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Journal Paper

An Approximation of Fuzzy Numbers Based on Polynomial Form Fuzzy Numbers

International Journal of Analysis and Applications, ‎ Vol. 16 No. 2, (2018), 290-305.

In this paper, we approximate an arbitrary fuzzy number by a polynomial fuzzy number through minimizing the distance between them. Throughout this work, we used a distance that is a meter on the set of all fuzzy numbers with continuous left and right spread functions. To support our claims analytically, we have proven some theorems and given supplementary corollaries.

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Journal Paper

‎Fuzzy Semi-Numbers and a Distance on Them with a Case Study in Medicine

Mathematical Sciences, Vol. 12 No. 1, (2018) 41-52.

In this paper, we present the novel concept of fuzzy semi-numbers. Then, a method for assigning distance between every pair of fuzzy semi-numbers is given. Moreover, it is shown that this distance is a metric on the set of all trapezoidal fuzzy semi-numbers with the same height and is a pseudo-metric on the set of all fuzzy semi-numbers. Also, by utilizing this distance, we propose an approximation of a fuzzy semi-number with given height and apply this approximation method in a medical case study.

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Journal Paper

Fuzzy Semi-Numbers and Their Elementary Arithmetic With a Medical Case Study

International Journal of Computational Intelligence Systems, Vol. 11 No. 1, (2018) 991-1004.

A new methodology for processing non-normal fuzzy sets is proposed. To break the predominant constraint on normality of fuzzy numbers the concept of fuzzy semi-numbers is introduced Then it is shown how to generalize operations defined on fuzzy numbers onto a family of fuzzy semi-numbers with possibly different heights.

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Journal Paper

A New Distance on Fuzzy Semi-Numbers

Soft Computing, Vol. 22 (2018) 4511–4524.

In this paper we firstly review the definition of fuzzy semi-numbers and study some of their properties. Then, we consider some methods for converting fuzzy semi-numbers to fuzzy numbers in order to find the distance between fuzzy semi-numbers. By presenting a new distance function, we also find the distance between fuzzy semi-numbers directly without any change to their originality. Finally, we prove some properties of the presented distance and study a practical motivational medical case study along with some numerical examples.

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conference paper

A New Distance on Generalized Fuzzy Numbers and a Glimpse on Their Properties

Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2017, Warsaw, Poland.

Normalization is the dominant but inexact method to handle any nonnormal fuzzy sets data. This stems from the fact that normalization ignores some parts of such data in order to prepare them for being used in computational operations. A subset of such data which satisfi es the property of convexity is called Generalized Fuzzy Numbers (GFN). In this paper, a new  distance is presented on the set of GFNs. In the special case, when GFNs are normal (i.e. Fuzzy Numbers), the proposed distance is converted to a well-known distance which in the fuzzy literature has already been proved to be a metric. Also, some of the features of the proposed distance are studied
through several examples.

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