scholarly journals A new approach to combine generalized interval valued fuzzy numbers based on average width of fuzzy set concept

2017 ◽  
Vol 13 (3) ◽  
pp. 359-378
Author(s):  
Palash Dutta
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Average Width ◽  
New Approach ◽  
Interval Valued

Interval-Valued Dual Hesitant Fuzzy Heronian Mean Aggregation Operators and their Application to Multi-Attribute Decision Making

2018 ◽  
Vol 17 (01) ◽  
pp. 1850005 ◽  
Author(s):  
Yuqi Zang ◽  
Xiaodong Zhao ◽  
Shiyong Li
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Aggregation Operators ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
New Approach ◽  
Dual Hesitant Fuzzy Set ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Heronian Mean

The interval-valued dual hesitant fuzzy set (IVDHFS) can depict the imprecise, vague and indeterminate information and Heronian mean (HM) has the prominent characteristic of capturing the correlation of the aggregated arguments. In this paper, we investigate multi-attribute decision making (MADM) problems based on HM, in which the attribute values are assumed in the form of interval-valued dual hesitant fuzzy information. Firstly, we briefly present some concepts of IVDHFS and HM. Then, we propose the interval-valued dual hesitant fuzzy Heronian mean (IVDHFHM) operator and the interval-valued dual hesitant fuzzy geometric Heronian mean (IVDHFGHM) operator. We also prove that they satisfy some desirable properties. Further, we consider the importance of the input arguments and derive the interval-valued dual hesitant fuzzy weighted Heronian mean (IVDHFWHM) operator and the interval-valued dual hesitant fuzzy weighted geometric Heronian mean (IVDHFWGHM) operator, and then develop the procedure of MADM. Finally, an illustrate example is given to demonstrate the practicality and effectiveness of the new approach.

Modeling Uncertainty with Interval Valued Fuzzy Numbers

2018 ◽  
Vol 11 (2) ◽  
pp. 1-17 ◽  
Author(s):  
Palash Dutta
Keyword(s):  
Risk Assessment ◽  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Small Sample Size ◽  
Small Sample ◽  
Model Parameters ◽  
Type I ◽  
Mathematical Tool ◽  
Risk Assessment Models ◽  
Interval Valued

This article describes how risk assessment is a significant aid in decision-making process. It is usually performed using models and a ‘model' is a function of some parameters which are usually affected by uncertainty due to lack of data, imprecision, vagueness, and a small sample size.. Fuzzy set is a well-established mathematical tool to handle this type of uncertainty. Normally, triangular fuzzy numbers (TFNs) or trapezoidal fuzzy numbers (TrFNs) are extensively deliberated to embody this type of uncertainty. However, in real world situations, bell-shaped fuzzy numbers may occur to characterize uncertainty. It is pragmatic that type-I fuzzy set may not always dispense single value from [0,1] and on the other hand, assigning a precise value to expert's judgment is excessively restrictive, therefore, the assignment of an interval value is more practical. Thus, interval valued fuzzy set (IVFS) comes into picture. It can be observed that representation of some model parameters of the risk assessment models are triangular interval valued fuzzy numbers (TIVFNs) while representation of some other parameters are bell-shaped IVFNs. In such circumstances, it is most important to devise a technique to combine TIVFNs and bell shaped IVFNs, as they are non-comparable. For this purpose, this article presents a technique to combine both types of incomparable IVFNs within the same framework and finally, a case study is carried out in risk assessment under this setting.

Rule Extraction Based on Interval-Valued Rough Fuzzy Sets

2014 ◽  
Vol 665 ◽  
pp. 668-673
Author(s):  
Hua Ni Qin ◽  
Da Rong Luo
Keyword(s):  
Knowledge Discovery ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Fuzzy Information ◽  
Modified Model ◽  
Sorting Method ◽  
Rough Fuzzy Set ◽  
General Sorting ◽  
Interval Valued

A model of interval-valued rough fuzzy set combining interval-valued fuzzy set and rough set is investigated in this paper. Firstly, considering the deficiency of general sorting method between any interval-valued fuzzy numbers, an improved sorting method and a pair of new approximation operators about minimum and maximum are presented. Based on the improved operators, a model of interval-valued rough fuzzy set is established. At last, by using the modified model of interval-valued rough fuzzy set, a method of knowledge discovery in interval-valued fuzzy information systems is investigated.

A new way of handling multi-attribute group decision making problems

2020 ◽  
Vol 39 (3) ◽  
pp. 3921-3929
Author(s):  
Aliya Fahmi ◽  
Muhammad Aslam ◽  
Rehan Ahmed
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Topsis Method ◽  
New Approach ◽  
Numerical Example ◽  
Operational Laws ◽  
Interval Valued

A novel idea of linguistic interval-valued intuitionistic neutrosophic fuzzy numbers (LIVINFNs) and operational laws of the numbers are introduced in this paper. LIVINF TOPSIS method is developed and application of the developed TOPSIS method to a multi-attribute group decision making (MAGDM) problem in a LIVINF environment is discussed. Finally, a numerical example is presented to validate this new approach in group decision making problems.

