Search results

This paper investigates the temporal inflow profile that minimises the total cost of travel for a single route. The problem is formulated to consider the case in which the total demand to be serviced is fixed. The approach used here is a direct calculation of the first order variation of total system cost with respect to variations in the inflow profile. Two traffic models are considered; the bottleneck with deterministic queue and the kinematic wave model. For the bottleneck model a known solution is recovered. The wave model proves more difficult and after eliminating the possibility of a smooth inflow profile the restricted case of constant inflow is solved. As the space of possible profiles is finite dimensional in this case, the standard techniques of calculus apply. We establish a pair of equations that are satisfied simultaneously by the optimal inflow and time of first departure.

In this paper, we define and examine the concept of a fuzzy recognizer. If L(M) is the language recognized by an incomplete fuzzy recognizer M, we show that there is a completion M of M such that L(M) = L(M). We also show that if A is a recognizable set of words, then there is a complete accessible fuzzy recognizer M_A such that L(M_A) = A. We lay groundwork to determine rational decompositions of recognizable sets.

The purpose of this research paper is to develop an algorithm/methodology for the reduction of a fuzzy recognizer through an algebraic concept such as homomorphism.

The approach of this research is to introduce the concepts, compatible with the purpose of this paper, and then to find a necessary and sufficient condition for the reduction of a fuzzy recognizer.

A fuzzy Σ‐recognizer M with non‐empty fuzzy initial state and the behavior A is reduced if and only if it is isomorphic to M^A.

The research proposes an algebraic method for the reduction of a fuzzy recognizer. The problem of finding dispensable fuzzy productions of a regular fuzzy grammar may be tackled by the use this algebraic method, as fuzzy recognizers and fuzzy regular grammars are equivalent.

The concepts and the methodology are original. The work is useful to the researchers in the field of fuzzy automata, fuzzy grammars and pattern recognition.

Let p_[1,r;t] be defined by ∑n=0∞p[1,r;t](n)qn=(E1Er)t, where t is a non-zero rational number, r ≥ 1 is an integer and Er=∏n=0∞(1−qr(n+1)) for |q| < 1. The function p_[1,r;t](n) is the generalisation of the two-colour partition function p_[1,r;−1](n). In this paper, the authors prove some new congruences modulo odd prime ℓ by taking r = 5, 7, 11 and 13, and non-integral rational values of t.

Using q-series expansion/identities, the authors established general congruence modulo prime number for two-colour partition function.

In the paper, the authors study congruence properties of two-colour partition function for fractional values. The authors also give some particular cases as examples.

The partition functions for fractional value is studied in 2019 by Chan and Wang for Ramanujan's general partition function and then extended by Xia and Zhu in 2020. In 2021, Baruah and Das also proved some congruences related to fractional partition functions previously investigated by Chan and Wang. In this sequel, some congruences are proved for two-colour partitions in this paper. The results presented in the paper are original.

Tolerance automata are defined and a decomposition theory for such entities is sought. It is shown that two major procedures of the classical algebraic theory produce difficulties in the tolerance case. A weaker approach, employing the idea of inertial tolerance, is presented. Finally, an explicit example is given which illustrates both the difficulties encountered and the theorems proved in the text.

Presents fundamental results on fuzzy Mealy machines. Unlike the classical Mealy machine which requires two functions, one to describe the next state and another to describe the output, a fuzzy Mealy machine requires only one fuzzy function to characterize completely the next state and the output produced. Apart from the obvious generalization that can be obtained from corresponding results on fuzzy finite state machines by introduction of an output associated with each transition, introduces the concept of an interval partition of [0, 1] and uses it to obtain more general results.

A simple adaption of Dijkstra's algorithm for finding a minimum weight path on a weighted directed graph serves to solve the optimal control problem posed by Arbib for tolerance automata with cost function. Cumulative cost automata and the application of network theory to cost automata are also discussed.

Introduces incentive strategy as a market‐oriented and highly efficient macro‐economy management system (MEMS). By means of the hierarchical decision‐making theory and the stochastic optimization theory, two static models with perfect information structure and partial information structure respectively are designed.

Suitable ways of putting tolerance structures onto automata are sought. Inertial tolerance on the state set is discussed, but for black box automata an observed or even inertial tolerance on the output set is thought to be more appropriate. Tolerance inductions and coinductions are used to tolerate the remaining two sets in each case. A general definition of a tolerance automaton is suggested and the morphisms of the category defined. The particular case of an (M‐R) automaton is considered and required to yield a stable tolerance structure. Some illustrative examples are given.

Studies the concept of the Cartesian composition of fuzzy finite state machines. Shows that fuzzy finite state machines and their Cartesian composition share many structural properties. Some of these properties are singly generated; retrievability, connectedness, strong connectedness, commutativity, perfection and state independence. Thus a fuzzy finite state machine which is a Cartesian composition of submachines can be studied in terms of smaller machines.