Łukasiewicz Logic Research Articles

FUZZY MODELING AND CONTROL OF BATCH BEER FERMENTATION+

Fuzzy reasoning based modeling of heuristic control rules are employed for control of batch beer fermentation. The effect of different types of membership functions, viz., line, triangular and phi membership functions is evaluated for the fuzzy subset. Various fuzzy model based controllers are presented using two approaches, namely simple fuzzy controller of few rules (FCFR) and rigorous fuzzy controller of many rules (FCM R), and also applied for the temperature control of fermenter. Zadeh's logic and Lukasiewicz's logic are adopted for computing the compositional rule of fuzzy logic inference. The results demonstrate that the proposed fuzzy controllers show better performance than the conventional controllers. FCFR approach provides better control performance, but needs optimum tuning or selection of gains for the fuzzy input and output variables, whereas FCMR approach is preferred due to flexibility in the operation of many control rules. Further, FCMR approach is free from optimum tuning or selection ...

The simplest fuzzy controllers using different inference methods are different nonlinear proportional-integral controllers with variable gains

The author analytically proves that the simplest fuzzy controllers using different inference methods are different nonlinear proportional-integral (PI) controllers with proportional-gains and integral-gains changing with inputs of the controllers. The inference methods involved are Mamdani's minimum inference method, Larsen's product inference method, the drastic product inference method and the bounded product inference method. Configuration of the fuzzy controllers is minimal, which includes two input fuzzy sets, three output fuzzy sets, four control rules, Zadeh fuzzy logic AND, Lukasiewicz fuzzy logic OR and a center of gravity defuzzification algorithm. After analytically investigating properties of the nonlinear PI controllers, the author reveals that the bounded product inference method is inappropriate for the control purpose while the other three inference methods are appropriate. Dynamic and static control behaviors of the fuzzy controllers with the appropriate inference methods are analytically compared with each other, and are also compared with those of the linear PI controller. Finally, it is analytically proven that the fuzzy control systems have the same local stability at the equilibrium point as the corresponding linear PI control system does.

Fuzzy control of SMES for levelling load power fluctuation based on Lukasiewicz logic

Provided that superconducting magnetic energy storage (SMES) is located near the consumer in the power system, levelling of fluctuating load power and compensation of reactive power can be achieved. Thus, loss in the power system can be reduced and the power system stability can be improved. An SMES control strategy for levelling the fluctuating load power based on Lukasiewicz logic is proposed. The control characteristics are discussed by comparing a simulation with the control results of other methods proposed by the authors. The variance achieved by the proposed method is smaller than those obtained with the other control methods. Thus, the proposed control method is superior to other control methods

REPRESENTATION OF EXPERT KNOWLEDGE AS A FUZZY AXIOMATIC THEORY

The aim of the paper is to present an original fuzzy logic based approach for dealing with uncertainties in expert systems. Its essence consists in understanding a knowledge base as a fuzzy axiomatic theory, i.e. a set of formulae in which each formula is assigned a weight specifying the degree of membership in the fuzzy set of special axioms. According to this principle, the task of inference in expert systems can be analyzed from the many-valued (fuzzy) logic perspective. As a result of theoretical considerations, Lukasiewicz's logic is preferred because of its completeness property. The inference mechanism based on this logic has been implemented and compared with the standard in different applications.

Social choice and Lukasiewicz logic

An approach to the social choice problem based on multiple valued logic is suggested. It is assumed that individual preference are classical binary relations, whereas the social preference is a valued binary relation. The role of Lukasiewicz logic in modelling valued transitive relations is discussed. We argue that this logic is a natural choice for contructing valued social preference. The paper is concerned with Arrow's theory of social welfare functions. Standard conditions of Unrestricted Domain, Pareto, Independence of Irrelevant Alternatives, and Nondictatorship are employed. We show that certain means in binary relations spaces are social welfare functions satisfying conditions of the classical Arrow's Possibility Theorem. It is also shown that collective choice rules given by means are completely characterized by the conditions of Unrestrict Domain, Anomymity, Neutrality, and Positive Responsiveness.

A look at metrics and norms through the Lukasiewicz logic

ABSTRACT In this paper we look, at metrics and norms through many-valued logics, especially through the infinite-valued Lukasiewicz logic. It appears that the roots of those notions and constructions are just in many-valued logics rather than in the classical two-valued logic. This fact and some interpretations following therefrom can stimulate new approaches and ideas in the area of applied mathematics and applications of mathematics.

Fuzzy control theory: The linear case

A linear fuzzy proportional-integral (PI) controller with one input and one output is defined in terms of piecewise linear membership functions for fuzzification; control rules; and defuzzification algorithm. It is shown that a linear fuzzy controller is not equivalent to a linear non-fuzzy PI controller if the rules are evaluated using the Zadeh, probability or Lukasiewicz fuzzy logic alone. However, the linear fuzzy controller is precisely equivalent to a linear non-fuzzy PI controller if mixed fuzzy logic is used to evaluate the control rules, when the fuzzy logics used are selected with due regard to prior associations implied by the control rule operands themselves. This finding has relevance to the selection of fuzzy logics in fuzzy expert systems and for fuzzy logics in general.

Application of Fuzzy Controller to Automobile Speed Control System

This paper deals with the synthesis of fuzzy logic controller by using the fuzzy reasoning based on Lukasiewicz logic proposed by Y.Tsukamoto and its application to automobile speed control system. The controller is composed of a set of linguistic control rules which are conditional linguistic statements expressing the relationship between inputs and outputs. The inputs are the ‘error’ which is the difference between the set point and the present speed, and the ‘change in error’ which is the difference between error values at the present and last sampling instants. The output, that is, manipulated variable is inferred by using truth qualification, converse of truth qualification and fuzzy modus ponens which are based on the fuzzy logic introducing the linguistic truth value.An algorithm to compute the values of manipulated variable on the microprocessor (Intel 8085) is developed in order to make a real time speed control of autombile. We discuss the results of road test of automobile (TOYOPET CROWN ’72) equipped with the microprocessor and we also discuss about usefulness of fuzzy logic controller applied to the automobile speed control sys tem.

A method of axiomatization of Łukasiewicz logics

By the language of Lukasiewicz logics we understand the algebra of formulas L = 〈L,→,∼〉. The μ-valued Lukasiwicz matrix 〈Aμ, {1}〉, μ = 2, 3, . . ., א0, (cf. [1]), will be denoted here by Mμ. Lμ = R(Mμ) is the set of tautologies of Mμ and is called the μ-valued Lukasiewicz system. All the unexplained notation in this text will come from Wojcicki’s paper [4]. Let us define two versions of א0-valued Lukasiewicz consequence: (A) Cא0(X) is the least set of formulas including X∪ Lא0 and closed under modus ponens. (B) α ∈ C∗ א0(X) iff for every h : L → hom Aא0 we have hα = 1 whenever h(X) ⊆ {1}.