Type-II Fuzzy Decision Support System for Fertilizer

Type-II fuzzy sets are used to convey the uncertainties in the membership function of type-I fuzzy sets. Linguistic information in expert rules does not give any information about the geometry of the membership functions. These membership functions are mostly constructed through numerical data or range of classes. But there exists an uncertainty about the shape of the membership, that is, whether to go for a triangle membership function or a trapezoidal membership function. In this paper we use a type-II fuzzy set to overcome this uncertainty, and develop a fuzzy decision support system of fertilizers based on a type-II fuzzy set. This type-II fuzzy system takes cropping time and soil nutrients in the form of spatial surfaces as input, fuzzifies it using a type-II fuzzy membership function, and implies fuzzy rules on it in the fuzzy inference engine. The output of the fuzzy inference engine, which is in the form of interval value type-II fuzzy sets, reduced to an interval type-I fuzzy set, defuzzifies it to a crisp value and generates a spatial surface of fertilizers. This spatial surface shows the spatial trend of the required amount of fertilizer needed to cultivate a specific crop. The complexity of our algorithm isO(mnr), wheremis the height of the raster,nis the width of the raster, andris the number of expert rules.

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The role of properties of the membership function in construction of fuzzy sets ranking

Computer Science and Mathematical Modelling ◽

10.5604/01.3001.0015.2732 ◽

2021 ◽

Vol 0 (11-12/2020) ◽

pp. 5-12

Author(s):

Andrzej Ameljańczyk

Keyword(s):

Decision Making ◽

Decision Support ◽

Fuzzy Sets ◽

Membership Function ◽

Fuzzy Set ◽

The Membership Function

The paper presents a several new definitions of concepts regarding the properties of fuzzy sets in the aspect of their use in decision support processes. These are concepts such as the image and counter – image of the fuzzy set, the proper fuzzy set, the fuzzy support and the ranking of fuzzy set. These concepts can be important in construction decision support algorithms. Particularly a lot of space was devoted to the study of the properties of membership function of the fuzzy set as a result of operations on fuzzy sets. Two additional postulates were formulated that should be fulfilled by the membership function product of fuzzy sets in decision making.

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Approximation of real data by fuzzy sets for the classification problem

Ukrainian journal of remote sensing ◽

10.36023/ujrs.2019.22.154 ◽

2019 ◽

pp. 22-26

Author(s):

Kostiantyn Sukhanov

Keyword(s):

Fuzzy Sets ◽

Membership Function ◽

Fuzzy Set ◽

Real Data ◽

Training Data ◽

Learning Object ◽

Membership Functions ◽

One Dimensional ◽

Set Membership ◽

The Membership Function

The article deals with the method of classification of real data using the apparatus of fuzzy sets and fuzzy logic as a flexible tool for learning and recognition of natural objects on the example of oil and gas prospecting sections of the Dnieper-Donetsk basin. The real data in this approach are the values for the membership function that are obtained not through subjective expert judgment but from objective measurements. It is suggested to approximate the fuzzy set membership functions by using training data to use the approximation results obtained during the learning phase at the stage of identifying unknown objects. In the first step of learning, each traditional future of a learning data is matched by a primary traditional one-dimensional set whose membership function can only take values from a binary set — 0 if the learning object does not belong to the set, and 1 if the learning object belongs to the set. In the second step, the primary set is mapped to a fuzzy set, and the parameters of the membership function of this fuzzy set are determined by approximating this function of the traditional set membership. In the third step, the set of one-dimensional fuzzy sets that correspond to a single feature of the object is mapped to a fuzzy set that corresponds to all the features of the object in the training data set. Such a set is the intersection of fuzzy sets of individual features, to which the blurring and concentration operations of fuzzy set theory are applied in the last step. Thus, the function of belonging to a fuzzy set of a class is the operation of choosing a minimum value from the functions of fuzzy sets of individual features of objects, which are reduced to a certain degree corresponding to the operation of blurring or concentration. The task of assigning the object under study to a particular class is to compare the values of the membership functions of a multidimensional fuzzy set and to select the class in which the membership function takes the highest value. Additionally, after the training stage, it is possible to determine the degree of significance of an object future, which is an indistinctness index, to remove non-essential data (object futures) from the analysis.

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My Early Researches on Fuzzy Set and Fuzzy Logic

International Journal of Computers Communications & Control ◽

10.15837/ijccc.2021.1.4090 ◽

2020 ◽

Vol 16 (1) ◽

Author(s):

Yong Shi

Keyword(s):

Fuzzy Logic ◽

Fuzzy Sets ◽

Fuzzy Set ◽

Convergence Theorem ◽

Fuzzy Systems ◽

Theoretical Basis ◽

Fuzzy Integral ◽

Type I ◽

Type Ii ◽

Fuzzy Subgroups

This paper presents the author’s works on fuzzy sets and fuzzy systems in early 1980’s to celebrate the 100-year birthday of Lotfi A. Zadeh. They were originally published in Chinese. The first part of the paper is about an isomorphic theorem on fuzzy subgroups and fuzzy series of invariant subgroups, which could be a theoretical basis when the multiple-valued computer system will be reconsidered or redeveloped in the future. The second part of the paper describes the convergence theorem of fuzzy integral of type II which was contributed by Wenxiu Zhang and Ruhuai Zhao. Both fuzzy integral of type I developed by M. Sugeno and the fuzzy integral of type II have been playing an important role in the design of various engineering devices for last 40 years.

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