Eigenlogic: a Quantum View for Multiple-Valued and Fuzzy Systems

We propose a matrix model for two- and many-valued logic using families of observables in Hilbert space, the eigenvalues give the truth values of logical propositions where the atomic input proposition cases are represented by the respective eigenvectors. For binary logic using the truth values {0,1} logical observables are pairwise commuting projectors. For the truth values {+1,-1} the operator system is formally equivalent to that of a composite spin 1/2 system, the logical observables being isometries belonging to the Pauli group. Also in this approach fuzzy logic arises naturally when considering non-eigenvectors. The fuzzy membership function is obtained by the quantum mean value of the logical projector observable and turns out to be a probability measure in agreement with recent quantum cognition models. The analogy of many-valued logic with quantum angular momentum is then established. Logical observables for three-value logic are formulated as functions of the Lz observable of the orbital angular momentum l=1. The representative 3-valued 2-argument logical observables for the Min and Max connectives are explicitly obtained.Comment: 11 pages, 2 table

Comparison between prediction capabilities of neural network and fuzzy logic techniques for L and slide susceptibility mapping.

Preparation of L and slide susceptibility maps is important for engineering geologists and geomorphologists. However, due to complex nature of L and slides, producing a reliable susceptibility map is not easy. In recent years, various data mining and soft computing techniques are getting popular for the prediction and classification of L and slide susceptibility and hazard mapping. This paper presents a comparative analysis of the prediction capabilities between the neural network and fuzzy logic model for L and slide susceptibility mapping in a geographic information system (GIS) environment. In the first stage, L and slide-related factors such as altitude, slope angle, slope aspect, distance to drainage, distance to road, lithology and normalized difference vegetation index (ndvi) were extracted from topographic and geology and soil maps. Secondly, L and slide locations were identified from the interpretation of aerial photographs, high resolution satellite imageries and extensive field surveys. Then L and slide-susceptibility maps were produced by the application of neural network and fuzzy logic approahc using the aforementioned L and slide related factors. Finally, the results of the analyses were verified using the L and slide location data and compared with the neural network and fuzzy logic models. The validation results showed that the neural network model (accuracy is 88%) is better in prediction than fuzzy logic (accuracy is 84%) models. Results show that "gamma" operator (X = 0.9) showed the best accuracy (84%) while "or" operator showed the worst accuracy (66%)

Safe Recursion on Notation into a Light Logic by Levels

We embed Safe Recursion on Notation (SRN) into Light Affine Logic by Levels (LALL), derived from the logic L4. LALL is an intuitionistic deductive system, with a polynomial time cut elimination strategy. The embedding allows to represent every term t of SRN as a family of proof nets |t|^l in LALL. Every proof net |t|^l in the family simulates t on arguments whose bit length is bounded by the integer l. The embedding is based on two crucial features. One is the recursive type in LALL that encodes Scott binary numerals, i.e. Scott words, as proof nets. Scott words represent the arguments of t in place of the more standard Church binary numerals. Also, the embedding exploits the "fuzzy" borders of paragraph boxes that LALL inherits from L4 to "freely" duplicate the arguments, especially the safe ones, of t. Finally, the type of |t|^l depends on the number of composition and recursion schemes used to define t, namely the structural complexity of t. Moreover, the size of |t|^l is a polynomial in l, whose degree depends on the structural complexity of t. So, this work makes closer both the predicative recursive theoretic principles SRN relies on, and the proof theoretic one, called /stratification/, at the base of Light Linear Logic

The history of fuzzy logic methods

Prediction and interpretation of behavior of complex medical or industrial systems are possible due to application of expert systems. This kind of expert systems emulates an ability to make decisions like a human expert. The emulation built on the fuzzy logic, which is integrated into the system. The author of the theory of the fuzzy logic or fuzzy sets is a professor from the University of California, Berkeley - L. Zadeh. His theory permits the determination of quantitative degree of the belonging of all elements included in a certain set. However, in common theory of sets elements have only to states - an element must belong or must not belong to the pack

IMPLEMENTATION OF FUZZY LOGIC CONTROLLERS TO MAINTAIN WATER TEMPERATURE IN HYDROPONICS NFT FOR LOLLO VERDE LETTUCE (LACTUCA SATIVA L.)

