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1

Introducing hesitant fuzzy equations and determining market equilibrium price

Babakordi Fatemeh, Taghi-Nezhad N. A.

Control and Cybernetics

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2021

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Vol. 50, No. 3

363--382

EN

A vast majority of research has been performed in the field of hesitant fuzzy sets (HFSs), involving the introduction of some properties, operations, relations and modifications of such sets or considering the application of HFSs in MCDM (multicriteria decision making). On the other hand, no research has been performed in the field of fully hesitant fuzzy equations. Therefore, in this paper, fully hesitant fuzzy equations and dual hesitant fuzzy equations are introduced. First, a method is proposed to solve one-element hesitant fuzzy equations. Then, the proposed method is extended to solve n-element hesitant fuzzy equations effectively. Moreover, to show the applicability of the proposed method, it is used to solve a real world problem. Thus, the proposed method is applied to determine market equilibrium price. Also, some other numerical examples are presented to better show the performance of the proposed method.

2

Decision-theoretic Rough Sets in Incomplete Information System

Yang X., Lu Z., Li T-J.

Fundamenta Informaticae

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2013

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Vol. 126, nr 4

353--375

EN

Decision-theoretic rough sets in two kinds of incomplete information systems are discussed in this paper. One is for the classical decision attribute and the other for the fuzzy decision attribute. In complete information system, the universe is partitioned with the equivalence relation. Given a concept, we get a pair of approximations of the concept using rough set theory, and the universe can be partitioned into three regions for making a decision. An incomplete information table can be expressed as a family of complete information tables. The universe is partitioned by the equivalence relation for each complete information table. The probability of each object belonging to the concept can be calculated in a completion from incomplete information system, and then the total probability of the object belonging to the concept can be obtained. Decision rules are derived using total probability instead of conditional probability in decision-theoretic rough sets. Finally, the universe is divided into three regions according to the total probability. A similar approach to fuzzy incomplete information system is examined and the universe is also divided into three regions.

3

A direct algorithm of possibilistic clustering with partial supervision

Viattchenin D.

Journal of Automation Mobile Robotics and Intelligent Systems

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2007

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Vol. 1, No. 3

29-38

EN

Fuzzy clustering plays an important role in intelligent systems design and the respective methods constitute a part of the areas of automation and robotics. This paper describes a modification of a direct algorithm of possibilistic clustering that takes into account the information coming from the labeled objects. The clustering method based on the concept of allotment among fuzzy clusters is the basis of the new algorithm. The paper provides the description of basic ideas of the method and the plan of the basic version of a direct possibilistic-clustering algorithm. A plan of modification of the direct possibilistic-clustering algorithm in the presence of information from labeled objects is proposed. An illustrative example of the method's application to the Sneath and Sokal's two-dimensional data in comparison with the Gaussian-clustering method is carried out. Preliminary conclusions are formulated.

4

A new heuristic algorithm of fuzzy clustering

Viattchenin D. A.

Control and Cybernetics

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2004

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Vol. 33, no 2

323-340

EN

This paper deals with a new method of fuzzy clustering. The basic concepts of the method are introduced as resulting from the consideration of the fundamental fuzzy clustering problem. The paper provides the description of the general plan of the algorithm and an illustrative example. An analysis of the experimental results of the method's application to the Anderson's Iris data is carried out. Some preliminary conclusions and the ways of prospective investigations are given.