Fuzzy Propositions Research Articles

Adaptive extreme learning machine using soft computing fuzzy propositions—Validating operating state of solar energy system

In this paper soft computing fuzzy proposition/rule based adaptive extreme learning is proposed. This article illustrates the impact of agricultural solar panel (AgSP) and its operating condition/state during the farming seasons and hence safety of energy system sustained. Extreme learning machine (ExLM) used as learning machine (LM) for artificial intelligence (AI) training to predict the operating state of applied AgSP green energy unit. soft computing Fuzzy rules are framed for every instant of leaning machine to identifying the lower mismatch conditions and avoid the false prediction. Higher and lower limits of adaptive resonance theory (ART) support LM (ART-LM) is properly used by providing unusual dust formation (UnDFR) data and usual/normal dust formation (UsDFR) data for AI training. Outcome of AI neural net is determined by resonant neuron net (RSNN). Predicted variable from ART-LM is calculated with higher and lower limits of dataset captured from applied energy common node (CN). Many test conditions of dust formation on solar photovoltaic (PV) has been validated to predict the state of applied energy system. For any UnDFR confirmation, entire AgSP based distributed generator (DG) unit will isolate from common node/utility grid. Proposed ART-LM based AI algorithm has been validated even for charging state events of electrical vehicle (EV) during the abnormal conditions.

Construction of Comprehensive Evaluation Model for Financial Risk Management in Colleges and Universities Based on Fuzzy Logic

Abstract Among the many risks faced by colleges and universities, financial risk is one of the most important risks and has a large complexity. This paper evaluates the financial risk management level of colleges and universities using the fuzzy logic method based on the four dimensions of financial risk. The affiliation function is used to quantitatively describe fuzzy logic, and weighted summation is used to ensure the accuracy of fuzzy propositions. After selecting the evaluation indexes, the weights of the evaluation index system are determined, and a comprehensive evaluation system for financial risk management of colleges and universities is constructed. Taking Q colleges and universities in G city as the research object, the comprehensive evaluation coefficient of financial risk management of the subject colleges and universities is calculated, and the average value of the extensive risk coefficient of the subject colleges and universities in 2015–2017 is between 0 and 0.4, which belongs to the level of significant risk. The test university ranked second among 7 universities, but the comprehensive score index coefficient is 0.4898. However, there is still a large financial risk possibility. We need to formulate a corresponding risk management policy slightly.

Modeling Contexts as Fuzzy Propositions in Optimization Problems

Modeling Contexts as Fuzzy Propositions in Optimization Problems

A Fuzzy Model for Reasoning and Predicting Student’s Academic Performance

Evaluating students’ academic performance is crucial for assessing the quality of education and educational strategies. However, it can be challenging to predict and evaluate academic performance under uncertain and imprecise conditions. To address this issue, many research works have employed fuzzy concepts to analyze, predict, and make decisions about students’ academic performance. This paper investigates the use of fuzzy concepts in research related to evaluating, analyzing, predicting, or making decisions about student academic performance. The paper proposes a fuzzy model, called FPM (Fuzzy Propositional Model), for reasoning and predicting students’ academic performance. FPM aims to address the limitations of previous studies by incorporating propositional logic with fuzzy sets concept, which allows for the representation of uncertainty and imprecision in the data. FPM integrates and transforms if-then rules into weighted fuzzy production rules to predict and evaluate academic performance. This paper tests and evaluates the FPM in two scenarios. In the first scenario, the model predicts and examines the impact of absenteeism on academic performance where there is no clear relation between the two parts of the dataset. In the second scenario, the model predicts the final exam results using the lab exam results, where the data are more related. The FPM provides good results in both scenarios, demonstrating its effectiveness in predicting and evaluating students’ academic performance. A comparison study of the FPM’s results with a linear regression model and previous work showed that the FPM performs better in predicting academic performance and provides more insights into the underlying factors affecting it. Therefore, the FPM could be useful in educational institutions to predict and evaluate students’ academic performance, identify underlying factors affecting it, and improve educational strategies.

