Complex Bipolar Fuzzy Soft Expert Sets

JPRM-Vol. 18 (2022), Issue 1, pp. 60 – 74 Open Access Full-Text PDF
Abd Ulzeez Alkouri
Abstract: The idea of representing information with its periodic nature has been extensively studied and applied in many fields. Many researchers have developed several tools to transfer uncertainty information that has the same data but with different meanings that happening in different phases/times. The novelty of combining complex numbers and uncertainty information appears in its ability to represent two values uncertainty and periodicity semantics in one mathematical tool. In this paper, we generalize existence concept of bipolar fuzzy soft expert sets (BFSES) from real number to complex numbers to be complex bipolar fuzzy soft expert sets (CBFSES). This generalization allows us to convey data that carry benefits, features, and specifications of BFSES in different phases or carrying periodic nature of the BFSE information to mathematical formula and vice versa without losing full meaning of information. The range of value becomes to be in unit disk in a complex plane for both positive and negative membership functions of BFSES. The main benefit of CBFSES that amplitude and phase terms can convey bipolar fuzzy information. Moreover, formal definition of CBFSES and illustration examples are introduced. Also, we define basic operations and their properties on CBFSES. Finally, OR and AND operations are generalized to the form of CBFSES.
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An Introduction to Soft Hypergraphs

JPRM-Vol. 18 (2022), Issue 1, pp. 43 – 59 Open Access Full-Text PDF
Bobin George, Jinta Jose, Rajesh K. Thumbakara
Abstract: This is an introductory paper on Soft Hypergraph. In 1999, D. Molodtsov initiated the concept of soft set theory. This is an approach for modeling vagueness and uncertainty. The concept of soft graphs introduced by Rajesh K. Thumbakara and Bobin George is used to provide a parameterized point of view for graphs. Theory of soft graphs is a fast developing area in graph theory due to its capability to deal with the parameterization tool. Hypergraph is a generalization of graph. In this paper we introduce the concept of soft hypergraph by applying the idea of soft set in hypergraph. By means of parameterization, soft hypergraph produces a series of descriptions of a relation described using a hypergraph.
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Correction on General Convergence Analysis for Two-Step Projection Methods and Applications to Variational Problems

JPRM-Vol. 18 (2022), Issue 1, pp. 38 – 42 Open Access Full-Text PDF
Ayache Benhadid
Abstract: The aim of this study is to illustrate that the main result of the paper [1] is incorrect by giving an counterexample. I also present and study a new algorithm 4.1 to correct the main result of [1]. The possible impact of this study is rather important, it puts a question mark on results in all references that have been cited This publication ( 203 times just in Google Scholar alone).
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Fuzzy L\(^P\)-Spaces

JPRM-Vol. 18 (2022), Issue 1, pp. 28 – 37 Open Access Full-Text PDF
Shams Yousef, Forouzan Farahrooz
Abstract: The purpose of this paper is to introduce the fuzzy L\(^P\)-Spaces. We give some basic definitions and main properties of fuzzy spaces. The fuzzy Holder’s inequality will be proved. Also we show that the dual offuzzy L\(^P\)-spaces is fuzzy L\(^q\)-spaces, where the scalars p and q are conjugate exponents.
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On Metric Dimension of Chemical Networks

JPRM-Vol. 18 (2022), Issue 1, pp.18 – 27 Open Access Full-Text PDF
Muhammad Hussain, Saqib Nazeer, Hassan Raza
Abstract: Metric Dimension of any graph G is termed as the minimum number of basis element in the resolving set. Let G = (V, E) be any connected graph and length of the shortest path between s and h is known as distance, denoted by d(s, h) in G. Let B = {b1, b2, …, bq} be any ordered subset of V and representation r(u|B) with respect to B is the q−tuple (d(u, b1), d(u, b2), d(u, b3), …, d(u, bq)}, here B is called the resolving set or the locating set if every vertex of G is uniquely represented by distances from the vertices of B or if distinct vertices of G have distinct representations with respect to B. Any resolving set containing minimum cardinality is named as basis for G and its cardinality is the metric dimension of G is denoted by dim(G). We investigated metric dimension of Polythiophene Network, Backbone Network, Hex-derive Network and Nylone6,6.
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Fixed Point Approximations of a Family of α-nonexpansive Mappings in CAT(0) Spaces

JPRM-Vol. 18 (2022), Issue 1, pp. 7 – 17 Open Access Full-Text PDF
Sundus Shahzeen, Maqbool Ahmed, Liliana Guran
Abstract: In this article, the results deal with the strong convergence of Halpern iteration in CAT(0) spaces. The study revolves around finding a fixed point for nonexpansive mappings, which are also the metric projection points in CA(0) space.Moreover, the strong convergence of Halpern iteration for α-nonexpansive mapping sequence is also given.Our results extend some known results which appeared in the literature.
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On A Mathematical Contradiction to Rethink Associativity and Commutativity for Infinite Series and Infinite Products

JPRM-Vol. 18 (2022), Issue 1, pp. 1 – 6 Open Access Full-Text PDF
Md. Shafiqul Islam, Sumit Bhowmick
Abstract: This paper deals with two contradictory values of π, focusing on the invalidity of associative and commutative laws for infinite series. The argument shows that operating with some infinite products leads to some dangerous contradictions such as the π value turns out to be 4 or 8/3. The study and the findings embedded with the article’s methodology points out that these classical operations like associativity and commutativity on infinite series or infinite products must be handled carefully.
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