Objective: The purpose of this study was to maintain the nutritional water temperature in the range of 25-27 °C for Lollo Verde lettuce (Lactuca sativa L.). Methods: The method was the Fuzzy Logic Mamdani (FLM) with two inputs, i.e. real time clock and temperature. The output was crisp speed PWM with the center of area method. Results: The results showed that Fuzzy logic was succeeded in reducing water temperature in the NFT system from 28-32 °C to 26-27 °C, with an average delta of 3.5 °C. Fuzzy logic maintained the nutrient water temperature in the Lollo Verde lettuce with an average of 26.57±0.5 °C. Water temperature affected the yield of Lollo Verde lettuce. Conclusion: The yield of NFT FLM system was better compared to the conventional NFT system

Fuzzy Maximum Satisfiability

In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to {\L}ukasiewicz logic. The MaxSAT problem for a set of formulae {\Phi} is the problem of finding an assignment to the variables in {\Phi} that satisfies the maximum number of formulae. Three possible solutions (encodings) are proposed to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem (WCSP). Like its Boolean counterpart, the extended fuzzy MaxSAT will have numerous applications in optimization problems that involve vagueness.Comment: 10 page

A fuzzy-logic based expert system for diagnosis and control of an integrated wastewater treatment

A supervisory expert system based on fuzzy logic rules was developed for diagnosis and control of a lab- scale plant comprising anaerobic/anoxic/aerobic modules for combined high rate biological N and C removal. The design and implementation of a computational environment in LabVIEW for data acquisition, plant operation and distributed equipment control is described. The Fuzzy Logic toolbox for MATLAB was also used for the development of the fuzzy logic rule based system. The fuzzy rules were generated from quantitative and qualitative information, to identify the status of the plant operation and to decide the best commands to be sent to the final control elements to recover the stable operation in case of disturbances of the processes. A step increase in ammonia concentration from 20 to 60 mg N/L was applied during a trial period of 73 hours. Recycle flow rate from the aerobic to the anoxic module and by-pass flow rate from the influent directly to the anoxic reactor were the output of the fuzzy system that were automatically changed (from 34 to 111 L/day and from 8 to 13 L/day, respectively), when new plant conditions were recognized by the expert system. Denitrification efficiency higher than 85% was achieved 30 hours after the disturbance and 15 hours after the system response at an HRT as low as 1.5 hours. Nitrification efficiency gradually increased from 12 to 50% at an HRT of 3 hours. The system proved to properly react in order to set adequate operating conditions that timely led to recover efficient N and C removal rates.Fundação para a Ciência e a Tecnologia (FCT) - doctoral research grant BD/1299/2000.União Europeia (UE) - Fundo Social Europeu (FSE) - doctoral research grant BD/13317/2003

Geometric Fuzzy Logic Systems

There has recently been a significant increase in academic interest in the field oftype-2 fuzzy sets and systems. Type-2 fuzzy systems offer the ability to model and reason with uncertain concepts. When faced with uncertainties type-2 fuzzy systems should, theoretically, give an increase in performance over type-l fuzzy systems. However, the computational complexity of generalised type-2 fuzzy systems is significantly higher than type-l systems. A direct consequence of this is that, prior to this thesis, generalised type-2 fuzzy logic has not yet been applied in a time critical domain, such as control. Control applications are the main application area of type-l fuzzy systems with the literature reporting many successes in this area. Clearly the computational complexity oftype-2 fuzzy logic is holding the field back. This restriction on the development oftype-2 fuzzy systems is tackled in this research. This thesis presents the novel approach ofdefining fuzzy sets as geometric objects - geometric fuzzy sets. The logical operations for geometric fuzzy sets are defined as geometric manipulations of these sets. This novel geometric approach is applied to type-I, type-2 interval and generalised type-2 fuzzy sets and systems. The major contribution of this research is the reduction in the computational complexity oftype-2 fuzzy logic that results from the application of the geometric approach. This reduction in computational complexity is so substantial that generalised type-2 fuzzy logic has, for the first time, been successfully applied to a control problem - mobile robot navigation. A detailed comparison between the performance of the generalised type-2 fuzzy controller and the performance of the type-l and type-2 interval controllers is given. The results indicate that the generalised type-2 fuzzy logic controller outperforms the other robot controllers. This outcome suggests that generalised type-2 fuzzy systems can offer an improved performance over type-l and type-2 interval systems