Fuzzy Reasoning for Mixture of Fuzzy/Intuitionistic Fuzzy Information Based on Triple I Method

Generalized modus ponens (GMP) is a basic model of approximate reasoning. GMP in fuzzy propositions is called fuzzy modus ponen (FMP) and it is called intuitionistic fuzzy modus ponens (IFMP) when fuzzy propositions are generalized to intuitionistic fuzzy propositions. In this paper, we aim to investigate fuzzy reasoning methods for GMP with mixture of fuzzy/intuitionistic fuzzy information. For mixed types of GMP, we present two basic methods to solve GMP problems based on the triple I method (TIM). One is to transform the GMP problem into two FMP problems by decomposition and aggregate the solutions of TIM for FMP problems to obtain the solution for GMP problem. The other is to transform the GMP problem into the IFMP problem by expansion and aggregate the solutions of TIM for the IFMP problem to obtain the solution for the GMP problem. These two methods are called the decomposition triple I method (DTIM) and expansion triple I method (ETIM), respectively. We analyze the relationship between DTIM and ETIM. Furthermore, we discuss the reversibility of DTIM and ETIM.

On Z-Intuitionistic Fuzzy Fractional Valuations for Medical Diagnosis: An Intuitionistic Fuzzy Knowledge-Based Expert System

In an uncertain situation, data may present in continuous form or discrete form. We have various techniques to deal with continuous data in a realistic situation. However, when data are in discrete form, the existing techniques are inadequate to deal with these situations, and these techniques cannot provide the proper modulation for adequate analysis of the system. In order to provide the proper acceleration to discrete data, we need an appropriate modulation technique that can help us to handle unconditional boundedness on the technique and will operate like the techniques used for continuous data with fractional variables. In this work, we developed an intuitionistic fuzzy fractional knowledge-based expert system using unconditional and qualified fuzzy propositions based on the Z-intuitionistic fuzzy fractional valuation probability density function. In this proposed method, the discrete fractional variables will be converted into intuitionistic fuzzy fractional numbers and then be used in our algorithm. The proposed Z-intuitionistic fuzzy fractional valuation knowledge-based system can easily be applied in the medical field for the diagnosis of diseases in a vague environment due to the ordered-pair characteristics of the Z-intuitionistic fuzzy fractional valuation. In this study, we collected data of dengue patients, which included seven clinical findings: Temperature, sugar, Pulse Rate (PR), age, cough, and Blood Pressure (BP). A numerical example was also carried out to elaborate on the present technique. In addition, a comparative study is discussed in this work. We also provide the managerial implications of the data, with the limitations of the proposed technique presented at the end of this work.

Fuzzy Logic in the Quantum Mechanical Worldview; Related to Zadeh, Wittgenstein, Moore, Saussure, Quine, Lewis Carroll, etc.

Recently we proposed the linguistic Copenhagen interpretation of quantum mechanics, which is called quantum language or measurement theory. This theory is valid for both quantum and classical systems. Thus we think that quantum language is one of the most powerful scientific theories, like statistics. In this paper we justify Zadeh’s fuzzy sets theory in quantum language, that is, fuzzy propositions are identified with binary measurements. This implies that the definition of “proposition” is, for the first time, acquired in the field of non-mathematics. Further, we assert that fuzzy logic is more natural than crisp logic in science. And furthermore, we discuss and solve Saussure’s linguistics, Moore’s paradox, Quine’s analytic-synthetic distinction and Lewis Carroll’s logical paradox. Therefore, from the philosophical point of view, our result gives a complete answer to Wittgenstein’s problem: “Why does logic work in our world?” and “What is a scientific proposition?” in his picture theory. That is, we simultaneously justify both Zadeh’s fuzzy sets and Wittgenstein’s picture theory in the quantum mechanical worldview.

Perspectives of Fuzzy Logic and Their Applications

Fuzzy logic is a highly suitable and applicable basis for developing knowledge-based systems in engineering and applied sciences. The concepts of a fuzzy number plays a fundamental role in formulating quantitative fuzzy variable. These are variable whose states are fuzzy numbers. When in addition, the fuzzy numbers represent linguistic concepts, such as very small, small, medium, and so on, as interpreted in a particular contest, the resulting constructs are usually called linguistic variables. Each linguistic variable the states of which are expressed by linguistic terms interpreted as specific fuzzy numbers is defined in terms of a base variable, the value of which are real numbers within a specific range. A base variable is variable in the classical sense, exemplified by the physical variable (e.g., temperature, pressure, speed, voltage, humidity, etc.) as well as any other numerical variable (e.g., age, interest rate, performance, salary, blood count, probability, reliability, etc.). Logic is the science of reasoning. Symbolic or mathematical logic is a powerful computational paradigm. Just as crisp sets survive on a 2-state membership (0/1) and fuzzy sets on a multistage membership [0 - 1], crisp logic is built on a 2-state truth-value (true or false) and fuzzy logic on a multistage truth-value (true, false, very true, partly false and so on). The author now briefly discusses the crisp logic and fuzzy logic. The aim of this paper is to explain the concept of classical logic, fuzzy logic, fuzzy connectives, fuzzy inference, fuzzy predicate, modifier inference from conditional fuzzy propositions, generalized modus ponens, generalization of hypothetical syllogism, conditional, and qualified propositions. Suitable examples are given to understand the topics in brief.

