference which uses “max-min composition.”

Fuzzy conditional inference under max-⊙ composition

This paper shows that the majority of fuzzy inference methods for a fuzzy conditional proposition “If x is A then y is B,” with A and B fuzzy concepts, can infer very reasonable consequences which fit our intuition with respect to several criteria such as modus ponens and modus tollens, if a new composition called “max-⊙ composition” is used in the compositional rule of inference, though reasonable consequences cannot always be obtained when using the max-min composition, which is used usually in the compositional rule of inference. Furthermore, it is shown that a syllogism holds for the majority of the methods under the max-⊙ composition, though they do not always satisfy the syllogism under the max-min composition.

NOTE ON THE ARITHMETIC RULE BY ZADEH FOR FUZZY CONDITIONAL INFERENCE

Abstract This paper shows that Zadeh's arithmetic rule for fuzzy conditional propositions “If x is A then y is B” and “If x is A then y is B else y is C” can infer quite reasonable consequences in a fuzzy conditional inference if new compositions of “max-[Odot] composition” and “max- composition” are used in the compositional rule of inference, though, as was pointed out before, this arithmetic rule cannot get suitable consequences in the compositional rule of inference which uses max-min composition. Moreover, it is shown that the arithmetic rule satisfies a syllogism under these two compositions.

Some considerations on fuzzy conditional inference

In much of human reasoning, the form of reasoning is approximate rather than exact as in ‘A red apple is ripe and this apple is more or less red. Then this apple is more or less ripe.’ L.A. Zadeh and E.H. Mamdani suggested methods for such a fuzzy reasoning as an application of fuzzy set theory. The method involves an inference rule and a conditional proposition which contains fuzzy concepts. In this paper we point out that the consequence inferred by their methods does not always fit our intuitions and we suggest the improved methods which fit our intuitions under several criteria.