Fuzzy majority functions

Fuzzy logic function f is unate if and only if f is either monotone increasing or monotone decreasing with regards to every variable. This paper studies some fundamental properties of fuzzy unate logic function. Based on the properties, this paper clarifies a necessary and sufficient condition of any given incompletely specified function to be unate fuzzy logic function.

Copyright c 2013 Omar Salazar, Jairo Soriano, and Humberto Serrano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract It is known that any binary logic function (in binary logic) can be rep- resented by at least one logic formula, however this is not always true for a ternary logic function (in ternary logic). A ternary logic function can be represented by at least one logic formula if and only if it satises a mathematical condition which is called regularity. Also, it is known that a fuzzy logic formula (in standard fuzzy logic) can be obtained by means of truth tables in ternary logic. This paper presents a method destined for extending a binary logic function into one (or more) ter- nary logic function(s) representable by at least one logic formula, and therefore, to obtain fuzzy logic formulas from a binary logic function. Mathematics Subject Classication: 03B52, 06D72, 08A72, 94D05

Introduction: With regard to increasing population of country, need to high agricultural production is essential. The most suitable method for this issue is high production per area unit. Preparation much food and other environmental resources with conservation of biotic resources for futures will be possible only with optimum exploitation of soil. Among effective factors for the most production balanced addition of fertilizers increases production of crops higher than the others. With attention to this topic, determination of soil fertility degree is essential tobetter use of fertilizers and right exploitation of soils. Using fuzzy logic and Analytic Hierarchy Process (AHP) could be useful in accurate determination of soil fertility degree. Materials and Methods: The study area (at the east of Rasht city) is located between 49° 31' to 49° 45' E longitude and 37° 7' to 37° 27' N latitude in north of Guilan Province, northern Iran, in the southern coast of the Caspian sea. 117 soil samples were derived from0-30 cm depth in the study area. Air-dried soil samples were crushed and passed through a 2mm sieve. Available phosphorus, potassium and organic carbon were determined by sodium bicarbonate, normal ammonium acetate and corrected walkly-black method, respectively. In the first stage, the interpolation of data was done by kriging method in GIS context. Then S-shape membership function was defined for each parameter and prepared fuzzy map. After determination of membership function weight parameters maps were determined using AHP technique and finally soil fertility map was prepared with overlaying of weighted fuzzy maps. Relative variance and correlation coefficient criteria used tocontrol groups separation accuracy in fuzzy fertility map. Results and Discussion: With regard to minimum amounts of parameters looks some lands of study area had fertility difficulty. Therefore, soil fertility map of study area distinct these lands and present soil fertility groups for better management of soil and plant nutrition. Weight of soil parameters was0.54, 0.29 and 0.17 for organic carbon, available phosphor and potassium, respectively. Fuzzy map of study area includes five soil fertility groups as: 22.9% very high fertility, 27.7% high fertility, 35.53% medium fertility, 10.48% low fertility and 3.39% very low fertility. Consequently, a separated map for soil fertility prepared to evaluate soil fertility of study area for rice cultivation. Toinvestigatethe efficiency of fuzzy model and AHP in increasing the accuracy of soil fertility map, soil fertility map with Boolean method prepared as well. Boolean map showed 58.88% fertile and 41.12% unfertile.15 soil samples from different soil fertility groups of study area were derived fromcontrol of maps accuracy. 13 renewed samples of 15 and 9 soil samples have matched with fuzzy and Boolean map, respectively. Comparison of parameters mean in fuzzy map fertility groups showed that parameters mean amounts of very high and high fertility groups are higher than optimum level except potassium that is a few lower than optimum level in high fertility group, therefore, addition of fertilizers in these groups could not be useful to increase rice crop production. Phosphorus parameter amount is lower than the critical level in very low, low and medium fertility groups, then in these groups phosphorus fertilizer should be added to the soil toincreaserice production. The amount of potassium parameter is higher than the critical level and lower than optimum limit in very low, low, medium and high fertility groups, then in these groups addition of potassium fertilizer will results in theincrease of production. Organic carbon amount is lower than optimum level in very low and low fertility groups. With regard to the relation between organic carbon andnitrogen and phosphorus, therefore, the addition of organic carbon fertilizer could compensate deficit of nitrogen and phosphorus in these groups as well. Attention to the presented explanations and comparison of fuzzy and Boolean maps using parameters amounts in renewed sampling points for control of maps accuracy, it is distinct that fuzzy logic could influencetheoptimum using of fertilizers with increasing map efficiency and accuracy. In addition, relative variance and correlation coefficient amounts showed that fuzzy map has separatedquite wellparameters changes. Conclusion: Effective parameters in soil fertility, includingorganic carbon, phosphorus and potassium were used topreparesoil fertility map for rice cultivation. With regard to the minimum amounts of parameters looks some lands of study area had fertility difficulty. Therefore, soil fertility map of study area distinct these lands and presents soil fertility groups tobetter management of soil and plant nutrition. Fuzzy and Boolean methods were used topreparesoil fertility map. Comparison of these two approaches showed that fuzzy method with AHP caused to increase theefficiency and accuracy of fertility map for rice. Separated and distinguish soil fertility groups in fuzzy map help suitable distribution and optimum use of fertilizers for rice production.

The paper presents a novel, transistor level, implementation of selected fuzzy set operators suitable for fuzzy control systems realized in low-power hardware. We propose a fully digital, asynchronous realization of basic fuzzy logic (FL) functions, such as the bounded sum, bounded difference, bounded product, bounded complement, fuzzy logic union (MAX) and fuzzy logic intersection (MIN). All of the proposed operators has been implemented in the CMOS TSMC 180nm Technology and verified by means of transistor level simulations in Hspice environment. The proposed structures of the FL functions can easily be scaled to any signal resolutions.

