Rajkumar Verma

New operations over hesitant fuzzy sets

Hesitant fuzzy sets are considered to be the way to characterize vague phenomenon. Their study has opened a new area of research and applications. Set operations on them lead to a number of properties of these sets which are not evident in classical (crisp) sets make the area mathematically also very productive. Since these sets are defined in terms of functions and set of functions, which is not the case when the sets are crisp, it is possible to define several set operations. Such a study enriches the use of these sets. In this paper, four new operations are envisaged, defined and taken up to study a score of new identities on hesitant fuzzy sets.

Prioritized Information Fusion Method for Triangular Fuzzy Information and Its Application to Multiple Attribute Decision Making

This study investigates the multiple attribute decision making under triangular fuzzy environment in which the attributes and experts are in different priority level. By combining the idea of quasi arithmetic mean and prioritized weighted average (PWA) operator, we first propose two new prioritized aggregation operators called quasi fuzzy prioritized weighted average (QFPWA) operator and the quasi fuzzy prioritized weighted ordered weighted average (QFPWOWA) operator for aggregating triangular fuzzy information. The properties of the new aggregation operators are studied in detail and their special cases are examined. Furthermore, based on the QFPWA operator and QFPWOWA operator, an approach to deal with multiple attribute decision-making problems under triangular fuzzy environments is developed. Finally, a practical example is provided to illustrate the multiple attribute decision making process.

Fuzzy Generalized Prioritized Weighted Average Operator and its Application to Multiple Attribute Decision Making

The prioritized weighted average (PWA) operator was originally introduced by Yager. The prominent characteristic of the PWA operator is that it takes into account prioritization among attributes and decision makers. By combining the idea of generalized mean and PWA operator, we propose a new prioritized aggregation operator called fuzzy generalized prioritized weighted average (FGPWA) operator for aggregating triangular fuzzy numbers. The properties of the new aggregation operator are studied out and their special cases are examined. Furthermore, based on the FGPWA operator, an approach to deal with multiple attribute group decision making problems under triangular fuzzy environments is developed. Finally, a practical example is provided to illustrate the multiple attribute group decision making process.

Operations on hesitant fuzzy sets: Some new results

Hesitant fuzzy sets, introduced by Torra and Narukawa [10] present a powerful tool for study of hesitancy in decision making. The main strength of this generalization will be realized by studying the properties and the operations that can be defined on hesitant fuzzy sets. This paper presents a number of properties in the light of operations defined by Torra [11] and Xia and Xu [13] on hesitant fuzzy sets.

Trapezoid fuzzy linguistic prioritized weighted average operators and their application to multiple attribute group decision-making

The prioritized weighted average (PWA) operator was originally introduced by Yager. The prominent characteristic of the PWA operator is that it takes into account prioritization among attributes and decision makers. Motivated by the idea of PWA operator, we develop some prioritized weighted aggregation operators for aggregating trapezoid fuzzy linguistic information. The properties of the new aggregation operators are studied in detail. Furthermore, based on the proposed operators, some approaches to deal with multiple attribute group decision-making problems under trapezoid fuzzy linguistic environments are developed. Finally, a practical example is provided to illustrate the multiple attribute group decision-making process.