PRESERVATION THEOREMS IN LUKASIEWICZ MODEL THEORY

The article presents refutational resolution theorem proving system for Fuzzy Description Logic (FDL) based on general (non-clausal) resolution rule. It brings several new notions of refutation degree and proves its relation to provability degree in fuzzy predicate logic.

Results on arithmetical complexity of sets of tautologies and satisfiable formulas of various fuzzy logics (with respect to their standard t-norm based semantics as well as with respect to their general BL-algebra based semantics) are surveyed. Some new results are also obtained.

Fuzzy Logic (Fuzzy Logic) is a branch of science based on thinking like human beings and solving them with mathematical functions. Fuzzy logic theory is a mathematical theory. Based on fuzzy set theory, it also uses intermediate values. The fuzzy logic that emerged in 1965 is used in many fields. In the production of pacemakers, in the production of artificial organs, in many electronic devices, company efficiency estimation, etc. situations are used. Fuzzy logic, which is frequently used in the solution of problems that occur in uncertain situations such as quality assessment in recent years, is one of the artificial intelligence methods. With the help of machines, people-specific data and experiences are studied using the fuzzy logic approach. In this study, by using Matlab Fuzzy Toolbox, it was aimed to design a system that gives information about the breeding performances of cows. The expert system was designed based on the optimal values under the ideal conditions specified in the literature. The architecture of the system presented in this paper is designed as three input parameters and one output. The designed system was tested with 100 sample values. Afterwards, expert results were evaluated and system decisions were compared. The success of the decision support system was 94%. As a result, the reproductive efficiency of cows can be determined with this designed system. With this determination, the handling or disposal of cows can be determined.

The first and second order lattices in fuzzy logics are identified as generalization of the first and second order lattices in two-valued logic. In this context, the language of fuzzy theory are restated in order to show the flexibility gained by the relaxation of basic axioms of the two-valued logic. Example of knowledge representation are presented with Type I and Type II fuzzy sets and logics together with second order semantic uncertainty information contained within the boundaries of Type II fuzzy sets.

Summary form only given. Interpolative reasoning plays a key role in both fuzzy logic and neural network theory. The basic approaches to interpolative reasoning in both fuzzy logic and neural networks were surveyed, and their differences and similarities were analyzed. An important issue in interpolative reasoning in fuzzy logic relates to the solution of a system of fuzzy algebraic equations. Various approaches to this problem, including fuzzy Lagrangian interpolation and the use of FA-Prolog, were described and analyzed. Among other issues discussed were the compression of a system of fuzzy if-then rules and the induction of rules from observations. >

A many‐valued sentential logic with truth values in an injective MV‐algebra is introduced and the axiomatizability of this logic is proved. The paper develops some ideas of Goguen and generalizes the results of Pavelka on the unit interval. The proof for completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if and only if the algebra of the truth values is a complete MV‐algebra. In the well‐defined fuzzy sentential logic holds the Compactness Theorem, while the Deduction Theorem and the Finiteness Theorem in general do not hold. Because of its generality and good‐behaviour, MV‐valued logic can be regarded as a mathematical basis of fuzzy reasoning.

As we sketched in [Godo and Hajek, 1996], most of fuzzy inference in Zadeh’s style is well formalized in the many-sorted many-valued Pavelka-style fuzzy predicate logic — and this can be done in several ways. The most important fact is that patterns of fuzzy inference can be presented as sound deduction rules, with all necessary assumptions expressed by some formulas of predicate logic (with the usual quantifiers ∀, ∃) in the premisse part of the rule. Here we complement the presentation of [Godo and Hajek, 1996] by a somewhat unexpected formalization of Zadeh’s Generalized Modus Ponens (GMP, cf. e.g. Zadeh [1988; 1990; 1994]). We shall be sketchy; a full detailed presentation is to be found in [Godo and Hajek, to appear]. For the reader’s convenience we repeat the definition of the many-sorted RQL (rational quantification logic, cf. [Hajek, 1995; Hajek, 1997]).

Cellular automata (CA) theory in a geographic information systems (GIS) based framework is commonly used for modeling complex system such as urban growth or land-use change. However the geospatial data used in GIS databases and in CA models rely on the traditional crisp/Boolean representation of land-use classes with sharp boundaries. Furthermore, the definition of a CA set of transition rules is based on the concept of crisp rules despite the fact that some descriptive or uncertain knowledge of the system behavior can be better represented with fuzzy logic rules. This paper presents the potential of coupling fuzzy sets and fuzzy logic theory in current GIS-based cellular automata models of land-use transformations.

