On Interval-Valued Fuzzy Soft Preordered Sets and Associated Applications in Decision-Making

Recently, using interval-valued fuzzy soft sets to rank alternatives has become an important research area in decision-making because it provides decision-makers with the best option in a vague and uncertain environment. The present study aims to give an extensive insight into decision-making processes relying on a preference relationship of interval-valued fuzzy soft sets. Firstly, interval-valued fuzzy soft preorderings and an interval-valued fuzzy soft equivalence are established based on the interval-valued fuzzy soft topology. Then, two crisp preordering sets, namely lower crisp and upper crisp preordering sets, are proposed. Next, a score function depending on comparison matrices is expressed in solving multi-group decision-making problems. Finally, a numerical example is given to illustrate the validity and efficacy of the proposed method.

Fixed point theorems in preordered sets

Ran and Reurings (Proc Am Math Soc 132(5):1435–1443, 2003) extended the Banach contraction principle to the setting of partially ordered metric spaces and recently Proinov (J Fixed Point Theory Appl 22:21, 2020) extended and unified many earlier fixed point theorems. In this paper we will present analogous results for the significantly wider class of mappings on preordered metric spaces. We give non-trivial examples of Kannan-type mappings.

Logic of Typical and Atypical Instances of a Concept—A Mathematical Model

In this paper, we give a mathematical model of the logic of determination of objects (LDO) based on preordered sets, and a mathematical model of the logic of typical and atypical instances (LTA). We prove that LTA is an extension of LDO. It can manipulate several types of “exceptions”. Finally, we show that the structural part of LTA can be modeled by a quasi topology structure (QTS).

Extended Nash Equilibria of Nonmonetized Noncooperative Games on Preordered Sets

A noncooperative game is said to be nonmonetized if the ranges of the utilities (payoffs) of the players are preordered sets. In this paper, we examine some nonmonetized noncooperative games in which both of the collection of strategies and the ranges of the utilities for the players are preordered sets. Then, we spread the concept of extended Nash equilibria of noncooperative games from posets to preordered sets. By applying some fixed point theorems on preordered sets and by using the order preserving property of the utilities, we prove an existence theorem of extended Nash equilibria for nonmonetized noncooperative games.