/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Mathematical programming

(1962). Management Models and Industrial Applications of Linear Programming. Journal of the Operational Research Society: Vol. 13, No. 3, pp. 274-275.

https://link.springer.com/content/pdf/10.1057%2Fjors.1962.42.pdf

Management Models and Industrial Applications of Linear Programming

https://cyberleninka.org/article/n/662470.pdf

Literature review of deteriorating inventory models by key topics from 2012 to 2015

The emergence of fuzzy sets makes job-shop scheduling problem (JSSP) become better aligned with the reality. This article addresses the JSSP with fuzzy execution time and fuzzy completion time (FJSSP). We choose the classic differential evolution (DE) algorithm as the basic optimization framework. The advantage of the DE algorithm is that it uses a special evolutionary strategy of difference vector sets to carry out mutation operation. However, DE is not very effective in solving some instances of FJSSP. Therefore, we propose a novel selection mechanism augmenting the generic DE algorithm (NSODE) to achieve better optimization results. The proposed selection operator adopted in this article aims at a temporary retention of all children generated by the parent generation, and then selecting N better solutions as the new individuals from N parents and N children. Various examples of fuzzy shop scheduling problems are experimented with to test the performance of the improved DE algorithm. The NSODE algorithm is compared with a variety of existing algorithms such as ant colony optimization, particle swarm optimization, and cuckoo search. Experimental results show that the NSODE can obtain superior feasible solutions compared with solutions produced by several algorithms reported in the literature.

Solving Fuzzy Job-Shop Scheduling Problem Using DE Algorithm Improved by a Selection Mechanism

In this paper, we propose a new mathematical model to analyze bimatrix goal game under entropy environment. This new approach incorporates the entropy function of the players as an objective to the bimatrix game. The solution concepts behind this game are based on getting the probability to achieve some specified goals. We consider the solution, not only by the payoff values, but also by the probability to get them. Numerical examples are presented to illustrate the methodology in the paper.

Fuzzy based ga for entropy bimatrix goal game

In the field of decision making, three-way decision making has been proven more fruitful for providing scopes to make delayed decision along with acceptance and rejection simultaneously. As a result, the decision risk and loss, which could occur due to take rapid decisions in traditional two-way decision making, are effectively reduced. Accordingly, this paper offers a novel three-way multi-attribute decision making model by combining three-way decision making and multi-attribute decision making under an incomplete information system. The incertitude in the information system is illustrated by introducing interval-valued Fermatean connection number based on interval-valued Fermatean fuzzy number and set pair analysis theory. Thereafter, the achievement of this study is five-fold. First, a possibility dominance relation is developed under incomplete information system in the basis of possibility degree measure of interval-valued Fermatean connection number. Second, we put forward a novel procedure to set up the fuzzy state set. Third, the conditional probability is estimated in light of the fuzzy state set and probability dominance relation. Fourth, the relative utility functions are determined in the virtue of regret theory. Lastly, a three-way multi-attribute decision making model is implemented in incomplete information system and exploited to deal with incomplete multi-attribute decision making problems. Eventually, the propriety, stability and superiority of the proposed model is established via conducting the comparative and experimental analysis. • Introducing a novel uncertainty, namely, interval-valued Fermatean connection number. • Developing a new approach to derive fuzzy state set and conditional probability. • Calculating relative utility functions by using regret theory. • Proposing a novel three-way multi-attribute decision making model. 

Regret-based three-way decision making with possibility dominance and SPA theory in incomplete information system

This article presents a multiple objective fractional fixed-charge transportation problem (MFFTP) in a rough decision-making framework. A transformation procedure is modified to convert non-linear multi-objective transportation problem to its linear version. The parameters of the designed model are considered to be fuzzy. We employ separate kinds of fuzzy scale, i.e. , possibility, credibility and necessity measures, to deal with the fuzzy parameters. Using the fuzzy chance-constrained rough approximation (FCRA) technique, we extract the more preferable optimal solution from our suggested MFFTP. The initial result is compared with that of the robust ranking (RR) technique. We also use the theory of rough sets for expanding as well as dividing the feasible domain of the MFFTP to accommodate more information by considering two approximations. Employing these approximations, we introduce two variants, namely, the lower approximation (LA) and the upper approximation (UA), of the suggested MFFTP. Finally, by using these models, we provide the optimal solutions for our proposedproblem. We also associate our MFFTP with a real-world example to showcase its applicability as well as performance. Our core concept of this article is that it tackles an MFFTP using two separate kinds of uncertainty and expands its feasible domain for optimal solutions. Optimal solutions of the designed model (obtained from FCRA technique) belong to two separate regions, namely, “surely region” and “possible region”. The optimal solution which belongs to the “surely region” is better (as these are minimum values) than the one in the “possible region” and other cases. An interpretation of our approach along with offers about the intended future research work are provided at last.

/pdf/fuzzy-multiple-objective-fractional-optimization-in-rough-3j1s0g68z5.pdf

Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

In this paper, we first describe soft congruence relation over a lattice. We then define the concepts of complete soft congruence relation. Besides this, the concepts of upper and lower approximations of a subset in a lattice are depicted based on this soft congruence relation. We then give their related properties with examples to investigate their characterizations.

/pdf/soft-congruence-relation-over-lattice-23oh88ddvz.pdf

Soft congruence relation over lattice

This paper is designed based on the combined bioeconomic harvesting of Holling-Tanner prey-predator competition model with Beddington-DeAngelis functional response with two different delays. The si...

Sankar Kumar Roy

Papers

Fuzzy based ga for entropy bimatrix goal game

Regret-based three-way decision making with possibility dominance and SPA theory in incomplete information system

Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

Soft congruence relation over lattice

Holling-Tanner prey-predator model with Beddington-DeAngelis functional response including delay