This paper presents an original method of fuzzy approximate reasoning that can open a new direction of research in the uncertainty inference of Artificial Intelligence(AI) and Computational Intelligence(CI). Fuzzy modus ponens (FMP) and fuzzy modus tollens(FMT) are two fundamental and basic models of general fuzzy approximate reasoning in various fuzzy systems. And the reductive property is one of the essential and important properties in the approximate reasoning theory and it is a lot of applications. This paper suggests a kind of extended distance measure (EDM) based approximate reasoning method in the single input single output(SISO) fuzzy system with discrete fuzzy set vectors of different dimensions. The EDM based fuzzy approximate reasoning method is consists of two part, i.e., FMP-EDM and FMT-EDM. The distance measure based fuzzy reasoning method that the dimension of the antecedent discrete fuzzy set is equal to one of the consequent discrete fuzzy set has already solved in other paper. In this paper discrete fuzzy set vectors of different dimensions mean that the dimension of the antecedent discrete fuzzy set differs from one of the consequent discrete fuzzy set in the SISO fuzzy system. That is, this paper is based on EDM. The experimental results highlight that the proposed approximate reasoning method is comparatively clear and effective with respect to the reductive property, and in accordance with human thinking than existing fuzzy reasoning methods.
This paper shows a novel fuzzy approximate reasoning method based on the least common multiple (LCM). Its fundamental idea is to obtain a new fuzzy reasoning result by the extended distance measure based on LCM between the antecedent fuzzy set and the consequent one in discrete SISO fuzzy system. The proposed method is called LCM one. And then this paper analyzes its some properties, i.e., the reductive property, information loss occurred in reasoning process, and the convergence of fuzzy control. Theoretical and experimental research results highlight that proposed method meaningfully improve…
In order to involve user knowledge in determining equality of sets, which may not be equal in the mathematical sense, three types of approximate (rough) equalities were introduced by Novotny and Pawlak ([8, 9, 10]). These notions were generalized by Tripathy, Mitra and Ojha ([13]), who introduced the concepts of approximate (rough) equivalences of sets. Rough equivalences capture equality of sets at a higher level than rough equalities. More properties of these concepts were established in [14]. Combining the conditions for the two types of approximate equalities, two more approximate equaliti…
A major aspect of human reasoning involves the use of approximations. Particularly in situations where the decision-making process is under stringent time constraints, decisions are based largely on approximate, qualitative assessments of the situations. Our work is concerned with the application of approximate reasoning to real-time control. Because of the stringent processing speed requirements in such applications, hardware implementations of fuzzy logic inferencing are being pursued. We describe a programming environment for translating fuzzy control rules into hardware realizations. Two m…
Sharif University of Technology（谢里夫理工大学）；University of Neyshabur（内沙布尔大学）；Kharazmi University（哈拉兹米大学）；Azad University of Mashhad（马什哈德阿扎德大学）
In recent years, descriptive evaluation has been introduced as a new model for educational evaluation of Iranian students. The current descriptive evaluation method is based on four-valued logic. Assessing all students with only four values is led to a lack of relative justice and the creation of unrealistic equality. Also, the complexity of the evaluation process in the current method increases teacher errors likelihood. As a suitable solution, in this paper, a fuzzy descriptive evaluation system has been proposed. The proposed method is based on fuzzy logic, which is an infinite-valued logic…
In this article, we study the approximate solutions set $Λ_b$ of an inconsistent system of $\max-\min$ fuzzy relational equations $(S): A \Box_{\min}^{\max}x =b$. Using the $L_\infty$ norm, we compute by an explicit analytical formula the Chebyshev distance $Δ~=~\inf_{c \in \mathcal{C}} \Vert b -c \Vert$, where $\mathcal{C}$ is the set of second members of the consistent systems defined with the same matrix $A$. We study the set $\mathcal{C}_b$ of Chebyshev approximations of the second member $b$ i.e., vectors $c \in \mathcal{C}$ such that $\Vert b -c \Vert = Δ$, which is associated to the app…
Centro de Investigación en Tecnoloxías da Información (CITIUS)（信息技术研究中心（CITIUS））；University of Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）
Syllogism is a type of deductive reasoning involving quantified statements. The syllogistic reasoning scheme in the classical Aristotelian framework involves three crisp term sets and four linguistic quantifiers, for which the main support is the linguistic properties of the quantifiers. A number of fuzzy approaches for defining an approximate syllogism have been proposed for which the main support is cardinality calculus. In this paper we analyze fuzzy syllogistic models previously described by Zadeh and Dubois et al. and compare their behavior with that of the classical Aristotelian framewor…
The treatment of complex systems often requires the manipulation of vague, imprecise and uncertain information. Indeed, the human being is competent in handling of such systems in a natural way. Instead of thinking in mathematical terms, humans describes the behavior of the system by language proposals. In order to represent this type of information, Zadeh proposed to model the mechanism of human thought by approximate reasoning based on linguistic variables. He introduced the theory of fuzzy sets in 1965, which provides an interface between language and digital worlds. In this paper, we propo…
The role of inferencing with uncertainty is becoming more important in rule-based expert systems (ES), since knowledge given by a human expert is often uncertain or imprecise. We have succeeded in designing a VLSI chip which can perform an entire inference process based on fuzzy logic. The design of the VLSI fuzzy inference engine emphasizes simplicity, extensibility, and efficiency (operational speed and layout area). It is fabricated in 2.5 um CMOS technology. The inference engine consists of three major components; a rule set memory, an inference processor, and a controller. In this impleme…