Fuzzy Model for Risk Assessment of Machinery Failures

The main goal of this research was the development of an algorithm for the implementation of negative risk parameters in a synthesis model for a risk level assessment for a specific machine used in the mining industry. Fuzzy sets and fuzzy logic theory, in combination with statistical methods, were applied to analyze the time picture state of the observed machine. Fuzzy logic is presented through fuzzy proposition and a fuzzy composition module. Using these tools, the symmetric position of the fuzzy sets with regard to class was used, and the symmetric fuzzy inference approach was used in an outcome calculation. The main benefit of the proposed model is being able to use numerical and linguistic data in a risk assessment model. The proposed risk assessment model, using fuzzy logic conclusions and min–max composition, was used on a mobile crushing machine. The results indicated that the risk level of the mobile crushing machine was in the “high” category, which means that it is necessary to introduce maintenance policies based on this high risk. The proposed risk assessment model is useful for any engineering system.

Diabetes Diagnostic Model Based on Truth-value Restrictions Method Using Inference of Intuitionistic Conditional and Qualified Fuzzy Propositions

Diabetes is a challenging problem nowadays. Not only in India, but it also spreads over worldwide, In the present research paper a novel scheme based on intuitionistic fuzzy propositions to explore the knowledge base rule system with uncertainty has been developed and for the extension of fuzzy propositions to the domain of factors causing diabetes. In this paper, we have constructed the conditional and qualified intuitionistic fuzzy proposition mathematically for the diabetes diagnostic model. We have also developed an algorithm for Truth-value restriction method using the conditional and qualified intuitionistic fuzzy proposition;with the help of developed algorithm for truth-value restriction method we will give a scheme to check this severity of the diabetes. Numerical computations have also been carried out to demonstrate our approach.

Pseudomonadic BL-algebras: an algebraic approach to possibilistic BL-logic

Fuzzy possibilistic logic is an important formalism for approximate reasoning. It extends the well-known basic propositional logic BL, introduced by Hajek, by offering the ability to reason about possibility and necessity of fuzzy propositions. We consider an algebraic approach to study this logic, introducing Pseudomonadic BL-algebras. These algebras turn to be a generalization of both Pseudomonadic algebras introduced by Bezhanishvili (Math Log Q 48:624–636, 2002) and serial, Euclidean and transitive Bimodal Godel algebras proposed by Caicedo and Rodriguez (J Log Comput 25:37–55, 2015). We present the connection between this class of algebras and possibilistic BL-frames, as a first step to solve an open problem proposed by Hajek (Metamathematics of fuzzy logic. Trends in logic, Kluwer, Dordrecht, 1998, Chap. 8, Sect. 3).

Some characterizations of T-power based implications

Recently, the so-called family of T-power based implications was introduced. These operators involve the use of Zadeh's quantifiers modelled by powers of t-norms in its definition. Due to the fact that Zadeh's quantifiers constitute the usual method to modify fuzzy propositions, most of the members of this family of fuzzy implication functions satisfy an important property in approximate reasoning such as the invariance of the truth value of the fuzzy conditional when both the antecedent and the consequent are modified using the same quantifier. In this paper, an in-depth analysis of this property is performed by characterizing all binary functions satisfying it. From this general result, a fully characterization of the subfamily of T-power based implications which satisfy the invariance property is presented. Furthermore, a characterization of the whole family of T-power based implications is proved in which a novel property which slightly resembles the hypothetical syllogism plays a key role.

