New Mathematics and Natural Computation

The main aim of this paper is to establish the concepts of soft seminorm and soft norm with the help of balanced, absorbing and convex soft sets. Also, we have established equivalent concepts of soft seminorm as well as of soft norm.

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. This paper introduces the convergence concepts of convergence almost surely (a.s.), convergence in measure, convergence in mean, convergence in distribution and convergence uniformly almost surely complex uncertain double sequences. In addition, relationships among the introduced classes of sequences have been introduced.

The aim of this paper is to introduce the concept of soft compact spaces by using the notion of soft $p_c$-open sets and soft $p_c$-open covers, which we call soft $p_c$-compact spaces. Many characterizations and properties of this space are obtained. Also, we discuss the concept of soft $p_c$-compact subspaces and soft $p_c$-compact subsets relative to the space.

The purpose of this work is to use the concepts of reachability and coreachability maps to provide a solution of a well-known characterization for $L$-valued multiset regular languages. In between, we associate two deterministic $L$-valued multiset automata with a given deterministic $L$-valued multiset automaton (DLMA) and show that the reachability and coreachability maps of the given DLMA turn out to be morphisms in the category of deterministic $L$-valued multiset automata.

In this paper, the notion of soft elementwise ring is introduced and it is shown that the concepts of soft elementwise ring and soft int-ring of a ring are equivalent. The concept of soft direct sum of soft int-rings is defined and some equivalent conditions are given. The notions of minimal generating set for a soft int-ideal and soft principal int-ideal are presented. Some properties of soft principal int-ideal are discussed.

In this paper, the probability of failure of the components is introduced as a new type of fuzzy numbers called Gaussian patchy fuzzy number to insert parameters’ uncertainty. The reason for the use of such fuzzy numbers is also due to their realistic estimation. Hence, in order to obtain a more accurate estimate of each failure occurrence and overall system reliability analysis, we assume that the fundamental events of fault tree are in the form of Gaussian patchy fuzzy number on [0, 1], and then, by applying the fuzzy transmission average (TA) [F. Abbasi, T. Allahviranloo and S. Abbasbandy, A new attitude coupled with fuzzy thinking to fuzzy rings and fields, Journal of Intelligent and Fuzzy Systems, 29 (2015) 851-861], we will model the reliability of the fuzzy system (especially the series and the parallel). Applying such fuzzy operations and numbers will lead to a more realistic analysis of the reliability of the fuzzy system. Finally, the proposed model has been used for the lack of satisfaction of the University’s administrative and financial assistant.

In this paper, we introduce double sequences of complex uncertain variables defined by Orlicz function. We study some of their properties like solidness, symmetricity, completeness, etc. and prove some inclusion results.

In random experiments, the fact that the sets of events has a structure of a Boolean algebra, i.e. it follows the rules of classical logic, is the main hypothesis of classical probability theory. Bosbach states have been introduced on commutative and non-commutative algebras of fuzzy logics as a way of probabilistically evaluating the formulas. In this paper, we focus on the relationship between some properties of ideals and Bosbach states in the framework of commutative residuated lattices. In particular, we introduce the concept of co-kernel of a Bosbach state which is an ideal and we establish the relationship between the notion of co-kernel and the kernel. Moreover, we define and characterize maximal ideals and maximal MV-ideals in residuated lattices.

In this paper, we define almost convergence concepts of complex uncertain sequences: almost sure convergent, almost convergent in measure, almost convergent in mean and almost convergent in distribution and relationship among them are discussed. We also define Cesàro summable for complex uncertain sequence space. In addition, we derive relationships between convergent, Cesàro summable and almost convergent.

A stay region of a moving object is a region in which it spends a significant amount of time. Given the location of an object through a certain time interval, i.e. its trajectory, our goal is to find its stay regions. We consider axis-parallel square stay regions of fixed side length, which contain the longest continuous portion of the trajectory. We present an algorithm for answering time-windowed stay region queries, to find a stay region in any given time interval. The algorithm has an approximation factor of $1∕2$ and answers each query with the time complexity $O(logn)$, in which $n$ is the number of vertices of the input trajectory. The time complexity of the preprocessing step of the algorithm is $O(n)$. We also present two approximation algorithms for finding stay regions of whole trajectories.

In this paper, we introduce soaker filters in a residuated lattice, give some characterizations and investigate some properties of them. Then we define a topology on the set of all the soaker filters, which we call reflectional topology, show it is an Alexandrov topology and give a basis for it. We introduce the notion of join-soaker filters and prove that when the residuated lattice is a join-soaker filter, then the reflectional topology is compact. We also give a characterization of connectedness of the reflectional topology. Finally, we prove the reflectional topology is $T_0$, give necessary and sufficient conditions under which it is $T_1$ and prove that being $T_2$ is equivalent to being $T_1$. Several illustrative examples are given.

In category theory, Galois connection plays a significant role in developing the connections among different structures. The objective of this work is to investigate the essential connections among several categories with a weaker structure than that of $M$-fuzzifying topology, viz. category of $M$-fuzzifying approximation spaces based on reflexive $M$-fuzzy relations, category of $M$-fuzzifying pretopological spaces and the category of $M$-fuzzifying interior (closure) spaces. The interrelations among these structures are shown via the functorial diagram.

In this paper, we defined the concepts of $(\wedge ,\odot )$-derivation and $(\to ,\vee )$-derivation for $BL$-algebras and discuss some related results. We study the connection between these derivations on an $BL$-algebra $A$. Also, we study these derivations on Boolean center $B(A)$, $MV$ center, Godel center of a $BL$-algebra $A$.

Housing price time series is worth studying as it is closely related to the well-being of society. In the Hong Kong housing market from 1992 to 2010, signs of quasi-periodicity in housing price and transaction volume can be observed. We find that there is an overall periodicity of approximately 30 months in housing price changes and a strong lead–lag relationship between housing price and transaction volume. Analysis of the cross-covariance of the housing price, transaction volume and prime lending rate reveals that this quasi-periodicity is potentially driven by prime lending rates. Incorporation of quasi-periodicity into the kernel of Gaussian processes further enables us to construct a predictive model of the Hong Kong housing price trends that outperforms other traditional kernel functions.

The highway system is an important component of the modern society as it allows an efficient intercity communication. However, with the increase in the number of cars, the traffic congestion becomes a widespread problem around the world. Here, we study the traffic conditions in Hsuehshan tunnel in Taiwan. When there is traffic congestion, there is a remarkable fraction of vehicles choosing an alternative path, even if it cost more time than jamming on the highway. In addition, we evaluate through statistics and the government’s policy to improve the road condition of the tunnel.