N-Reciprocity Property for Interval-Valued Fuzzy Relations with an Application to Group Decision Making Problems in Social Networks

2017 ◽  
Vol 25 (Suppl. 1) ◽  
pp. 43-72 ◽  
Author(s):  
Urszula Bentkowska ◽  
Barbara Pȩkala ◽  
Humberto Bustince ◽  
Javier Fernandez ◽  
Aranzazu Jurio ◽  
...  
Keyword(s):  
Group Decision ◽  
Fuzzy Relations ◽  
Strict Preference ◽  
Linear Orders ◽  
Reciprocal Relations ◽  
Basic Interval ◽  
Aggregation Functions ◽  
Study Interval ◽  
Interval Valued ◽  
Voting Method

In this paper we study interval-valued fuzzy relations. We consider preference relations, i.e. a triplet consisting of strict preference, indifference and incomparability which are defined with the use of a fuzzy negation. We analyze the preservation of the fuzzy negation based reciprocity property of interval-valued fuzzy relations by aggregation functions and by some basic interval-valued fuzzy relations. We use diverse representa-tions of aggregation functions. We also consider the connection between N-reciprocal relations and transitivity properties. We provide a numerical example where the final alternative is chosen with the use of generalized voting method, where admissible linear orders for intervals are applied.

scholarly journals m-Polar Generalization of Fuzzy T-Ordering Relations: An Approach to Group Decision Making

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 51
Author(s):  
Azadeh Zahedi Khameneh ◽  
Adem Kilicman
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Fuzzy Data ◽  
Fuzzy Relations ◽  
Ranking Problem ◽  
Finite Case ◽  
Aggregation Functions ◽  
Infinite Case ◽  
Fuzzy Setting ◽  
Minimum Operator

Recently, T-orderings, defined based on a t-norm T and infimum operator (for infinite case) or minimum operator (for finite case), have been applied as a generalization of the notion of crisp orderings to fuzzy setting. When this concept is extending to m-polar fuzzy data, it is questioned whether the generalized definition can be expanded for any aggregation function, not necessarily the minimum operator, or not. To answer this question, the present study focuses on constructing m-polar T-orderings based on aggregation functions A, in particular, m-polar T-preorderings (which are reflexive and transitive m-polar fuzzy relations w.r.t T and A) and m-polar T-equivalences (which are symmetric m-polar T-preorderings). Moreover, the construction results for generating crisp preference relations based on m-polar T-orderings are obtained. Two algorithms for solving ranking problem in decision-making are proposed and validated by an illustrative example.

Composition of interval-valued fuzzy relations using aggregation functions

2016 ◽  
Vol 369 ◽  
pp. 690-703 ◽  
Author(s):  
Mikel Elkano ◽  
Jose Antonio Sanz ◽  
Mikel Galar ◽  
Barbara Pȩkala ◽  
Urszula Bentkowska ◽  
...  
Keyword(s):  
Fuzzy Relations ◽  
Aggregation Functions ◽  
Interval Valued

scholarly journals Interval-Valued Probabilistic Hesitant Fuzzy Set Based Muirhead Mean for Multi-Attribute Group Decision-Making

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 342 ◽  
Author(s):  
Krishankumar ◽  
Ravichandran ◽  
Ahmed ◽  
Kar ◽  
Peng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Partial Information ◽  
Programming Model ◽  
Hesitant Fuzzy Set ◽  
Occurrence Probability ◽  
Source Selection ◽  
Interval Valued

As a powerful generalization to fuzzy set, hesitant fuzzy set (HFS) was introduced, which provided multiple possible membership values to be associated with a specific instance. But HFS did not consider occurrence probability values, and to circumvent the issue, probabilistic HFS (PHFS) was introduced, which associates an occurrence probability value with each hesitant fuzzy element (HFE). Providing such a precise probability value is an open challenge and as a generalization to PHFS, interval-valued PHFS (IVPHFS) was proposed. IVPHFS provided flexibility to decision makers (DMs) by associating a range of values as an occurrence probability for each HFE. To enrich the usefulness of IVPHFS in multi-attribute group decision-making (MAGDM), in this paper, we extend the Muirhead mean (MM) operator to IVPHFS for aggregating preferences. The MM operator is a generalized operator that can effectively capture the interrelationship between multiple attributes. Some properties of the proposed operator are also discussed. Then, a new programming model is proposed for calculating the weights of attributes using DMs’ partial information. Later, a systematic procedure is presented for MAGDM with the proposed operator and the practical use of the operator is demonstrated by using a renewable energy source selection problem. Finally, the strengths and weaknesses of the proposal are discussed in comparison with other methods.

scholarly journals Gray Scale Edge Detection using Interval-Valued Fuzzy Relations

2015 ◽  
Vol 8 (sup2) ◽  
pp. 16-27 ◽  
Author(s):  
Agustina Bouchet ◽  
Pelayo Quirós ◽  
Pedro Alonso ◽  
Virginia Ballarin ◽  
Irene Díaz ◽  
...  
Keyword(s):  
Edge Detection ◽  
Fuzzy Relations ◽  
Gray Scale ◽  
Interval Valued

scholarly journals AN EXTENSION OF THE RATIO SYSTEM APPROACH OF MOORA METHOD FOR GROUP DECISION-MAKING BASED ON INTERVAL-VALUED TRIANGULAR FUZZY NUMBERS

2015 ◽  
Vol 22 (1) ◽  
pp. 122-141 ◽  
Author(s):  
Dragisa STANUJKIC
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
System Approach ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Weighted Averaging ◽  
Performance Ratings ◽  
Triangular Fuzzy Numbers ◽  
Moora Method ◽  
Interval Valued

Decision-making in fuzzy environment is often a very complex, especially when related to predictions and assessments. The Ratio system approach of the MOORA method and Intervalvalued fuzzy numbers have already proved themselves as the effective tools for solving complex decision-making problems. Therefore, in this paper an extension of the Ratio system approach of the MOORA method, which allows a group decision-making as well as the use of interval-valued triangular fuzzy numbers, is proposed. Interval-fuzzy numbers are rather complex, and therefore, they are not practical for direct assigning performance ratings. For this reason, in this paper it has also been suggested the approach which allows the expression of individual performance ratings using crisp, interval or fuzzy numbers, and their further transformation into the group performance ratings, expressed in the form of interval-valued triangular fuzzy numbers, which provide greater flexibility and reality compared to the use of linguistic variables. Finally, in this paper the weighted averaging operator was proposed for defuzzification of interval-valued triangular fuzzy numbers.

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