In this paper, we will show that (1) the results about the fuzzy reasoning algoritm obtained in the paper "Computer Sciences Vol. 34, No.4, pp.145-148, 2007" according to the paper "IEEE Transactions On systems, Man and cybernetics, 18, pp.1049-1056, 1988" are correct; (2) example 2 in the paper "An Algorithm of General Fuzzy Inference With The Reductive Property" presented by He Ying-Si, Quan Hai-Jin and Deng Hui-Wen according to the paper "An approximate analogical reasoning approach based on similarity measures" presented by Tursken I.B. and Zhong zhao is incorrect; (3) the mistakes in thei…
Netaji Subhas Open University（内塔吉·苏巴斯开放大学）；St. Xavier’s College（圣沙勿略学院）
The Fuzzy Modeling has been applied in a wide variety of fields such as Engineering and Management Sciences and Social Sciences to solve a number Decision Making Problems which involve impreciseness, uncertainty and vagueness in data. In particular, applications of this Modeling technique in Decision Making Problems have remarkable significance. These problems have been tackled using various theories such as Probability theory, Fuzzy Set Theory, Rough Set Theory, Vague Set Theory, Approximate Reasoning Theory etc. which lack in parameterization of the tools due to which they could not be appli…
Preparatory institute of engineering studies of Monastir（莫纳斯提尔工程研究预备学院）
The main objective of this paper is to develop a new semantic Network structure, based on the fuzzy sets theory, used in Artificial Intelligent system in order to provide effective on-line assistance to users of new technological systems. This Semantic Networks is used to describe the knowledge of an "ideal" expert while fuzzy sets are used both to describe the approximate and uncertain knowledge of novice users who intervene to match fuzzy labels of a query with categories from an "ideal" expert. The technical system we consider is a word processor software, with Objects such as "Word" and Go…
Centro de Investigación en Tecnoloxías da Información (CITIUS), University of Santiago de Compostela（圣地亚哥-德孔波斯特拉大学信息技术研究中心（CITIUS））
In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional, comparative and exception) taken from Theory of Generalized Quantifiers and similarity quantifiers, taken from statistics, are considered and (ii) any number of premises can be taken into account within the reasoning process. Furthermore, a systematic reasoning procedure to solve the syllogism is also proposed, interpreting it as an equivalent mathematical optimi…
This paper describes application of information granulation theory, on the analysis of "lugeon data". In this manner, using a combining of Self Organizing Map (SOM) and Neuro-Fuzzy Inference System (NFIS), crisp and fuzzy granules are obtained. Balancing of crisp granules and sub- fuzzy granules, within non fuzzy information (initial granulation), is rendered in open-close iteration. Using two criteria, "simplicity of rules "and "suitable adaptive threshold error level", stability of algorithm is guaranteed. In other part of paper, rough set theory (RST), to approximate analysis, has been empl…
Systems of fuzzy relation equations and inequalities in which an unknown fuzzy relation is on the one side of the equation or inequality are linear systems. They are the most studied ones, and a vast literature on linear systems focuses on finding solutions and solvability criteria for such systems. The situation is quite different with the so-called weakly linear systems, in which an unknown fuzzy relation is on both sides of the equation or inequality. Precisely, the scholars have only given the characterization of the set of exact solutions to such systems. This paper describes the set of f…
This study describes application of some approximate reasoning methods to analysis of hydrocyclone performance. In this manner, using a combining of Self Organizing Map (SOM), Neuro-Fuzzy Inference System (NFIS)-SONFIS- and Rough Set Theory (RST)-SORST-crisp and fuzzy granules are obtained. Balancing of crisp granules and non-crisp granules can be implemented in close-open iteration. Using different criteria and based on granulation level balance point (interval) or a pseudo-balance point is estimated. Validation of the proposed methods, on the data set of the hydrocyclone is rendered.
Causal Autoencoder-like Generation of Feedback Fuzzy Cognitive Maps with an LLM Agent
Department of Electrical and Computer Engineering（电气与计算机工程系）；University of Southern California（南加州大学）；School of Computing and Information Sciences（计算与信息科学学院）；Florida International University（佛罗里达国际大学）
Modeling difficulty, time-varying model, and uncertain external inputs are the main challenges for energy management of fuel cell hybrid electric vehicles. In the paper, a fuzzy reinforcement learning-based energy management strategy for fuel cell hybrid electric vehicles is proposed to reduce fuel consumption, maintain the batteries' long-term operation, and extend the lifetime of the fuel cells system. Fuzzy Q-learning is a model-free reinforcement learning that can learn itself by interacting with the environment, so there is no need for modeling the fuel cells system. In addition, frequent…
Approximately more than 90% of all coal production in Iranian underground mines is derived directly longwall mining method. Out of seam dilution is one of the essential problems in these mines. Therefore the dilution can impose the additional cost of mining and milling. As a result, recognition of the effective parameters on the dilution has a remarkable role in industry. In this way, this paper has analyzed the influence of 13 parameters (attributed variables) versus the decision attribute (dilution value), so that using two approximate reasoning methods, namely Rough Set Theory (RST) and Sel…
Centro Singular de Investigación en Tecnoloxías da Información (CiTIUS)（信息技术研究中心（CiTIUS））；Universidade de Santiago de Compostela（圣地亚哥德孔波斯特拉大学）
The fuzzy quantification model FA has been identified as one of the best behaved quantification models in several revisions of the field of fuzzy quantification. This model is, to our knowledge, the unique one fulfilling the strict Determiner Fuzzification Scheme axiomatic framework that does not induce the standard min and max operators. The main contribution of this paper is the proof of a convergence result that links this quantification model with the Zadeh's model when the size of the input sets tends to infinite. The convergence proof is, in any case, more general than the convergence to…