Algorithms that extract knowledge from fuzzy big data: Conserving traditional science1

Big data have revealed unexpected and statistically significant correlations along with intractable propositions. In order to address this development, an algorithm is introduced that is consistent with Ramsey’s theorem for pairs and Gödel’s incompleteness theorem. The algorithm assigns one of thre e truth values to a fuzzy proposition in order to update automatic theorem proving. A unique feature of the algorithm is an AI module that selects the multiple axiom sets needed for a proof. A metric for the AI module is the probability that the database of axiom sets is inadequate for the context. The importance of context is illustrated by a simple analog electrical circuit applied to Fermat’s last theorem as contrasted with a similar exponential equation having positive real numbers for bases. Another algorithm or decision tree is introduced to differentiate risk factors from necessary conditions. A failure to recognize this distinction has impaired the public health sector for centuries and continues to do so. The second algorithm introduced here represents an effort to conserve science in general. The risk that big data pose for science is the misuse of positive, statistically significant correlations to infer causality when the correlations actually reflect risk factors or even rare coincidences.

Fuzzy implication functions based on powers of continuous t-norms

The modification (relaxation or intensification) of the antecedent or the consequent in a fuzzy “If, Then” conditional is an important asset for an expert in order to agree with it. The usual method to modify fuzzy propositions is the use of Zadeh's quantifiers based on powers of t-norms. However, the invariance of the truth value of the fuzzy conditional would be a desirable property when both the antecedent and the consequent are modified using the same quantifier. In this paper, a novel family of fuzzy implication functions based on powers of continuous t-norms which ensure the aforementioned property is presented. Other important additional properties are analyzed and from this study, it is proved that they do not intersect the most well-known classes of fuzzy implication functions.

Handling Knowledge Imperfection in Hybrid Logic Inference

When transforming information into knowledge, various forms of imperfection can be introduced. Most imperfections typically result through randomization and fuzzification. The Interval-Valued Confidence (IVC) technique has been introduced to represent the fuzzy truth for facts and knowledge in hybrid knowledge-based systems. An extended format used to represent hybrid imperfection in reasoning with hybrid logic is proposed. The credibility of resulting fuzzy proposition transforms probability into an uncertainty measure on truth. This article modifies existing effort to Extend the Interval-Valued Confidence (EIVC) technique to handle uncertain fuzzy truth of fuzzy proposition. It also considers the fuzzy likelihood of the random proposition for reasoning with hybrid logic in a unified format.

A METHOD FOR THE EVALUATION AND SELECTION OF AN APPROPRIATE FUZZY IMPLICATION BY USING STATISTICAL DATA

JEL Classification: C02, C60, C611.INTRODUCTIONWe know that the implication in classic logic depends only on whether the premise is true or false. That is, whether the syllogism (reasoning) is true or false depends solely on if the premise and the conclusion is true or false.Every proposition in classic logic has two values 0 or 1, true or false, holds or does not hold. Let us assume that we have two such propositions p and q. We symbolize the conjunction (AND) of the propositions with λ and the disjunction (OR) with v, while -p is used to symbolize the negation of p (i.e. NOT-p).The conjunction pAq is true, if and only if both propositions p and q are true. In such a case, it holds that pAq = min {p, q}, (Table 1). Indeed, let p be the proposition number is and q the proposition number 6 is a multiple of 2 (true). Then, the conjunction pAq: number is a prime and the number 6 is a multiple of (true) has truth value equal to 1.The disjunction pvq is true, if one of the two propositions is true, that is if it holds that pvq = max {p, q}, (Table 1). Indeed, let p be the proposition number 3 is an and q the proposition number 16 is a multiple of (false). Then, the disjunction pvq number 3 is an integer and the number 16 is a multiple of 5 (false) has truth value equal to 1.Let us consider the proposition p population of Spain is less than that of China which is true. The negation of proposition p, i.e. the proposition -p population of Spain is greater than or equal to that of China is false.For determining the truth value of an implication, (denoted as ^) between two propositions p and q (we assume the implication p^q, i.e. the proposition p implies the proposition q), it would be enough to determine the truth value of the conjunction -pvq (Table 2).From the last column of Table 2, it is obvious that the implication p^q is always true, except in the case where the proposition p is true and the proposition q is false, i.e. the case where from a false premise, we arrive at a false conclusion.From Table 2, we also see that whenever we start from a false premise (p=0), the reasoning, i.e. the implication, is true regardless of the conclusion that we arrive at (q=0 or q=1). Finally, another characteristic feature of the classical logic is that the property of symmetry does not hold i.e. the truth value of the implication p^q generally has a different value from the truth value of the implication q^p. Indeed, from Table 2, we can observe that the implication 1 ^0 has truth value of 0, while the symmetric equivalent implication 0^1, has a truth value of 1, [1], [2].2.THE FUZZY IMPLICATIONThe fuzzy implication assigns a truth value J(x,y) to the fuzzy proposition If p then qfor every truth value x, y of the fuzzy propositions p, q. It is a function of the form J : [0,1]x [0,1] ^[0,1] which satisfies the following nine conditions, every one of which does not contain symmetry [3], [4], [5], [6]:1. Vx,y,z e [0,1], x J(z,y),2. Vx,y,z e [0,1], y 3. Vy e [0,1], J(0,y) = 1,4. Vz e [0,1], J(1, z) = 1,5. Vx e [0,1], J(x,x)=1,6. Vx, y, z e[0,1], J(x,J(y,z))=J(y,J(x,z)),7. Vx,y e [0,1], J(x,y) = 1 when x 8. Vx,y e [0,1], J(x,y) = J(c(y),c(x)), for a fuzzy complement c,9. J is a continuous function.In many applications, e.g. in the fuzzy inference system of MATLAB (such an application can be found in [7]), the classic forms of implication, min (Mamdani) [8] and the prod (Larsen) [9] are used as first choices, where: These implications are symmetric, since x^y = y^x, and they are called engineering implications. These implications are widely used in the field of engineering, where the cause and effect are often intertwined, hence the symmetry is acceptable. …

