The Relationship Between Intuitionistic Fuzzy Programming and Goal Programming

In 2020, Kang, Song and Jun introduced the notion of multipolar intuitionistic fuzzy set with finite degree, which is a generalization of intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. In this paper, we used this notion to study p-ideals of BCI-algebras. The notion of k-polar intuitionistic fuzzy p-ideals in BCI-algebras is introduced, and several properties were investigated. An example to illustrate the k-polar intuitionistic fuzzy p-ideal is given. The relationship between k-polar intuitionistic fuzzy ideal and k-polar intuitionistic fuzzy p-ideal is displayed. A k-polar intuitionistic fuzzy p-ideal is found to be k-polar intuitionistic fuzzy ideal, and an example to show that the converse is not true is provided. The notions of p-ideals and k-polar ( ∈ , ∈ ) -fuzzy p-ideal in BCI-algebras are used to study the characterization of k-polar intuitionistic p-ideal. The concept of normal k-polar intuitionistic fuzzy p-ideal is introduced, and its characterization is discussed. The process of eliciting normal k-polar intuitionistic fuzzy p-ideal using k-polar intuitionistic fuzzy p-ideal is provided.

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Linguistic Interval-Valued Intuitionistic Fuzzy Copula Heronian Mean Operators for Multiattribute Group Decision-Making

Journal of Mathematics ◽

10.1155/2020/6179468 ◽

2020 ◽

Vol 2020 ◽

pp. 1-25

Author(s):

Lei Xu ◽

Yi Liu ◽

Haobin Liu

Keyword(s):

Decision Making ◽

Fuzzy Number ◽

Group Decision ◽

Decision Makers ◽

Intuitionistic Fuzzy Number ◽

Intuitionistic Fuzzy ◽

Uncertainty Information ◽

The Relationship ◽

Interval Valued ◽

Heronian Mean

As a generalization of the intuitionistic fuzzy number (IFN), the linguistic interval-valued intuitionistic fuzzy number (LIVIFN) is a flexible and superior tool to describe complex fuzzy uncertainty information. Heronian mean (HM) operator has the characteristic of considering the relationship between attributes. Extended copulas (ECs) and extended cocopulas (ECCs) are the promotion form of Archimedean t-norm and t-conorm (ATT). ECs and ECCs can generate versatile operational rules and can provide more choice for decision makers (DMs). Therefore, it is very necessary to take advantages of them. In this paper, ECs and ECCs, some specifics of ECs and ECCs, and score and accuracy functions of IVILFNs are gained first. Then, we propose the linguistic interval-valued intuitionistic fuzzy weighted copula Heronian mean (LIVIFWCHM) operator; also, some properties and five specific expressions of the LIVIFWCHM operator are discussed. Moreover, we also propose a new MAGDM approach based on the proposed LIVIFWCHM operator. Finally, a set of examples are used to demonstrate the effectiveness, generality, and flexibility of the proposed method.

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Resolving Indeterminacy Approach to Solve Multi-Criteria Zero-Sum Matrix Games with Intuitionistic Fuzzy Goals

Mathematics ◽

10.3390/math8030305 ◽

2020 ◽

Vol 8 (3) ◽

pp. 305 ◽

Cited By ~ 1

Author(s):

M. G. Brikaa ◽

Zhoushun Zheng ◽

El-Saeed Ammar

Keyword(s):

Intuitionistic Fuzzy Set ◽

Implementation Process ◽

Fuzzy Programming ◽

Matrix Game ◽

Great Success ◽

Matrix Games ◽

Intuitionistic Fuzzy ◽

Fuzzy Goals ◽

Linear Programming Problems ◽

Zero Sum

The intuitionistic fuzzy set (IFS) is applied in various decision-making problems to express vagueness and showed great success in realizing the day-to-day problems. The principal aim of this article is to develop an approach for solving multi-criteria matrix game with intuitionistic fuzzy (I-fuzzy) goals. The proposed approach introduces the indeterminacy resolving functions of I-fuzzy numbers and discusses the I-fuzzy inequalities concept. Then, an effective algorithm based on the indeterminacy resolving algorithm is developed to obtain Pareto optimal security strategies for both players through solving a pair of multi-objective linear programming problems constructed from two auxiliary I-fuzzy programming problems. It is shown that this multi-criteria matrix game with I-fuzzy goals is an extension of the multi-criteria matrix game with fuzzy goals. Moreover, two numerical simulations are conducted to demonstrate the applicability and implementation process of the proposed algorithm. Finally, the achieved numerical results are compared with the existing algorithms to show the advantages of our algorithm.

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