necessity

Facility location problems have often vagueness and uncertain properties. In P-center problems, this uncertainty can be in the parameters of demand nods. Firstly, in this paper, a vertex-center problem with uncertain demand nodes is considered in which the demand nodes are fuzzy and fuzzy random variables. Then, new solving methods are proposed based on possibility and necessity measures, using fuzzy and fuzzy random programming, respectively. Finally, a real case study in the city of Tabriz in Iran is presented to clarify the methods discussed in this paper. The computational results of the study indicate that these methods can be implemented for center problem with uncertain framework.

This study employs a descriptive-analytical method and a critical comparative approach to examine, critique, and compare the proofs for the existence of God in Western and Islamic philosophy. The introduction clarifies the meaning of proof and distinguishes it from faith and reasoning. It then outlines key concepts necessary for a deeper understanding of the proofs for God’s existence, including the role of Western and Islamic philosophers in shaping these arguments, the distinction between horizontal and vertical proofs in Western and Islamic traditions, and the empiricist and rationalist approaches to these arguments in both intellectual traditions. Following this foundation, the article systematically analyzes four categories of arguments for God's existence: ontological, cosmological, teleological (design), and moral arguments, as presented by Western thinkers. These arguments are then examined and critiqued based on the principles of Islamic philosophy. Throughout the discussion, the study highlights how misunderstandings or misinterpretations of key concepts and rational principles unique to Islamic philosophy—particularly in general and special metaphysics—have contributed to certain misapprehensions in the history of Western philosophy regarding proofs for God’s existence.

This paper proposes a distinct realist perspective on the laws of nature, rooted in the tradition of late Islamic philosophy, which may offer a new solution to one of the difficult challenges of scientific realism, termed the ‘Central Dilemma’ by Mumford. It begins with a brief introduction to the problem of scientific realism concerning the concept of the laws of nature. Then, in the first part, we compare the realist theories of the laws of nature developed by Lewis, Armstrong, and Bird, focusing on their account of the three key concepts of causation, necessity, and law. Based on this analysis, the second part formulates a new realist theory, drawing from the doctrine of “Motion in Substance” from Late Islamic Philosophy, particularly the philosophical thought of Tabatabai. This will be done by extending the idea of motion in substance and examining some of its implications. This new account is, in some respects, similar to Bird’s view, yet in other respects Humean and similar to Lewis’s. By comparing this new approach with the aforementioned three theories, concerning their accounts of causation, necessity, and law in relation to the ‘Central Dilemma’ challenge, we conclude that it could bring a new vision that could potentially resolve this challenge.