Truth-Valued-Flow Inference (TVFI) and its applications in approximate reasoning

The framework of the theory of Truth-valued-flow Inference (TVFI) is introduced. Even though there are dozens of papers presented on fuzzy reasoning, we think it is still needed to explore a rather unified fuzzy reasoning theory which has the following two features: (1) it is simplified enough to be executed feasibly and easily; and (2) it is well structural and well consistent enough that it can be built into a strict mathematical theory and is consistent with the theory proposed by L.A. Zadeh. TVFI is one of the fuzzy reasoning theories that satisfies the above two features. It presents inference by the form of networks, and naturally views inference as a process of truth values flowing among propositions

Gödel Description Logics

In the last few years there has been a large effort for analysing the computational properties of reasoning in fuzzy Description Logics. This has led to a number of papers studying the complexity of these logics, depending on their chosen semantics. Surprisingly, despite being arguably the simplest form of fuzzy semantics, not much is known about the complexity of reasoning in fuzzy DLs w.r.t. witnessed models over the Gödel t-norm. We show that in the logic G-IALC, reasoning cannot be restricted to finitely valued models in general. Despite this negative result, we also show that all the standard reasoning problems can be solved in this logic in exponential time, matching the complexity of reasoning in classical ALC

IVTURS: A linguistic fuzzy rule-based classification system based on a new interval-valued fuzzy reasoning method with tuning and rule selection

Interval-valued fuzzy sets have been shown to be a useful tool for dealing with the ignorance related to the definition of the linguistic labels. Specifically, they have been successfully applied to solve classification problems, performing simple modifications on the fuzzy reasoning method to work with this representation and making the classification based on a single number. In this paper we present IVTURS, a new linguistic fuzzy rule-based classification method based on a new completely interval-valued fuzzy reasoning method. This inference process uses interval-valued restricted equivalence functions to increase the relevance of the rules in which the equivalence of the interval membership degrees of the patterns and the ideal membership degrees is greater, which is a desirable behaviour. Furthermore, their parametrized construction allows the computation of the optimal function for each variable to be performed, which could involve a potential improvement in the system’s behaviour. Additionally, we combine this tuning of the equivalence with rule selection in order to decrease the complexity of the system. In this paper we name our method IVTURS-FARC, since we use the FARC-HD method to accomplish the fuzzy rule learning process. The experimental study is developed in three steps in order to ascertain the quality of our new proposal. First, we determine both the essential role that interval-valued fuzzy sets play in the method and the need for the rule selection process. Next, we show the improvements achieved by IVTURS-FARC with respect to the tuning of the degree of ignorance when it is applied in both an isolated way and when combined with the tuning of the equivalence. Finally, the significance of IVTURS-FARC is further depicted by means of a comparison by which it is proved to outperform the results of FARC-HD and FURIA, which are two high performing fuzzy classification algorithms.This work was supported in part by the Spanish Ministry of Science and Technology under projects TIN2011-28488 and TIN2010-15055 and the Andalusian Research Plan P10-TIC-6858 and P11-TIC-7765

Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets

AbstractWe begin the paper studying the axioms that the indicators of the grade of inclusion of a fuzzy set in another fuzzy set must satisfy. Next, we present an expression of such indicator, first for fuzzy sets and then for interval-valued fuzzy sets, analyzing in both cases their main properties. Then, we suggest an expression for the similarity measure between interval-valued fuzzy sets. Besides, we study two methods for inference in approximate reasoning based on interval-valued fuzzy sets, the inclusion grade indicator and the similarity measure. Afterwards, we expose some of the most important properties of the methods of inference presented and we compare these methods to Gorzalczany's. Lastly, we use the indicator of the grade of inclusion for interval-valued fuzzy sets as an element that selects from the different methods of inference studied, the one that will be executed in each case

A Framework of Subjective Performance Evaluation Using Fuzzy Technique

This research proposes the framework of subjective performance evaluation using fuzzy technique for ranking the attributes of different types of datasets under a multi-criteria environment. Some previous studies on fuzzy techniques have been attempted in assessment and evaluation methods. The techniques such as fuzzy similarity function, fuzzy synthetic decision and satisfaction function have been adopted in these fuzzy evaluation methods. However, research that discover a scaling measurement which can express the subjectivity element and integrate the organisation‘s objectives and goals into the evaluation processes by utilising the fuzzy rule in the subjective evaluation method seem limited. Hence, this framework uses the application of fuzzy sets, and approximate reasoning to determine the performance evaluation of various characteristics in decision-making. The framework based upon fuzzy sets has initiated the idea of membership set score valued evaluation of each criterion alternative enables to include requirements which are incomplete and imprecise. The approximate reasoning of the method allows decision maker to make the best choice in accordance of human thinking and reasoning processes. The method introduces an approach of normalising data using similarity function which dampens the extreme value that exists in the data. The framework is suitable for dealing with evaluations in situations that involve subjectivity, vagueness and imprecise information, such as the grading system of evaluation which involves subjectivity, vagueness and imprecise information, such as the grading system evaluation which involves many hedges like "good", "bad" and "satisfactory"

Design of Self-tuning PID Controller Parameters Using Fuzzy Logic Controller for Quad-rotor Helicopter

This paper presents the design of a Fuzzy PID controller (FPID) based on fuzzy logic with a PID structure with many valued logic and reasoning. The self-turning Fuzzy PID control take in an error and the rate of change of error of the altitude and attitude of the quadrotor as the input to the fuzzy controller and use the fuzzy rules to adjust the PID parameter automatically. Simulations have been conducted to observe the differences in controlling the quadrotor in flight using the new FPID controller instead of using PID controller. The effectiveness of the developed FPID is verified using the dSPACE platform whereby the Simulink model of the controller is converted to a real time system to generate the control signals for the control of quad rotor helicopter