Showing papers on "Fuzzy associative matrix published in 2023"
TL;DR: In this paper , a mamdani fuzzy model was developed to evaluate the quality of tilapia based on its texture, taste, and size, and the results showed that the higher the input value of size, the more the output value of price.
Abstract: Fish are living things with the highest trophic level in a body of water. Fish are living creatures that live in aquatic environments in fresh, brackish and marine waters. Tilapia is one of the leading commodities of aquaculture and is a widely used freshwater fish, and its production is quite high. Fuzzy logic is a logic that deals with the concept of partial truth, where classical logic states that everything can be expressed in binary terms (0 or 1). Various theories in the development of fuzzy logic show that fuzzy logic can be used to model various systems. A very adaptable and data-tolerant approach is mamdani fuzzy. Therefore, in this research, a mamdani fuzzy model will be developed to evaluate the quality of tilapia. This research uses fuzzy logic to evaluate the quality of tilapia based on its texture, taste, and size. In this study, researchers modeled 4 fuzzy variables, with 3 inputs (texture, taste, and size), 1 output (price), and a total of 4 fuzzy variables. The MIN IMPLICATION function was used in the inference procedure in the fuzzy operator application. Next, the MAX approach is used in the compilation of all fuzzy outputs. Then comes the affirmation, also known as defuzzification which is done using the Centroid method. The results show with 10 trial data it is seen that the higher the input value of size, the higher the output value of price.
01 Jan 2023
TL;DR: In this paper , the authors introduce the fundamentals of fuzzy logic (FL), fuzzy sets, and fuzzy model components such as the fuzzification, the fuzzy rule base, fuzzy inference engine, and the defuzzification.
Abstract: This chapter introduces the fundamentals of fuzzy logic (FL), fuzzy sets, and fuzzy model components such as the fuzzification, the fuzzy rule base, the fuzzy inference engine, and the defuzzification. The processes of the fuzzy model components are presented by working on the examples from the water resources engineering application problems. This chapter also discusses the merits and the shortcomings of the fuzzy modeling. Hydrological processes have inherent source of uncertainty, for which the fuzzy set theory can be an effective solution tool.
TL;DR: In this paper , an interval type-2 fuzzy relationship matrix (IT2 FRM) model is proposed, which is based on matrix semi-tensor product (STP) fuzzy representation technique.
Abstract: A new modeling idea of interval type-2 fuzzy logic system (IT2 FLS) is proposed on the basis of matrix semi-tensor product (STP) fuzzy representation technique, to construct an interval type-2 fuzzy relationship matrix (IT2 FRM) model. The model naturally inherits the advantages of STP theory, which enables the fuzzy logic reasoning process to be translated into algebraic form for computation. In most cases, the fuzzy rules in the IT2 FRM are generally unknown. To address the above situation, the parameters of this model can be trained with observed data pairs. Firstly, the fuzzy rules are generated by the space division method, and the initial parameters of the model are determined. Secondly, the parameters in the model are trained using the steepest descent algorithm. Finally, the IT2 FRM model is validated by simulation, and the results demonstrate that the IT2 FLS can be designed using the STP method.
01 Jan 2023
TL;DR: In this paper , the concept of fuzzy semi-essential (large) submodule was introduced, and a necessary and sufficient condition for a fuzzy submodule of a fuzzy module to be a fuzzy semi essential (large)-submodule was studied.
Abstract: In this paper, we introduce the concept of fuzzy semi-essential (large) submodule, and we study a necessary and sufficient condition for a fuzzy submodule of a fuzzy module to be a fuzzy semi-essential (large) submodule, also fuzzy images and fuzzy inverse-images of generalized fuzzy semi-essential (large) submodule are studied. Index Terms
TL;DR: In this article , a new approximate solution of a class of fully fuzzy linear systems was discussed, in which the coefficient matrix A is a positive fuzzy matrix and the original fuzzy linear system was extended into simple crisp linear equation using the obtained approximate multiplication of positive fuzzy number and near zero fuzzy number.
