ELECTRE is a family of multi-criteria decision analysis techniques which has the ability to provide as much as possible precise and suitable set of actions or alternatives to the underlying problem by eliminating the alternatives which are outranked by others. Group decision making is an effective process to provide the most appropriate solution to real-world decision-making scenarios by considering and merging the expert opinions of multiple individuals on problem. The purpose of this research study is to extend the ELECTRE I method to Pythagorean fuzzy ELECTRE I (PF-ELECTRE I) method in group decision-making environment, as Pythagorean fuzzy set model is more superior tool to capture vagueness and incompleteness in human evaluations. The developed method has ability to solve multi-criteria group decision-making problems in which the assessment information on available alternatives, provided by the experts, is presented as Pythagorean fuzzy decision matrices having each entry characterized by Pythagorean fuzzy number (PFN). The approach is formulated by introducing the concepts of strong, midrange and weak Pythagorean fuzzy concordance and discordance sets to elaborate the outranking relation among alternatives with respect to conflicting criteria. Framework of group decision supporting system based on PF-ELECTRE I is demonstrated by a flowchart. Finally, two illustrative examples in the field of health safety and environment management are given to verify and demonstrate the applicability of our proposed approach.

Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information

Fuzzy planar graph is a very important subclass of fuzzy graph. In this paper, two types of edges are mentioned for fuzzy graphs: effective edges and considerable edges. In addition, a comparative study between Kuratowski's graphs and fuzzy planar graph is made. A new concept of a strong fuzzy planar graph is introduced. Some related results are established. These results have certain applications in subway tunnels, routes, oil/gas pipelines representation, etc. It is also shown that an image can be represented by a fuzzy planar graph, and contraction of such an image can be made with the help of a fuzzy planar graph.

Fuzzy Planar Graphs

In this article, we introduce a new hybrid model called hesitant N-soft sets by a suitable combination of hesitancy with N-soft sets, a model that extends N-soft sets. Our novel concept is illustrated with real life examples. Moreover, we investigate some useful properties of hesitant N-soft sets and construct fundamental operations on them. We describe potential applications of hesitant N-soft sets in group decision-making, and finally we present some group decision-making methods as algorithms.

Group decision-making methods based on hesitant N-soft sets

Fuzzy N-soft sets: A novel model with applications

Many results have been obtained on isolated graphs and complete graphs. In this paper, a necessary and sufficient condition will be proved for a single valued neutrosophic graph to be an isolated single valued neutrosophic graph

Isolated Single Valued Neutrosophic Graphs

Bipolar fuzzy set theory, an extension of fuzzy set theory, deals with incomplete and vague information. The purpose of this research paper is to develop new methodologies in handling multi-criteria decision-making (MCDM) problems where the subjective data given by a decision maker are expressed with bipolar fuzzy information. Every alternative has a rating consists of two parts: positive and negative. The positive part represents the benefit (or satisfaction degree) and the negative part represents the cost (or dissatisfaction degree) of the alternative on the corresponding criterion. In this paper, we present bipolar fuzzy TOPSIS (BF-TOPSIS) method and bipolar fuzzy ELECTRE I (BF-ELECTRE I) method for solving MCDM problems that are equipped with bipolar fuzzy information. We illustrate our proposed methods with examples. We design algorithms of BF-TOPSIS method and BF-ELECTRE I method. We also give comparison of BF-TOPSIS method and BF-ELECTRE I method.

Multi-Criteria Decision-Making Methods in Bipolar Fuzzy Environment

We introduce notions of soft rough m-polar fuzzy sets and m-polar fuzzy soft rough sets as novel hybrid models for soft computing, and investigate some of their fundamental properties. We discuss the relationship between m-polar fuzzy soft rough approximation operators and crisp soft rough approximation operators. We also present applications of m-polar fuzzy soft rough sets to decision-making.

https://www.mdpi.com/2073-8994/9/11/271/pdf

A New Multi-Attribute Decision-Making Method Based on m-Polar Fuzzy Soft Rough Sets

Connectivity has an important role in neural networks, computer network, and clustering. In the design of a network, it is important to analyze connections by the levels. The structural properties of intuitionistic fuzzy graphs provide a tool that allows for the solution of operations research problems. In this paper, we introduce various types of intuitionistic fuzzy bridges, intuitionistic fuzzy cut vertices, intuitionistic fuzzy cycles, and intuitionistic fuzzy trees in intuitionistic fuzzy graphs and investigate some of their interesting properties. Most of these various types are defined in terms of levels. We also describe comparison of these types.

https://downloads.hindawi.com/journals/tswj/2014/305836.pdf

Intuitionistic Fuzzy Cycles and Intuitionistic Fuzzy Trees

Bipolar Fuzzy Digraphs in Decision Support Systems.

Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. We introduce the notions of intuitionistic fuzzy multigraphs, intuitionistic fuzzy planar graphs, and intuitionistic fuzzy dual graphs and investigate some of their interesting properties. We also study isomorphism between intuitionistic fuzzy planar graphs.

/pdf/intuitionistic-fuzzy-planar-graphs-1l6isc1eye.pdf

Noura Omair Alshehri

Papers

Multi-Criteria Decision-Making Methods in Bipolar Fuzzy Environment

A New Multi-Attribute Decision-Making Method Based on m-Polar Fuzzy Soft Rough Sets

Intuitionistic Fuzzy Cycles and Intuitionistic Fuzzy Trees

Bipolar Fuzzy Digraphs in Decision Support Systems.

Intuitionistic Fuzzy Planar Graphs