Semantics of Fuzzy Propositional Multi-Dimension Three-Layer Logic

Semantics of Fuzzy Propositional Multi-Dimension Three-Layer Logic

Extending the Contraposition Property of Propositional Logic for Fuzzy Abduction

Abduction deals with assumption-based reasoning to explain an observation. In the context of fuzzy reasoning, abduction attempts to determine the membership function of the fuzzy propositions present in the antecedent of a rule when the membership functions for the propositions in the consequent of the rule are given. Currently available models of fuzzy abduction are capable of inferring the membership function of the antecedent clause accurately when the antecedent includes single fuzzy proposition. However, when the antecedent clause of a rule contains multiple fuzzy propositions, these models fail to determine the independent membership function of the individual propositions present in the antecedent. This paper presents a new formulation to handle the above problem by fuzzy extension of the well-known contraposition property of propositional logic. Several interesting properties due to the fuzzy extension of the classical contraposition have been derived. An algorithm for automated abduction using the extended contraposition property has been developed to demonstrate the principle of abduction with rules containing one or more fuzzy propositions in the antecedent/consequent. The time complexity of the proposed fuzzy abduction for a sequence of n-chained rules, where each rule has m fuzzy propositions, is O (mn), considering a uniform cost for composition operation and t-norm computation of the antecedent.

Relations among similarity measure, subsethood measure and fuzzy entropy

In this paper we study the relations among similarity measure, subsethood measure and fuzzy entropy and present several propositions that similarity measure, subsethood measure and fuzzy entropy ca...

Reduction method based on fuzzy principal component analysis in multi-objective possibilistic programming

Most of real problems are modeling as multi-objective problems (MOPs) with imprecise coefficients. Coefficients or parameters are commonly imprecise because information is incomplete or unavailable. One category of these problems is multi-objective possibilistic problem (MOPP). Possibility theory is favorable for modeling incomplete information expressed by fuzzy propositions. On the other hand, MOPPs are a class of MOPs with imprecise parameters. Solving of MOPPs is usually difficult. Therefore, we should design approaches or extend exciting algorithms for solving them. This paper is a pre-processing stage for solving MOPPs. In other words, it discusses simple and useful integrated approach for reducing the number of objectives in multi-objective possibilistic problems. For this purpose, fuzzy principal component analysis (FPCA) can be used. The approach consists of a two-stage algorithm that in the first stage, we use FPCA for reducing objectives. In the second stage, we use results of previous stage for solving reduced problem. The new objective functions cover maximum variances of primal functions. We show that the proposed approach can generate efficient solutions without added extra constraints and variables than the general problems found in the literatures. An example illustrates steps of the procedure.