Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics

Recently, algebraic Routley–Meyer-style semantics was introduced for basic substructural logics. This paper extends it to fuzzy logics. First, we recall the basic substructural core fuzzy logic MIAL (Mianorm logic) and its axiomatic extensions, together with their algebraic semantics. Next, we introduce two kinds of ternary relational semantics, called here linear Urquhart-style and Fine-style Routley–Meyer semantics, for them as algebraic Routley–Meyer-style semantics.

Research on intuitionistic fuzzy negations

In the theories of intuitionistic fuzzy sets and intuitionistic fuzzy logics, there are 54 different negations. Here, we check the relationship between every two of them.

Analysis of Economic Relationship Using the Concept of Complex Pythagorean Fuzzy Information

Fuzzy set theory and fuzzy logics are the powerful mathematical tools to model the imprecision and vagueness. In this research, the novel concept of complex Pythagorean fuzzy relation (CPFR) is introduced. Furthermore, the types of CPFRs are explained with appropriate examples such as CPF composite relation, CPF equivalence relation, CPF order relation, and CPF equivalence classes. Moreover, numerous results and interesting properties of CPFRs are discussed in detail. Furthermore, the impacts of economic parameters over each other are studied through the proposed concepts of CPFRs. In addition, the application also discusses the effects of economic parameters of one country over the other countries’ economic parameters.

Automated Generation of EQ-Algebras through Genetic Algorithms

This article introduces an approach to the automated generation of special algebras through genetic algorithms. These algorithms can be also used for a broader variety of applications in mathematics. We describe the results of research aiming at automated production of such algebras with the help of evolutionary techniques. Standard approach is not relevant due to the time complexity of the task, which is superexponential. Our research concerning the usage of genetic algorithms enabled the problem to be solvable in reasonable time and we were able to produce finite algebras with special properties called EQ-algebras. EQ-algebras form an alternate truth–value structure for new fuzzy logics. We present the algorithms and special versions of genetic operators suitable for this task. Then we performed experiments with application EQ-Creator are discussed with proper statistical analysis through ANOVA. The genetic approach enables to automatically generate algebras of sufficient extent without superexponential complexity. Our main results include: that elitism is necessary at least for several parent members, a high mutation ratio must be set, optional axioms fulfilment increases computing time significantly, optional properties negatively affect convergence, and colorfulness was defined to prevent trivial solutions (evolution tends to the simplest way of achieving results).

Fuzzy Logic Method for the Speed Estimation in All-Wheel Drive Electric Racing Vehicles

This paper presents a method for the vehicle speed estimation with a Fuzzy Logic based algorithm. The algorithm acquires the measurements of the yaw rate, steering angle, wheel velocities and exploits a set of five Fuzzy Logics dedicated to different driving conditions. The technique estimates the speed exploiting a weighted average of the contributions provided by the longitudinal acceleration and the credibility assigned by the Fuzzy Logics to the measurements of the wheels’ speed. The method is experimentally evaluated on an all-wheel drive electric racing vehicle and is valid for the front and rear wheel drive configurations. The experimental validation is performed by comparing the obtained estimation with the result of computing the speed as the average of the linear velocity of the four wheels. A comparison to the integral of the vehicle acceleration over time is reported.

Assessment of Technical Condition of an Accumulator Common Rail Injector by Temperature of its Units

This paper presents a method for the vehicle speed estimation with a Fuzzy Logic based algorithm. The algorithm acquires the measurements of the yaw rate, steering angle, wheel velocities and exploits a set of five Fuzzy Logics dedicated to different driving conditions. The technique estimates the speed exploiting a weighted average of the contributions provided by the longitudinal acceleration and the credibility assigned by the Fuzzy Logics to the measurements of the wheels’ speed. The method is experimentally evaluated on an all-wheel drive electric racing vehicle and is valid for the front and rear wheel drive configurations. The experimental validation is performed by comparing the obtained estimation with the result of computing the speed as the average of the linear velocity of the four wheels. A comparison to the integral of the vehicle acceleration over time is reported.

Fuzzy Logic Design Approach for A Singly Reinforced Concrete Beam

This paper presents the Fuzzy logics approach for a singly reinforced concrete beam. The rules are generated for the FIS for the variables. The width, and the moment constitutes the crisp data for the inputs and the steel ratio represents the crisp output. The MATLAB fuzzy tool kit is used to execute the simulation. The code prescription of the design of a singly reinforced concrete beam is a straight forward calculation. However, the overestimation of reinforcement can be enormous. This can be very impacting on the cost of the project. This work attempts to use fuzzy logic predictive power to design a singly reinforced concrete beam. The result reasonable agreement between the code provisions and the fuzzy logic predictions. It was established that fuzzy logic can be adopted as a significant technique for the optimization of the design of a singly reinforced concrete beam.

A Fuzzy Take on the Logical Issues of Statistical Hypothesis Testing

Statistical Hypothesis Testing (SHT) is a class of inference methods whereby one makes use of empirical data to test a hypothesis and often emit a judgment about whether to reject it or not. In this paper, we focus on the logical aspect of this strategy, which is largely independent of the adopted school of thought, at least within the various frequentist approaches. We identify SHT as taking the form of an unsound argument from Modus Tollens in classical logic, and, in order to rescue SHT from this difficulty, we propose that it can instead be grounded in t-norm based fuzzy logics. We reformulate the frequentists’ SHT logic by making use of a fuzzy extension of Modus Tollens to develop a model of truth valuation for its premises. Importantly, we show that it is possible to preserve the soundness of Modus Tollens by exploring the various conventions involved with constructing fuzzy negations and fuzzy implications (namely, the S and R conventions). We find that under the S convention, it is possible to conduct the Modus Tollens inference argument using Zadeh’s compositional extension and any possible t-norm. Under the R convention we find that this is not necessarily the case, but that by mixing R-implication with S-negation we can salvage the product t-norm, for example. In conclusion, we have shown that fuzzy logic is a legitimate framework to discuss and address the difficulties plaguing frequentist interpretations of SHT.