Since the invention of fuzzy sets and maturing of the fuzzy logic theory, fuzzy logic systems have been widely applied to various fields, such as fuzzy controller, data mining, and so on. New potential areas using fuzzy logic are also being explored with the emergence of other technologies. One booming technology today is the Internet, due to its fast growing number of users and rich contents. With huge data storage and speedy networks becoming available, multimedia contents like image, video, and audio are fast increasing. In order to search and index these media effectively, various content-based multimedia retrieval systems have been studied.

In fuzzy logic, linguistic variables are used to represent operating parameters in order to apply a more human-like way of thinking [Zadeh, 1965, 1968, 1973, 1988, 1989]. Fuzzy logic incorporates a simple, IF-THEN rule-based approach to solve a problem rather than attempting to model a system mathematically and this property plays a central role in most of fuzzy logic applications [Kang et al., 2000; Lin & Wang, 1999; Shi et al., 1999]. Recently, the main features of fuzzy logic theory make it highly applicable in many systematic designs in order to obtain a better performance when data analysis is too complex or impractical for conventional mathematical models. This chapter represents how fuzzy logic, as explained theoretically in the previous chapters, can practically be applied on a real case. For this aim, a clinical application of fuzzy logic was taken into account for cancer treatment by developing a fuzzy correlation model.

The purpose of this study is to describe the design of a prototype of an automatic traffic system with vehicle tracking using motion detection dlob and fuzzy logic control based control. Data collection techniques in this study used library research and laboratory research. The research was carried out by processing the data obtained by the author, data collection was carried out from March 2023. Based on the results and discussion it can be concluded that the calculation to obtain the traffic light signal time can be carried out by utilizing the Fuzzy Logic Toolbox found in Matlab computer program, and the performance generated by using Fuzzy logic theory has a smaller delay of 9.02 seconds. The duration of the green light generated by fuzzy logic corresponds to the volume of vehicles both in terms of vehicle arrivals and in terms of vehicle queues. The minimum value for the duration of the green light is 0 seconds and the maximum value is 15 seconds.

This paper is a tutorial on the use of fuzzy logic system, providing a broad-scope overview, especially on fuzzy logic design, and also the results of research of fuzzy application in robotics. At first, the fuzzy sets and fuzzy rules are explained as well as fuzzy logic theory regarding our research. A neural network (connectionist) model for fuzzy logic control and decision system in their neural network structure and learning ability. The description of the system by using mathematical model, linguistic rules, and parameter distribution are discussed.

In this article it has been tried to show that fuzzy theory performs better than probability theory in monitoring the product quality.A method that uses statistical techniques to monitor and control product quality is called statistical process control (SPC), where control charts are test tools frequently used for monitoring the manufacturing process.In this study, statistical quality control and the fuzzy set theory are aimed to combine.As known, fuzzy sets and fuzzy logic are powerful mathematical tools for modeling uncertain systems in industry, nature and humanity; and facilitators for common-sense reasoning in decision making in the absence of complete and precise information.In this basis for a textile firm for monitoring the yarn quality, control charts according to fuzzy theory by considering the quality in terms of grades of conformance as opposed to absolute conformance and nonconformance.And then with the same data for a textile factory, the control chart based on probability theory is constructed.The results of control charts based on two different approaches are compared.It's seen that fuzzy theory performs better than probability theory in monitoring the product quality.

Habitat suitability analysis is complex and requires integration of multiple attributes at a range of spatial scales. We use fine- and broad-scale variables within a spatial modelling framework to determine the suitability of greater sage-grouse nesting habitat using fuzzy logic. Fuzzy theory allows for a landscape component to have full, partial, or no membership in a particular management target. We used seven biophysical and anthropogenic variables correlated with nest site locations to build the fuzzy model. Using field and remotely sensed data and expert opinion, we developed fuzzy functions to define numerical membership values describing relationships between landscape characteristics and nesting habitat suitability. We used a fuzzy gamma overlay function to define five suitability classes in the resulting habitat map. Using a fuzzy logic model, we were able to spatially distinguish the suitability of nesting habitat using fine- and broad-scale attributes and characterise the uncertainty of the habitat model.

The article describes the concept of deploying IoT technologies within the environment of agrarian operations using a system approach with a focus on fuzzy logic. In addition to the introductory acquaintance with IoT and fuzzy theory, the paper focuses on specific possibilities of applying the fuzzy approach, especially in the case of animal husbandry. The main benefit for this field is the fulfillment of welfare principles and the achievement of economic savings based on optimization. The article also showcases a practical implementation of a demonstrative solution in the JavaScript programming language using data from IoT sensors.