Abstract: This paper discusses a new approximate solution of a class of fully fuzzy linear systems A ˜ x ˜ = b ˜ in which the coefficient matrix A ˜ is a positive fuzzy matrix. The original fuzzy linear systems is extended into simple crisp linear equation using the obtained approximate multiplication of positive fuzzy number and near zero fuzzy number. Two cases are analysed: (a) the unknown vector x ˜ is a near zero fuzzy vector with positive mean value; (b) the unknown vector x ˜ is a near zero fuzzy vector with negative mean value. Two computing models are established and respective expression of the solution to fully fuzzy linear system are derived, and the sufficient condition for the existence of strong fuzzy solution are analyzed correspondingly. Some numerical examples are given to illustrated our proposed method.
TL;DR: In this paper , a transitivity equation system with a parameterized trapezoidal fuzzy vector is built and computational formulas are devised to identify values of parameters from imprecision indices of cores and supports for fuzzy elements in a TFARPM.
Abstract: Multiplication and division of fuzzy arithmetic have brought out theoretical drawbacks to fuzzy analytic hierarchy process based decision making systems. To cope with the drawbacks, trapezoidal fuzzy additive reciprocal preference matrices (TFARPMs) are utilized to characterize preference information and addition and subtraction of fuzzy arithmetic are applied to fuzzy numbers. This paper introduces formulas to calculate left and right spread indices and imprecision indices of cores and supports for fuzzy elements in a TFARPM. Based on the addition of fuzzy arithmetic, a transitivity equation system with a parameterized trapezoidal fuzzy vector is built and computational formulas are devised to identify values of parameters from imprecision indices of cores and supports of the trapezoidal fuzzy elements in a TFARPM. A fuzzy addition based non-parametric transitivity equation is then established to define additive consistency of TFARPMs. Properties of additively consistent TFARPMs are proposed and an index formula is brought forward to compute additive inconsistency degrees of TFARPMs. A novel approach is presented to generate additively consistent TFARPMs from fuzzy vectors and a new framework is put forward to normalize [0, 1]-valued trapezoidal fuzzy vectors. An absolute deviation based minimization model is developed and converted equivalently into a linear program to acquire normalized trapezoidal fuzzy priority vectors from TFARPMs. A closed-form solution of the minimization model is found to calculate normalized optimal trapezoidal fuzzy priority vectors of additively consistent TFARPMs. Two illustrating examples including a multi-criteria decision making problem are provided to validate the proposed models.
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TL;DR: In this paper , the authors introduce fuzzy minimax nets as a novel tool to compute the greatest fuzzy bisimulation/simulation between two finite fuzzy labeled graphs, and design the first algorithms for the mentioned computational problems in the case of using the product t-norm.
Abstract: We introduce fuzzy minimax nets as a novel tool to compute the greatest fuzzy bisimulation/simulation between two finite fuzzy labeled graphs. Fuzzy labeled graphs are a universal data structure for representing fuzzy systems such as fuzzy automata, fuzzy labeled transition systems, fuzzy Kripke models, fuzzy social networks and fuzzy interpretations in description logic. The greatest fuzzy bisimulation between two such systems characterizes the similarity between their states, actors or individuals. Using fuzzy minimax nets, we design the first algorithms for the mentioned computational problems in the case of using the product t-norm, as well as the first algorithms whose complexity order does not depend on the fuzzy values occurring in the inputs for those problems in the case of using the Łukasiewicz t-norm.
06 Apr 2023
TL;DR: In this paper , the complexity involved in fuzzy derivatives when both input and output are from nonempty, convex, and compact fuzzy space is dealt with, and for fuzzy differentiation of fuzzy valued function, the Modified Hukuhara derivative is proposed.
Abstract: This article deals with the complexity involved in fuzzy derivatives when both input and output are from nonempty, convex, and compact fuzzy space. Consider a fuzzy valued mapping, and for fuzzy differentiation of fuzzy valued function, we propose Modified Hukuhara derivative. To evaluate this derivative, we need to take the parametric form of, input and the mapping which is involved in it. Our definition gives a more realistic explanation of fuzzy derivatives, under this derivative, we also develop fuzzy Taylor series along with its convergence. Lastly, we solve a fully fuzzy differential equation with initial condition using Fuzzy Taylor series.