Normal forms for fuzzy logic functions and their approximation ability

We discuss extensions to a controlled natural language allowing spatiotemporal expressions to be interpreted as fuzzy logic functions. The extensions first required new sentence templates. Next, changes to a GPSG parser modified its lexicon, and then extended its parsing and logical form rules to allow user-defined spatial and temporal constraints to be extracted. The sentence templates ground user-defined culturally-specific times and places to boundaries surrounding prototypical ideals. Query points, defined by location and time, are compared to these definitions using Gaussians centered at prototypical 'ideal' times or places. The Gaussians provide soft fall-off at the boundaries. Fuzzy logic operators allow larger expressions to be interpreted, analogous to Boolean combinations of terms. The mathematically-interpreted spatiotemporal terms act as domain features for a machine learning algorithm. They allow easy specification (compared to programming) of basis functions for an inverse reinforcement learning algorithm that detects anomalous vehicle tracks or suspicious agent behavior.

Improving feeding strategies for shrimp farming using fuzzy logic, based on water quality parameters

On fuzzy quasi continuity and an application of fuzzy set theory

This paper presents a new approach to detect and classify power quality disturbances in the power system using Fuzzy C-means clustering, Fuzzy logic (FL) and Radial basis Function Neural Networks (RBFNN). Feature extracted through wavelet is used for training, after training, the obtained weight is used to classify the power quality problems in RBFNN, but it suffers from extensive computation and low convergence speed. Then to detect and classify the events, FL is proposed, the extracted characters are used to find out membership functions and fuzzy rules being determined from the power quality inherence. For the classification,5 types of disturbance are taken in to account. The classification performance of FL is compared with RBFNN.The clustering analysis is used to group the data in to clusters to identifying the class of the data with Fuzzy C-means algorithm. The classification accuracy of FL and Fuzzy C-means clustering is improved with the help of cognitive as well as the social behavior of particles along with fitness value using Particle swarm optimization (PSO),just by determining the ranges of the feature of the membership funtion for each rules to identify each disturbance specifically.The simulation result using Fuzzy C-means clustering possess significant improvements and gives classification results in less than a cycle when compared over other considered approach.

This paper presents the way of implementation of fuzzy set operators at the transistor level. We propose a novel realization of basic fuzzy logic (FL) functions, such as bounded sum, bounded difference, bounded product, bounded complement, fuzzy logic union (MAX) and fuzzy logic intersection (MIN). The proposed structures of the operators may be easily connected in chains, creating larger FL systems.

The aim of this project was to propose an original approach c to predetermine the topology of a surface from the point cloud obtained during a digitizing process. This method has been applied for the predefinition of the different main regions of a surface, in order to be able to divide the point cloud in different separate clouds corresponding to these regions. It should be also possible to optimize locally the surface when taking into account tangency and curvature conditions. The main advantage of this method is that, for a given accuracy, the complexity of the surface is lower than a traditional method, an the computations are quite the same than those obtained when using traditional surface modeling algorithms. This method allows a qualitative decomposition of the surface defined from a function z equals f(x,y). In the paper, the fuzzification and defuzzification process and a study of the influence of the main parameters will also be presented. Some fuzzy logic algorithms and functions have been compared and analyzed when applied on the example.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Recognition and determination of fuzzy logical relationship in the system fault evolution process

The processes’ modeling is an important aspect in the industry since it allows to obtain high productivity with energy and material savings. The hybrid process electrochemical discharge machining (ECDM) is subject to uncertainty and inaccuracy levels in the parameters, so a viable option to model this process is through soft computing techniques such as fuzzy logic and artificial neural networks. In this work, we present three models using fuzzy logic, backpropagation network, and radial basis function network for the prediction of the material removal rate (MRR). The gap voltage (Vg), peak current (Ip), and frequency (f) were taken as input parameters. A 3-factor full factorial design was developed with 2 levels (23), two replicas, and four central points. The model with the higher accuracy according to experimental result was radial basis function artificial neural network with 97.25% of accuracy.

In this chapter we have collected together the basic ideas from fuzzy sets and fuzzy functions needed for the book. Any reader familiar with fuzzy sets, fuzzy numbers, the extension principle, a-cuts, interval arithmetic, possibility theory and fuzzy functions may go on to the rest of the book. A good general reference for fuzzy sets and fuzzy logic is [1], [6].

In this paper, we first study the stability and convergence property of fuzzy logic networks (FLN). A random approach is adopted to simulate the convergence speed and steady-state properties based on four fuzzy logical functions. The simulation results show that MV logical function causes the system to be on the edge of chaos when the number of nodes increases. Thus this logical function is more useful to infer real complex networks, such as gene regulatory networks. Then, a novel gene regulatory network inference algorithm based on the FLN theory is proposed and tested. The algorithm uses fuzzy logical functions to model gene regulatory relationships, and the degrees of regulations are represented as the length of accumulated distances during a period of time intervals. Based on the assumption that the distribution of connectivity in yeast protein-protein networks follows the Zipf's law, the criteria for algorithm parameter quantifications are deduced. One unique feature of this algorithm is that it makes limited a priori assumptions concerning the modeling; hence the algorithm is categorized as a data-driven algorithm. The algorithm was applied to the S. pombe time-series dataset and 407 cell cycle regulated genes were used. The algorithm inferred 59 functionally verified regulations, 47 regulations involving genes with unknown functions, and 19 dubious regulations. The 125 regulatory pairs involve 108 genes, and the average connectivity of the inferred network, 1.157, confirms the Zipf's law.