A New Approach to Interval-Valued Choquet Integrals and the Problem of Ordering in Interval-Valued Fuzzy Set Applications

2013 ◽  
Vol 21 (6) ◽  
pp. 1150-1162 ◽  
Author(s):  
Humberto Bustince ◽  
Mikel Galar ◽  
Benjamin Bedregal ◽  
Anna Kolesarova ◽  
Radko Mesiar
Keyword(s):  
Fuzzy Set ◽  
New Approach ◽  
Choquet Integrals ◽  
Interval Valued

Classification of Ordered Semigroups in Terms of Generalized Interval-Valued Fuzzy Interior Ideals

2016 ◽  
Vol 25 (2) ◽  
pp. 297-318
Author(s):  
Hidayat Ullah Khan ◽  
Nor Haniza Sarmin ◽  
Asghar Khan ◽  
Faiz Muhammad Khan
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Decision Making Process ◽  
Ordered Semigroup ◽  
New Approach ◽  
Ordered Semigroups ◽  
Applied Fields ◽  
Interval Valued

AbstractSeveral applied fields dealing with decision-making process may not be successfully modeled by ordinary fuzzy sets. In such a situation, the interval-valued fuzzy set theory is more applicable than the fuzzy set theory. Using a new approach of “quasi-coincident with relation”, which is a central focused idea for several researchers, we introduced the more general form of the notion of (α,β)-fuzzy interior ideal. This new concept is called interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal of ordered semigroup. As an attempt to investigate the relationships between ordered semigroups and fuzzy ordered semigroups, it is proved that in regular ordered semigroups, the interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy ideals and interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals coincide. It is also shown that the intersection of non-empty class of interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals of an ordered semigroup is also an interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal.

scholarly journals Mehar Approach for Finding Shortest Path in Supply Chain Network

2021 ◽  
Vol 13 (7) ◽  
pp. 4016
Author(s):  
Tanveen Kaur Bhatia ◽  
Amit Kumar ◽  
Srimantoorao S. Appadoo ◽  
Yuvraj Gajpal ◽  
Mahesh Kumar Sharma
Keyword(s):  
Shortest Path ◽  
Fuzzy Numbers ◽  
New Approach ◽  
Shortest Path Problems ◽  
Shortest Distance ◽  
Lexicographic Method ◽  
Different Types ◽  
The Cost ◽  
Pythagorean Fuzzy Numbers ◽  
Interval Valued

The aim of each company/industry is to provide a final product to customers at the minimum possible cost, as well as to protect the environment from degradation. Ensuring the shortest travel distance between involved locations plays an important role in achieving the company’s/industry’s objective as (i) the cost of a final product can be minimized by minimizing the total distance travelled (ii) finding the shortest distance between involved locations will require less fuel than the longest distance between involved locations. This will eventually result in lesser degradation of the environment. Hence, in the last few years, various algorithms have been proposed to solve different types of shortest path problems. A recently proposed algorithm for solving interval-valued Pythagorean fuzzy shortest path problems requires excessive computational efforts. Hence, to reduce the computational efforts, in this paper, firstly, an alternative lexicographic method is proposed for comparing interval-valued Pythagorean fuzzy numbers. Then, using the proposed lexicographic comparing method, a new approach (named as Mehar approach) is proposed to solve interval-valued Pythagorean fuzzy shortest path problems. Furthermore, the superiority of the proposed lexicographic comparing method, as well as the proposed Mehar approach, is discussed.

scholarly journals Multiple Granulation Rough Set Approach to Interval-Valued Intuitionistic Fuzzy Ordered Information Systems

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 949
Author(s):  
Zhen Li ◽  
Xiaoyan Zhang
Keyword(s):  
Information Theory ◽  
Pattern Recognition ◽  
Information System ◽  
Information Systems ◽  
Rough Set ◽  
Fuzzy Set ◽  
Equivalence Relation ◽  
Target Concept ◽  
Actual Case ◽  
Interval Valued

As a further extension of the fuzzy set and the intuitive fuzzy set, the interval-valued intuitive fuzzy set (IIFS) is a more effective tool to deal with uncertain problems. However, the classical rough set is based on the equivalence relation, which do not apply to the IIFS. In this paper, we combine the IIFS with the ordered information system to obtain the interval-valued intuitive fuzzy ordered information system (IIFOIS). On this basis, three types of multiple granulation rough set models based on the dominance relation are established to effectively overcome the limitation mentioned above, which belongs to the interdisciplinary subject of information theory in mathematics and pattern recognition. First, for an IIFOIS, we put forward a multiple granulation rough set (MGRS) model from two completely symmetry positions, which are optimistic and pessimistic, respectively. Furthermore, we discuss the approximation representation and a few essential characteristics for the target concept, besides several significant rough measures about two kinds of MGRS symmetry models are discussed. Furthermore, a more general MGRS model named the generalized MGRS (GMGRS) model is proposed in an IIFOIS, and some important properties and rough measures are also investigated. Finally, the relationships and differences between the single granulation rough set and the three types of MGRS are discussed carefully by comparing the rough measures between them in an IIFOIS. In order to better utilize the theory to realistic problems, an actual case shows the methods of MGRS models in an IIFOIS is given in this paper.

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